# kb

id: combinatorial-design-20260505-1
file: data/en.wikipedia.org/wiki/Combinatorial_design-1.md
category: reference
title: Combinatorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorial_design
date_saved: 2026-05-05T09:49:37.423591+00:00
instance: kb-cron
parent: combinatorial-design-20260505-0
summary:
A balanced incomplete block design or BIBD (usually called for short a block design) is a collection B of b subsets (called blocks) of a finite set X of v elements, such that any element of X is contained in the same number r of blocks, every block has the same number k of elements, and each pair of distinct elements appear together in the same number λ of blocks. BIBDs are also known as 2-designs and are often denoted as 2-(v,k,λ) designs. As an example, when λ = 1 and b = v, we have a projective plane: X is the point set of the plane and the blocks are the lines. A symmetric balanced incomplete block design or SBIBD is a BIBD in which v = b (the number of points equals the number of blocks). They are the single most important and well studied subclass of BIBDs. Projective planes, biplanes and Hadamard 2-designs are all SBIBDs. They are of particular interest since they are the extremal examples of Fisher's inequality (b ≥ v). A resolvable BIBD is a BIBD whose blocks can be partitioned into sets (called parallel classes), each of which forms a partition of the


id: combinatorial-design-20260505-2
file: data/en.wikipedia.org/wiki/Combinatorial_design-2.md
category: reference
title: Combinatorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorial_design
date_saved: 2026-05-05T09:49:37.423591+00:00
instance: kb-cron
parent: combinatorial-design-20260505-0
summary:
== Other combinatorial designs == The Handbook of Combinatorial Designs (Colbourn & Dinitz 2007) has, amongst others, 65 chapters, each devoted to a combinatorial design other than those given above. A partial listing is given below: Association schemes A balanced ternary design BTD(V, B; ρ1, ρ2, R; K, Λ) is an arrangement of V elements into B multisets (blocks), each of cardinality K (K ≤ V), satisfying: Each element appears R = ρ1 + 2ρ2 times altogether, with multiplicity one in exactly ρ1 blocks and multiplicity two in exactly ρ2 blocks. Every pair of distinct elements appears Λ times (counted with multiplicity); that is, if mvb is the multiplicity of the element v in block b, then for every pair of distinct elements v and w, ∑ b = 1 B m v b m w b = Λ {\displaystyle \sum _{b=1}^{B}m_{vb}m_{wb}=\Lambda } . For example, one of the only two nonisomorphic BTD(4,8;2,3,8;4,6)s (blocks are columns) is: The incidence matrix of a BTD (where the entries are the multiplicities of the elements in the blocks) can be used to form a ternary error-correcting code analogous to the way binary codes are formed from the incidence matrices of BIBDs. A balanced


id: combinatorial-design-20260505-3
file: data/en.wikipedia.org/wiki/Combinatorial_design-3.md
category: reference
title: Combinatorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorial_design
date_saved: 2026-05-05T09:49:37.423591+00:00
instance: kb-cron
parent: combinatorial-design-20260505-0
summary:
An H(2n − 1, 2n) is a Room square of side 2n − 1, and thus the Howell designs generalize the concept of Room squares. The pairs of symbols in the cells of a Howell design can be thought of as the edges of an s regular graph on 2n vertices, called the underlying graph of the Howell design. Cyclic Howell designs are used as Howell movements in duplicate bridge tournaments. The rows of the design represent the rounds, the columns represent the boards, and the diagonals represent the tables. Linear spaces An (n,k,p,t)-lotto design is an n-set V of elements together with a set β of k-element subsets of V (blocks), so that for any p-subset P of V, there is a block B in β for which |P ∩ B | ≥ t. L(n,k,p,t) denotes the smallest number of blocks in any (n,k,p,t)-lotto design. The following is a (7,5,4,3)-lotto design with the smallest possible number of blocks: {1,2,3,4,7} {1,2,5,6,7} {3,4,5,6,7}. Lotto designs model any lottery that is run in the following way: Individuals purchase tickets consisting of k numbers chosen from a set of n numbers. At a certain point the sale of tickets is stopped and a


id: combinatorial-design-20260505-4
file: data/en.wikipedia.org/wiki/Combinatorial_design-4.md
category: reference
title: Combinatorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorial_design
date_saved: 2026-05-05T09:49:37.423591+00:00
instance: kb-cron
parent: combinatorial-design-20260505-0
summary:
A tuscan square on n symbols is equivalent to a decomposition of the complete graph with n vertices into n hamiltonian directed paths. In a sequence of visual impressions, one flash card may have some effect on the impression given by the next. This bias can be cancelled by using n sequences corresponding to the rows of an n × n tuscan-1 square. A t-wise balanced design (or t BD) of type t − (v,K,λ) is a v-set X together with a family of subsets of X (called blocks) whose sizes are in the set K, such that every t-subset of distinct elements of X is contained in exactly λ blocks. If K is a set of positive integers strictly between t and v, then the t BD is proper. If all the k-subsets of X for some k are blocks, the t BD is a trivial design. Notice that in the following example of a 3-{12,{4,6},1) design based on the set X = {1,2,...,12}, some pairs appear four times (such as 1,2) while others appear five times (6,12 for instance). 1 2 3 4 5 6 1 2 7 8 1 2 9 11 1 2 10 12 3


id: combinatorics-of-experimental-design-20260505-0
file: data/en.wikipedia.org/wiki/Combinatorics_of_Experimental_Design-0.md
category: reference
title: Combinatorics of Experimental Design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorics_of_Experimental_Design
date_saved: 2026-05-05T09:49:38.636786+00:00
instance: kb-cron
parent: combinatorics-of-experimental-design-20260505-0
summary:
Combinatorics of Experimental Design is a textbook on the design of experiments, a subject that connects applications in statistics to the theory of combinatorial mathematics. It was written by mathematician Anne Penfold Street and her daughter, statistician Deborah Street, and published in 1987 by the Oxford University Press under their Clarendon Press imprint. == Topics == The book has 15 chapters. Its introductory chapter covers the history and applications of experimental designs, it has five chapters on balanced incomplete block designs and their existence, and three on Latin squares and mutually orthogonal Latin squares. Other chapters cover resolvable block designs, finite geometry, symmetric and asymmetric factorial designs, and partially balanced incomplete block designs. After this standard material, the remaining two chapters cover less-standard material. The penultimate chapter covers miscellaneous types of designs including circular block designs, incomplete Latin squares, and serially balanced sequences. The final chapter describes specialized designs for agricultural applications. The coverage of the topics in the book includes examples, clearly written proofs, historical references, and exercises for students. == Audience and reception == Although intended as an advanced undergraduate textbook, this book can also be used as a graduate text, or as a reference for researchers. Its


id: completely-randomized-design-20260505-0
file: data/en.wikipedia.org/wiki/Completely_randomized_design-0.md
category: reference
title: Completely randomized design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Completely_randomized_design
date_saved: 2026-05-05T09:49:39.957288+00:00
instance: kb-cron
parent: completely-randomized-design-20260505-0
summary:
In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take other nuisance variables into account. This article describes completely randomized designs that have one primary factor. The experiment compares the values of a response variable based on the different levels of that primary factor. For completely randomized designs, the levels of the primary factor are randomly assigned to the experimental units. == Randomization == To randomize is to determine the run sequence of the experimental units randomly. For example, if there are 3 levels of the primary factor with each level to be run 2 times, then there are 6! (where ! denotes factorial) possible run sequences (or ways to order the experimental trials). Because of the replication, the number of unique orderings is 90 (since 90 = 6!/(2!*2!*2!)). An example of an unrandomized design would be to always run 2 replications for the first level, then 2 for the second level, and finally 2 for the third level. To randomize the runs, one way would be to put 6 slips of paper in a box with 2 having level 1, 2 having level 2, and 2 having


id: computer-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Computer_experiment-0.md
category: reference
title: Computer experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Computer_experiment
date_saved: 2026-05-05T09:49:41.205376+00:00
instance: kb-cron
parent: computer-experiment-20260505-0
summary:
A computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system. This area includes computational physics, computational chemistry, computational biology and other similar disciplines. == Background == Computer simulations are constructed to emulate a physical system. Because these are meant to replicate some aspect of a system in detail, they often do not yield an analytic solution. Therefore, methods such as discrete event simulation or finite element solvers are used. A computer model is used to make inferences about the system it replicates. For example, climate models are often used because experimentation on an earth sized object is impossible. == Objectives == Computer experiments have been employed with many purposes in mind. Some of those include: Uncertainty quantification: Characterize the uncertainty present in a computer simulation arising from unknowns during the computer simulation's construction. Inverse problems: Discover the underlying properties of the system from the physical data. Bias correction: Use physical data to correct for bias in the simulation. Data assimilation: Combine multiple simulations and physical data sources into a complete predictive model. Systems design: Find inputs that result in optimal system performance measures. == Computer simulation modeling


id: confirmation-bias-20260505-0
file: data/en.wikipedia.org/wiki/Confirmation_bias-0.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Confirmation bias (also confirmatory bias, myside bias, or congeniality bias) is the tendency to search for, interpret, favor and recall information in a way that confirms or supports one's prior beliefs, values, or decisions. People display this bias when they select information that supports their views, ignoring contrary information or when they interpret ambiguous evidence as supporting their existing attitudes. The effect is strongest for desired outcomes, emotionally charged issues and deeply entrenched beliefs. Biased search for information, biased interpretation of this information and biased memory recall have been invoked to explain four specific effects: attitude polarization (when a disagreement becomes more extreme despite the different parties being exposed to the same evidence) belief perseverance (when beliefs persist after the evidence for them is shown to be false) the irrational primacy effect (a greater reliance on information encountered early in a series) illusory correlation (when people falsely perceive an association between two events or situations). A series of psychological experiments in the 1960s suggested that people are biased toward confirming their existing beliefs. Later work reinterpreted these results as a tendency to test ideas in a one-sided way, focusing on one possibility and ignoring alternatives. Explanations for the observed biases


id: confirmation-bias-20260505-1
file: data/en.wikipedia.org/wiki/Confirmation_bias-1.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Experiments have found repeatedly that people tend to test hypotheses in a one-sided way, by searching for evidence consistent with their current hypothesis. Rather than searching through all the relevant evidence, they phrase questions to receive an affirmative answer that supports their theory. They look for the consequences that they would expect if their hypothesis were true, rather than what would happen if it were false. For example, someone using yes/no questions to find a number they suspect to be the number 3 might ask, "Is it an odd number?" People prefer this type of question, called a "positive test", even when a negative test such as "Is it an even number?" would yield exactly the same information. However, this does not mean that people seek tests that guarantee a positive answer. In studies where subjects could select either such pseudo-tests or genuinely diagnostic ones, they favored the genuinely diagnostic. The preference for positive tests in itself is not a bias, since positive tests can be highly informative. However, in combination with other effects, this strategy can confirm existing beliefs or assumptions, independently of whether they are true. In real-world situations, evidence is often complex and mixed. For example, various


id: confirmation-bias-20260505-2
file: data/en.wikipedia.org/wiki/Confirmation_bias-2.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Confirmation biases are not limited to the collection of evidence. Even if two individuals have the same information, the way they interpret it can be biased. A team at Stanford University conducted an experiment involving participants who felt strongly about capital punishment, with half in favor and half against it. Each participant read descriptions of two studies: a comparison of U.S. states with and without the death penalty, and a comparison of murder rates in a state before and after the introduction of the death penalty. After reading a quick description of each study, the participants were asked whether their opinions had changed. Then, they read a more detailed account of each study's procedure and had to rate whether the research was well-conducted and convincing. In fact, the studies were fictional. Half the participants were told that one kind of study supported the deterrent effect and the other undermined it, while for other participants the conclusions were swapped. The participants, whether supporters or opponents, reported shifting their attitudes slightly in the direction of the first study they read. Once they read the more detailed descriptions of the two studies, they almost all returned to their original belief regardless of the


id: confirmation-bias-20260505-3
file: data/en.wikipedia.org/wiki/Confirmation_bias-3.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
=== Biased recall of information === People may remember evidence selectively to reinforce their expectations, even if they gather and interpret evidence in a neutral manner. This effect is called "selective recall", "confirmatory memory", or "access-biased memory". Psychological theories differ in their predictions about selective recall. Schema theory predicts that information matching prior expectations will be more easily stored and recalled than information that does not match. Some alternative approaches say that surprising information stands out and so is memorable. Predictions from both these theories have been confirmed in different experimental contexts, with no theory winning outright. In one study, participants read a profile of a woman which described a mix of introverted and extroverted behaviors. They later had to recall examples of her introversion and extroversion. One group was told this was to assess the woman for a job as a librarian, while a second group were told it was for a job in real estate sales. There was a significant difference between what these two groups recalled, with the "librarian" group recalling more examples of introversion and the "sales" groups recalling more extroverted behavior. A selective memory effect has also been shown in experiments that manipulate the desirability


id: confirmation-bias-20260505-4
file: data/en.wikipedia.org/wiki/Confirmation_bias-4.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Before psychological research on confirmation bias, the phenomenon had been observed throughout history. Beginning with the Greek historian Thucydides (c. 460 BC – c. 395 BC), who wrote of misguided reason in The Peloponnesian War; "... for it is a habit of mankind to entrust to careless hope what they long for, and to use sovereign reason to thrust aside what they do not fancy". Italian poet Dante Alighieri (1265–1321) noted it in the Divine Comedy, in which St. Thomas Aquinas cautions Dante upon meeting in Paradise, "opinion—hasty—often can incline to the wrong side, and then affection for one's own opinion binds, confines the mind". Ibn Khaldun noticed the same effect in his Muqaddimah: Untruth naturally afflicts historical information. There are various reasons that make this unavoidable. One of them is partisanship for opinions and schools. ... if the soul is infected with partisanship for a particular opinion or sect, it accepts without a moment's hesitation the information that is agreeable to it. Prejudice and partisanship obscure the critical faculty and preclude critical investigation. The result is that falsehoods are accepted and transmitted. In the Novum Organum, English philosopher and scientist Francis Bacon (1561–1626) noted that biased assessment of evidence


id: confirmation-bias-20260505-5
file: data/en.wikipedia.org/wiki/Confirmation_bias-5.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
== Information processing explanations == There are currently three main information processing explanations of confirmation bias, plus a recent addition. === Cognitive versus motivational === According to Robert MacCoun, most biased evidence processing occurs through a combination of "cold" (cognitive) and "hot" (motivated) mechanisms. Cognitive explanations for confirmation bias are based on limitations in people's ability to handle complex tasks, and the shortcuts, called heuristics, that they use. For example, people may judge the reliability of evidence by using the availability heuristic that is, how readily a particular idea comes to mind. It is also possible that people can only focus on one thought at a time, so find it difficult to test alternative hypotheses in parallel. Another heuristic is the positive test strategy identified by Klayman and Ha, in which people test a hypothesis by examining cases where they expect a property or event to occur. This heuristic avoids the difficult or impossible task of working out how diagnostic each possible question will be. However, it is not universally reliable, so people can overlook challenges to their existing beliefs. Motivational explanations involve an effect of desire on belief. It is known that people prefer positive thoughts over negative ones


id: confirmation-bias-20260505-6
file: data/en.wikipedia.org/wiki/Confirmation_bias-6.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
=== Optimal information acquisition === Recent research in economics has challenged the traditional view of confirmation bias as purely a cognitive flaw. Under conditions where acquiring and processing information is costly, seeking confirmatory evidence can actually be an optimal strategy. Instead of pursuing contrarian or disconfirming evidence, it may be more efficient to focus on sources likely to align with one's existing beliefs, given the constraints on time and resources. Economist Weijie Zhong has developed a model demonstrating that individuals who must make decisions under time pressure, and who face costs for obtaining more information, will often prefer confirmatory signals. According to this model, when individuals believe strongly in a certain hypothesis, they optimally seek information that confirms it, allowing them to build confidence more efficiently. If the expected confirmatory signals are not received, their confidence in the initial hypothesis will gradually decline, leading to belief updating. This approach shows that seeking confirmation is not necessarily biased but may be a rational allocation of limited attention and resources. == Real-world effects == === Social media === In social media, confirmation bias is amplified by the use of filter bubbles and echo chambers (or "algorithmic editing"), which displays to individuals only


id: confirmation-bias-20260505-7
file: data/en.wikipedia.org/wiki/Confirmation_bias-7.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
=== Medicine and health === Cognitive biases are important variables in clinical decision-making by medical general practitioners (GPs) and medical specialists. Two important ones are confirmation bias and the overlapping availability bias. A GP may make a diagnosis early on during an examination, and then seek confirming evidence rather than falsifying evidence. This cognitive error is partly caused by the availability of evidence about the supposed disorder being diagnosed. For example, the client may have mentioned the disorder, or the GP may have recently read a much-discussed paper about the disorder. The basis of this cognitive shortcut or heuristic (termed anchoring) is that the doctor does not consider multiple possibilities based on evidence, but prematurely latches on (or anchors to) a single cause. In emergency medicine, because of time pressure, there is a high density of decision-making, and shortcuts are frequently applied. The potential failure rate of these cognitive decisions needs to be managed by education about the 30 or more cognitive biases that can occur, so as to set in place proper debiasing strategies. Confirmation bias may also cause doctors to perform unnecessary medical procedures due to pressure from adamant patients. Mental disorders may be prone to misdiagnosis in


id: confirmation-bias-20260505-8
file: data/en.wikipedia.org/wiki/Confirmation_bias-8.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
=== Paranormal beliefs === One factor in the appeal of alleged psychic readings is that listeners apply a confirmation bias which fits the psychic's statements to their own lives. By making a large number of ambiguous statements in each sitting, the psychic gives the client more opportunities to find a match. This is one of the techniques of cold reading, with which a psychic can deliver a subjectively impressive reading without any prior information about the client. Investigator James Randi compared the transcript of a reading to the client's report of what the psychic had said, and found that the client showed a strong selective recall of the "hits". As a striking illustration of confirmation bias in the real world, Nickerson mentions numerological pyramidology: the practice of finding meaning in the proportions of the Egyptian pyramids. There are many different length measurements that can be made of, for example, the Great Pyramid of Giza and many ways to combine or manipulate them. Hence it is almost inevitable that people who look at these numbers selectively will find superficially impressive correspondences, for example with the dimensions of the Earth. === Recruitment and selection === Unconscious cognitive bias (including confirmation bias) in


id: confirmation-bias-20260505-9
file: data/en.wikipedia.org/wiki/Confirmation_bias-9.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Confirmation biases provide one plausible explanation for the persistence of beliefs when the initial evidence for them is removed or when they have been sharply contradicted. This belief perseverance effect has been first demonstrated experimentally by Festinger, Riecken, and Schachter. These psychologists spent time with a cult whose members were convinced that the world would end on 21 December 1954. After the prediction failed, most believers still clung to their faith. Their book describing this research is aptly named When Prophecy Fails. The term belief perseverance, however, was coined in a series of experiments using what is called the "debriefing paradigm": participants read fake evidence for a hypothesis, their attitude change is measured, then the fakery is exposed in detail. Their attitudes are then measured once more to see if their belief returns to its previous level. A common finding is that at least some of the initial belief remains even after a full debriefing. In one experiment, participants had to distinguish between real and fake suicide notes. The feedback was random: some were told they had done well while others were told they had performed badly. Even after being fully debriefed, participants were still influenced by the feedback. They


id: confirmation-bias-20260505-10
file: data/en.wikipedia.org/wiki/Confirmation_bias-10.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
== Further reading == Leavitt, Fred (2015), Dancing with absurdity: Your most cherished beliefs (and all your others) are probably wrong, Peter Lang Publishers, ISBN 978-1-4539-1490-8, OCLC 908685982 Stanovich, Keith (2009), What intelligence tests miss: The psychology of rational thought (Lay), New Haven (Connecticut): Yale University Press, ISBN 978-0-300-12385-2 Westen, Drew (2007), The political brain: The role of emotion in deciding the fate of the nation, PublicAffairs, ISBN 978-1-58648-425-5, OCLC 86117725 Meppelink, Corine S., Edith G. Smit, Marieke L. Fransen, and Nicola Diviani. "'I Was Right about Vaccination': Confirmation Bias and Health Literacy in Online Health Information Seeking." Journal of Health Communication 24, no. 2 (2019): 129–40. https://doi.org/10.1080/10810730.2019.1583701. Pearson, George David Hooke, and Silvia Knobloch-Westerwick. "Is the Confirmation Bias Bubble Larger Online? Pre-Election Confirmation Bias in Selective Exposure to Online versus Print Political Information." Mass Communication & Society 22, no. 4 (2019): 466–86. https://doi.org/10.1080/15205436.2019.1599956. == External links == Skeptic's Dictionary: confirmation bias – Robert T. Carroll Teaching about confirmation bias – class handout and instructor's notes by K.H. Grobman Confirmation bias at You Are Not So Smart Confirmation bias learning object – interactive number triples exercise by Rod McFarland for Simon Fraser University Brief summary of the 1979 Stanford assimilation


id: confounding-20260505-0
file: data/en.wikipedia.org/wiki/Confounding-0.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
In causal inference, confounding is a form of systematic error (or bias) that can distort estimates of causal effects in observational studies. A confounder is traditionally understood to be a variable that (1) independently predicts the outcome (or dependent variable), (2) is associated with the exposure (or independent variable), and (3) is not on the causal pathway between the exposure and the outcome. Failure to control for a confounder results in a spurious association between exposure and outcome. Confounding is a causal concept rather than a purely statistical one, and therefore cannot be fully described by correlations or associations alone. The presence of confounders helps explain why correlation does not imply causation, and why careful study design and analytical methods (such as randomization, statistical adjustment, or causal diagrams) are required to distinguish causal effects from spurious associations. Several notation systems and formal frameworks, such as causal directed acyclic graphs (DAGs), have been developed to represent and detect confounding, making it possible to identify when a variable must be controlled for in order to obtain an unbiased estimate of a causal effect. Confounders are threats to internal validity. == Definition == Confounding is defined in terms of the data generating model.


id: confounding-20260505-1
file: data/en.wikipedia.org/wiki/Confounding-1.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
because the observational quantity contains information about the correlation between X and Z, and the interventional quantity does not (since X is not correlated with Z in a randomized experiment). It can be shown that, in cases where only observational data is available, an unbiased estimate of the desired quantity P ( y ∣ do ( x ) ) {\displaystyle P(y\mid {\text{do}}(x))} , can be obtained by "adjusting" for all confounding factors, namely, conditioning on their various values and averaging the result. In the case of a single confounder Z, this leads to the "adjustment formula": which gives an unbiased estimate for the causal effect of X on Y. The same adjustment formula works when there are multiple confounders except, in this case, the choice of a set Z of variables that would guarantee unbiased estimates must be done with caution. The criterion for a proper choice of variables is called the Back-Door and requires that the chosen set Z "blocks" (or intercepts) every path between X and Y that contains an arrow into X. Such sets are called "Back-Door admissible" and may include variables which are not common causes of X and Y, but merely proxies thereof. Returning to


id: confounding-20260505-2
file: data/en.wikipedia.org/wiki/Confounding-2.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
== Decreasing the potential for confounding == A reduction in the potential for the occurrence and effect of confounding factors can be obtained by increasing the types and numbers of comparisons performed in an analysis. If measures or manipulations of core constructs are confounded (i.e. operational or procedural confounds exist), subgroup analysis may not reveal problems in the analysis. Additionally, increasing the number of comparisons can create other problems (see multiple comparisons). Peer review is a process that can assist in reducing instances of confounding, either before study implementation or after analysis has occurred. Peer review relies on collective expertise within a discipline to identify potential weaknesses in study design and analysis, including ways in which results may depend on confounding. Similarly, replication can test for the robustness of findings from one study under alternative study conditions or alternative analyses (e.g., controlling for potential confounds not identified in the initial study). Confounding effects may be less likely to occur and act similarly at multiple times and locations. In selecting study sites, the environment can be characterized in detail at the study sites to ensure sites are ecologically similar and therefore less likely to have confounding variables. Lastly, the relationship between


id: confounding-20260505-3
file: data/en.wikipedia.org/wiki/Confounding-3.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
Case-control studies assign confounders to both groups, cases and controls, equally. For example, if somebody wanted to study the cause of myocardial infarct and thinks that the age is a probable confounding variable, each 67-year-old infarct patient will be matched with a healthy 67-year-old "control" person. In case-control studies, matched variables most often are the age and sex. Drawback: Case-control studies are feasible only when it is easy to find controls, i.e. persons whose status vis-à-vis all known potential confounding factors is the same as that of the case's patient: Suppose a case-control study attempts to find the cause of a given disease in a person who is 1) 45 years old, 2) African-American, 3) from Alaska, 4) an avid football player, 5) vegetarian, and 6) working in education. A theoretically perfect control would be a person who, in addition to not having the disease being investigated, matches all these characteristics and has no diseases that the patient does not also have—but finding such a control would be an enormous task. Cohort studies: A degree of matching is also possible and it is often done by only admitting certain age groups or a certain sex into the study population, creating


id: confounding-20260505-4
file: data/en.wikipedia.org/wiki/Confounding-4.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
== Criticism == Concerns have been raised that confounding in medical research can product false null results due to decreasing exposure reliability and increasing sibling-correlations. == Artifacts == Artifacts are variables that should have been systematically varied, either within or across studies, but that were accidentally held constant. Artifacts are thus threats to external validity. Artifacts are factors that covary with the treatment and the outcome. Campbell and Stanley identify several artifacts. The major threats to internal validity are history, maturation, testing, instrumentation, statistical regression, selection, experimental mortality, and selection-history interactions. One way to minimize the influence of artifacts is to use a pretest-posttest control group design. Within this design, "groups of people who are initially equivalent (at the pretest phase) are randomly assigned to receive the experimental treatment or a control condition and then assessed again after this differential experience (posttest phase)". Thus, any effects of artifacts are (ideally) equally distributed in participants in both the treatment and control conditions. == See also == Observational interpretation fallacy Anecdotal evidence – Evidence relying on personal testimony Causal inference – Branch of statistics Epidemiological method – Scientific method in the specific field Simpson's paradox – Error in statistical reasoning with groups


id: consecutive-case-series-20260505-0
file: data/en.wikipedia.org/wiki/Consecutive_case_series-0.md
category: reference
title: Consecutive case series
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Consecutive_case_series
date_saved: 2026-05-05T09:49:45.006467+00:00
instance: kb-cron
parent: consecutive-case-series-20260505-0
summary:
A consecutive case series is a type of case series clinical study that includes all eligible patients identified by the researchers during the study registration period. The patients are treated in the order in which they are identified. This type of study usually does not have a control group. For example, in Sugrue, et al. (2016), a consecutive case series design was used to determine trends in hand surgery research. == References == == External links == Consecutive case series entry in the public domain NCI Dictionary of Cancer Terms This article incorporates public domain material from Dictionary of Cancer Terms. U.S. National Cancer Institute.


id: consolidated-standards-of-reporting-trials-20260505-0
file: data/en.wikipedia.org/wiki/Consolidated_Standards_of_Reporting_Trials-0.md
category: reference
title: Consolidated Standards of Reporting Trials
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Consolidated_Standards_of_Reporting_Trials
date_saved: 2026-05-05T09:49:46.314658+00:00
instance: kb-cron
parent: consolidated-standards-of-reporting-trials-20260505-0
summary:
Consolidated Standards of Reporting Trials (CONSORT) encompasses various initiatives developed by the CONSORT Group to alleviate the problems arising from inadequate reporting of randomized controlled trials. It is part of the larger EQUATOR Network initiative to enhance the transparency and accuracy of reporting in research. == CONSORT Statement == The main product of the CONSORT Group is the CONSORT Statement, which is an evidence-based, minimum set of recommendations for reporting randomized trials. It offers a standard way for authors to prepare reports of trial findings, facilitating their complete and transparent reporting, reducing the influence of bias on their results, and aiding their critical appraisal and interpretation. The most recent version of the Statement—the CONSORT 2010 Statement—consists of a 25-item checklist and a participant flow diagram, along with some brief descriptive text. The checklist items focus on reporting how the trial was designed, analyzed, and interpreted; the flow diagram displays the progress of all participants through the trial. The Statement has been translated into several languages. The CONSORT "Explanation and Elaboration" document explains and illustrates the principles underlying the CONSORT Statement. It is strongly recommended that it be used in conjunction with the CONSORT Statement. Considered an evolving document, the CONSORT


id: controlling-for-a-variable-20260505-0
file: data/en.wikipedia.org/wiki/Controlling_for_a_variable-0.md
category: reference
title: Controlling for a variable
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Controlling_for_a_variable
date_saved: 2026-05-05T09:49:47.524084+00:00
instance: kb-cron
parent: controlling-for-a-variable-20260505-0
summary:
In causal models, controlling for a variable means binning data according to measured values of the variable. This is typically done so that the variable can no longer act as a confounder in, for example, an observational study or experiment. When estimating the effect of explanatory variables on an outcome by regression, controlled-for variables are included as inputs in order to separate their effects from the explanatory variables. A limitation of controlling for variables is that a causal model is needed to identify important confounders (backdoor criterion is used for the identification). Without having one, a possible confounder might remain unnoticed. Another associated problem is that if a variable which is not a real confounder is controlled for, it may in fact make other variables (possibly not taken into account) become confounders while they were not confounders before. In other cases, controlling for a non-confounding variable may cause underestimation of the true causal effect of the explanatory variables on an outcome (e.g. when controlling for a mediator or its descendant). Counterfactual reasoning mitigates the influence of confounders without this drawback. == Experiments == Experiments attempt to assess the effect of manipulating one or more independent variables on one or more


id: cooperative-pulling-paradigm-20260505-0
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-0.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
The cooperative pulling paradigm is an experimental design in which two or more animals pull rewards toward themselves via an apparatus that they cannot successfully operate alone. Researchers (ethologists, comparative psychologists, and evolutionary psychologists) use cooperative pulling experiments to try to understand how cooperation works and how and when it may have evolved. The type of apparatus used in cooperative pulling experiments can vary. Researcher Meredith Crawford, who invented the experimental paradigm in 1937, used a mechanism consisting of two ropes attached to a rolling platform that was too heavy to be pulled by a single chimpanzee. The standard apparatus is one in which a single string or rope is threaded through loops on a movable platform. If only one participant pulls the string, it comes loose and the platform can no longer be retrieved. Only by pulling together in coordination can the participants be successful; success by chance is highly unlikely. Some researchers have designed apparatus that involve handles instead of ropes. Although many animals retrieve rewards in their cooperative pulling tasks, the conclusions regarding cooperation are mixed and complex. Chimpanzees, bonobos, orangutans, capuchins, tamarins, wolves, elephants, ravens, and kea appear to understand the requirements of the task. For


id: cooperative-pulling-paradigm-20260505-1
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-1.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
=== Subjects === So far, fewer than twenty species have participated in cooperative pulling experiments: chimpanzees, bonobos, orangutans, capuchin monkeys, tamarins, macaques, humans, hyenas, wolves, dogs, elephants, otters, dolphins, rooks, ravens, parrots, and kea. Researchers have picked species that cooperate in the wild (e.g., capuchins), live in social structures (e.g., wolves), or have known cognitive abilities (e.g., orangutans). Most of the participating animals have been in human care at an animal research center; some lived semi-free at a sanctuary in their natural habitat. One study involved free animals (Barbary macaques) in the wild. === Conditions === To arrive at conclusions regarding cooperation, researchers have designed experiments with various conditions. ==== Delay ==== The first animal has access to the apparatus before the other one. If the animal does not wait for its partner this suggests a lack of understanding of the requirements for successful cooperation. === Recruitment === The subject recruits the partner (for example by opening a door) when the task requires cooperation. ==== Partner choice ==== The first animal gets to choose which animal from a pair it wants as a partner. In some cases individual animals from within a group can decide to join an animal already


id: cooperative-pulling-paradigm-20260505-2
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-2.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
=== Overview === Although many animals retrieve rewards in their cooperative pulling tasks, the conclusions regarding cooperation are mixed and complex. Some researchers have attributed successful cooperation to random simultaneous action, or to the simple reactive behavior of pulling the rope when it moves. Many trials with capuchins, hyenas, parrots and rooks led to failure because one partner pulled without the other present, suggesting a lack of understanding of cooperation. A few researchers have offered the possible explanation that animals may understand cooperation to some extent but simply can not suppress the desire to have food they see. But there is evidence that some species do have an understanding of cooperation and perform intentional coordination to achieve a goal. Specifically, chimpanzees, bonobos, orangutans, tamarins, capuchins, elephants, wolves, ravens, and kea appear to understand how cooperation works. Chimpanzees not only wait for a partner, but will actively solicit help when needed. They appear to recall previous outcomes to recruit the most effective partner. In a group setting, chimpanzees punish initial competitive behavior (taking food without pulling, displacing animals) such that eventually, after many trials, successful cooperation becomes the norm. Bonobos, which are social animals with higher tolerance levels, can outperform chimpanzees


id: cooperative-pulling-paradigm-20260505-3
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-3.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Similar mixed results, not matching the cooperative abilities observed in chimpanzees in the wild, were obtained in later studies by other researchers using a variety of experimental set-ups, including the loose-string task pioneered by Hirata. Povinelli and O'Neill, for example, found that trained chimpanzees were unable to teach naive chimpanzees to cooperate on a Crawford-like box-pulling task. The naive animals did not imitate the experts. Chalmeau and Gallo found only two chimpanzees consistently cooperating in their handle-pulling task, and this involved one ape holding his own handle and waiting for the other to pull his. They concluded that social factors and not limited cognitive abilities were the reason for lack of widespread success, as they observed dominant chimpanzees controlling the apparatus and preventing others from interacting. Melis, Hare, and Tomasello set up an experiment to control for such social factors. In a loose-string cooperative task without training they compared the ability of pairs of captive chimpanzees who in a non-cooperative setting were willing to share food with each other to pairs who were less inclined to do so. The results showed that food sharing was a good predictor for success in the cooperative pulling task. Melis, Hare, and Tomasello concluded


id: cooperative-pulling-paradigm-20260505-4
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-4.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Orangutans (Pongo pygmaeus) are tool-using apes that are mostly solitary. Chalmeau, Lardeux, Brandibas, and Gallo tested the cooperative capabilities of a pair of orangutans, using a device with handles. Only through simultaneous pulling could the pair retrieve a food reward. Without any training the orangutans succeeded in the first session. Over the course of 30 sessions, the apes succeeded more quickly, having learned to coordinate. Across trials the researchers found an increase in a sequence of actions that suggested understanding of cooperation: first looking at the partner; then if the partner holds or pulls the handle, starting to pull. The researchers also concluded that the orangutans learned a partner had to be present for success. For example, they observed that time spent alone at the apparatus decreased as the trials progressed. In some instances one orangutan pushed the other towards the free handle, soliciting cooperation. The researchers observed an asymmetry: one ape did all the monitoring and coordinating, the other one seemed to simply pull if the first one was present. Rewards did not have to be shared equally for success to appear, as one orangutan took 92% of all food. This ape anticipated the falling of food and stuck


id: cooperative-pulling-paradigm-20260505-5
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-5.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Molesti and Majolo tested a group of wild Barbary macaques (Macaca sylvanus) in Morocco to see if they would cooperate, and if so, what determined their partner choice. Macaques live in complex social environments and are relatively tolerant socially. After solo training, the researchers presented a loose-string apparatus for the cooperative task, which the animals were free to use. Most animals that passed solo training were successful in spontaneously cooperating to obtain food (22 out of 26). More than half the pairs that chose to cooperate were juvenile-adult pairs. More than two monkeys pulling was never observed; stealing food from a partner was rare. After a first successful cooperation, they were more likely to pull when a partner was directly available, but this was not always the case. Molesti and Majolo did not rule out that pulling while no one held or pulled the other end of the rope was simply a signal to actively recruit a potential partner. The researchers randomly introduced control trials in which the solo apparatus was set up as well. The macaques preferred to get the food alone when a partner was not needed during the control. The extent to which a monkey tolerated another


id: cooperative-pulling-paradigm-20260505-6
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-6.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Ostojić and Clayton administered the loose-string cooperation task to domestic dogs (Canis familiaris). Pet dogs first were given a solo task in which the string ends were close enough for one dog to pull at both. Then they were given a transfer test to assess if they could generalize their newly learned rule to novel situations. Finally, the joint task was administered. Dog pairs always came from the same household. In half of the joint tasks one of the pair of dogs was shortly delayed by an obstacle course. All dogs that learned to master the solo task solved the joint task within 60 trials. In the delayed condition, the not-delayed dog waited before pulling most of the time, but only for a few seconds. The researchers also tested dog–human pairs, again in delayed and not-delayed conditions. Dogs were equally successful when working with humans in the non-delayed condition, but far less successful when they had to wait for the human, who on average arrived with a 13-seconds longer delay than the delayed dog in the dog–dog trials. Ostojić and Clayton concluded that inhibiting the necessary action was not easy for dogs. They ruled out that dogs simply went for


id: cooperative-pulling-paradigm-20260505-7
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-7.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Elephants have a complex social structure and large brains that enable them to solve many problems. Their size and strength do not make them easy candidates for experiments. Researchers Plotnik, Lair, Suphachoksahakun, and de Waal adapted the apparatus and task to elephant requirements. They trained captive Asian elephants (Elephas maximus) to use a rope to pull a sliding platform with food on it towards themselves. Once the elephants managed this solo task, the researchers introduced a loose-string apparatus by threading the rope around the platform. At first, two elephants were released simultaneously to walk side by side in two lanes to the two loose ends of the rope. Using their trunks the animals coordinated their actions and retrieved the food. At this stage they could simply be applying a 'see the rope, pull the rope' strategy. To see whether they understood the requirements of the task the researchers introduced a delay for one elephant, initially of 5 seconds and ultimately of 45 seconds. At first the lead elephant failed to retrieve the food but was soon seen to wait for a partner. Across 60 trials the first elephant waited for the second one before pulling in most cases. In a


id: cooperative-pulling-paradigm-20260505-8
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-8.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Rooks (Corvus frugilegus) are large-brained members of the bird family Corvidae. They live in big groups and have a high level of social tolerance. Researchers Seed, Clayton, and Emery set up a loose-string experiment with eight captive rooks. They were first trained in a solo task, with the string ends placed at 1 cm, 3 cm and ultimately 6 cm apart (0.4, 1.2, and 2.4 inch respectively). A pair's willingness to share food was then tested, and was found to differ somewhat between pairs, although food was rarely monopolized by a dominant bird. In the cooperative task, all pairs were able to solve the cooperation problem and retrieve food; two pairs managed this in their first session. Food sharing was a good predictor for successful cooperation. In a subsequent delay test, where one partner had access to the apparatus first, all rooks pulled the string without waiting for their partner to enter the test area in the majority of trials. In a second variant, birds were given a choice between a platform they could operate successfully alone and one that required a pulling partner. When tested alone, four of the six rooks showed no significant preference for either platform. Seed,


id: cooperative-pulling-paradigm-20260505-9
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-9.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Kea (Nestor notabilis), parrots native to New Zealand, are a distant relative of the grey parrot. They live in complex social groups and do well on cognitive tests. Heaney, Gray, and Taylor gave four captive kea a series of cooperative loose-string tasks. After solo training and shaping with string ends increasingly further apart, two birds were released simultaneously in a joint loose-string task. Both pairs did very well, one pair failing only 5 in 60 trials. Shaping was then used in a delay task, with the partner released after one second, then two, and gradually up to 25 seconds later than the first bird. The birds managed to wait for a partner between 74% and 91% of test trials, including success at 65 seconds delay, longer than any other animal of any species had been tested for. To assess if this success could be explained by the learning of a combination of cues, such as seeing a partner while feeling tension on the string, or by a proper understanding of cooperation, the researchers randomly gave the kea a set-up they could solve alone or one in which they needed to cooperate with a delayed partner. Three of the four kea


id: crossover-study-20260505-0
file: data/en.wikipedia.org/wiki/Crossover_study-0.md
category: reference
title: Crossover study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Crossover_study
date_saved: 2026-05-05T09:49:50.139679+00:00
instance: kb-cron
parent: crossover-study-20260505-0
summary:
In medicine, a crossover study or crossover trial is a longitudinal study in which subjects receive a sequence of different treatments (or exposures). While crossover studies can be observational studies, many important crossover studies are controlled experiments, which are discussed in this article. Crossover designs are common for experiments in many scientific disciplines, for example psychology, pharmaceutical science, and medicine. Randomized, controlled crossover experiments are especially important in health care. In a randomized clinical trial, the subjects are randomly assigned to different arms of the study which receive different treatments. When the trial has a repeated measures design, the same measures are collected multiple times for each subject. A crossover trial has a repeated measures design in which each patient is assigned to a sequence of two or more treatments, of which one may be a standard treatment or a placebo. Nearly all crossover are designed to have "balance", whereby all subjects receive the same number of treatments and participate for the same number of periods. In most crossover trials each subject receives all treatments, in a random order. Statisticians suggest that designs should have four periods, which is more efficient than the two-period design, even if the study must


id: data-collection-20260505-0
file: data/en.wikipedia.org/wiki/Data_collection-0.md
category: reference
title: Data collection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Data_collection
date_saved: 2026-05-05T09:49:51.362272+00:00
instance: kb-cron
parent: data-collection-20260505-0
summary:
Data collection or data gathering is the process of gathering and measuring information on targeted variables in an established system, which then enables one to answer relevant questions and evaluate outcomes. Data collection is a research component in all study fields, including physical and social sciences, humanities, and business. While methods vary by discipline, the emphasis on ensuring accurate and honest collection remains the same. The goal for all data collection is to capture evidence that allows data analysis to lead to the formulation of credible answers to the questions that have been posed. Regardless of the field of or preference for defining data (quantitative or qualitative), accurate data collection is essential to maintain research integrity. The selection of appropriate data collection instruments (existing, modified, or newly developed) and delineated instructions for their correct use reduce the likelihood of errors. == Methodology == Data collection and validation consist of four steps when it involves taking a census and seven steps when it involves sampling. A formal data collection process is necessary, as it ensures that the data gathered are both defined and accurate. This way, subsequent decisions based on arguments embodied in the findings are made using valid data. The


id: data-dredging-20260505-0
file: data/en.wikipedia.org/wiki/Data_dredging-0.md
category: reference
title: Data dredging
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Data_dredging
date_saved: 2026-05-05T09:49:52.727198+00:00
instance: kb-cron
parent: data-dredging-20260505-0
summary:
Data dredging, also known as data snooping or p-hacking, is the misuse of data analysis to find patterns in data that can be presented as statistically significant, thus dramatically increasing and understating the risk of false positives. This is done by performing many statistical tests on the data and only reporting those that come back with significant results. Thus data dredging is also often a misused or misapplied form of data mining. The process of data dredging involves testing multiple hypotheses using a single data set by exhaustively searching—perhaps for combinations of variables that might show a correlation, and perhaps for groups of cases or observations that show differences in their mean or in their breakdown by some other variable. Conventional tests of statistical significance are based on the probability that a particular result would arise if chance alone were at work, and necessarily accept some risk of mistaken conclusions of a certain type (mistaken rejections of the null hypothesis). This level of risk is called the significance. When large numbers of tests are performed, some produce false results of this type; hence 5% of randomly chosen hypotheses might be (erroneously) reported to be statistically significant at the 5% significance


id: data-dredging-20260505-1
file: data/en.wikipedia.org/wiki/Data_dredging-1.md
category: reference
title: Data dredging
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Data_dredging
date_saved: 2026-05-05T09:49:52.727198+00:00
instance: kb-cron
parent: data-dredging-20260505-0
summary:
=== Post-hoc grouping === If a dataset contains multiple features, then one or more of the features can be used as grouping, and potentially create a statistically significant result. For example, if a dataset of patients records their age and sex, then a researcher can consider grouping them by age and check if the illness recovery rate is correlated with age. If it does not work, then the researcher might check if it correlates with sex. If not, then perhaps it correlates with age after controlling for sex, etc. The number of possible groupings grows exponentially with the number of features. === Hypothesis suggested by non-representative data === Suppose that a study of a random sample of people includes exactly two people with a birthday of August 7: Mary and John. Someone engaged in data dredging might try to find additional similarities between Mary and John. By going through hundreds or thousands of potential similarities between the two, each having a low probability of being true, an unusual similarity can almost certainly be found. Perhaps John and Mary are the only two people in the study who switched minors three times in college. A hypothesis, biased by data dredging, could


id: data-dredging-20260505-2
file: data/en.wikipedia.org/wiki/Data_dredging-2.md
category: reference
title: Data dredging
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Data_dredging
date_saved: 2026-05-05T09:49:52.727198+00:00
instance: kb-cron
parent: data-dredging-20260505-0
summary:
== Appearance in media == One example is the chocolate weight loss hoax study conducted by journalist John Bohannon, who explained publicly in a Gizmodo article that the study was deliberately conducted fraudulently as a social experiment. This study was widespread in many media outlets around 2015, with many people believing the claim that eating a chocolate bar every day would cause them to lose weight, against their better judgement. This study was published in the Institute of Diet and Health. According to Bohannon, to reduce the p-value to below 0.05, taking 18 different variables into consideration when testing was crucial. == Remedies == While looking for patterns in data is legitimate, applying a statistical test of significance or hypothesis test to the same data until a pattern emerges is prone to abuse. One way to construct hypotheses while avoiding data dredging is to conduct randomized out-of-sample tests. The researcher collects a data set, then randomly partitions it into two subsets, A and B. Only one subset—say, subset A—is examined for creating hypotheses. Once a hypothesis is formulated, it must be tested on subset B, which was not used to construct the hypothesis. Only where B also supports such a


id: dependent-and-independent-variables-20260505-0
file: data/en.wikipedia.org/wiki/Dependent_and_independent_variables-0.md
category: reference
title: Dependent and independent variables
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Dependent_and_independent_variables
date_saved: 2026-05-05T09:49:55.288751+00:00
instance: kb-cron
parent: dependent-and-independent-variables-20260505-0
summary:
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are the outcome of the test they depend on, by some law or rule (e.g., by a mathematical function). Independent variables, on the other hand, are not seen as depending on any other variable in the scope of the experiment in question. Rather, they are controlled by the experimenter. == In pure mathematics == In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) and providing an output (which may also be a number or set of numbers). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is x, and the most common symbol for the output is y; the function itself is commonly written y = f(x). It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and


id: dependent-and-independent-variables-20260505-1
file: data/en.wikipedia.org/wiki/Dependent_and_independent_variables-1.md
category: reference
title: Dependent and independent variables
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Dependent_and_independent_variables
date_saved: 2026-05-05T09:49:55.288751+00:00
instance: kb-cron
parent: dependent-and-independent-variables-20260505-0
summary:
== Other variables == A variable may be thought to alter the dependent or independent variables, but may not actually be the focus of the experiment. So that the variable will be kept constant or monitored to try to minimize its effect on the experiment. Such variables may be designated as either a "controlled variable", "control variable", or "fixed variable". Extraneous variables are candidate independent variables which may be included in a regression analysis to aid a researcher with accurate response parameter estimation, prediction, and goodness of fit, but are not of substantive interest to the hypothesis under examination. For example, in a study examining the effect of post-secondary education on lifetime earnings, some extraneous variables might be gender, ethnicity, social class, genetics, intelligence, age, and so forth. A variable is extraneous only when it can be assumed (or shown) to influence the dependent variable. If included in a regression, it can improve the fit of the model. If it is excluded from the regression and if it has a non-zero covariance with one or more of the independent variables of interest, its omission will bias the regression's result for the effect of that independent variable of interest. This effect


id: design-effect-20260505-0
file: data/en.wikipedia.org/wiki/Design_effect-0.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
In survey research, the design effect is a number that shows how well a sample of people may represent a larger group of people for a specific measure of interest (such as the mean). This is important when the sample comes from a sampling method that is different than just picking people using a simple random sample. The design effect is a positive real number, represented by the symbol Deff {\displaystyle {\text{Deff}}} . If Deff = 1 {\displaystyle {\text{Deff}}=1} , then the sample was selected in a way that is just as good as if people were picked randomly. When Deff > 1 {\displaystyle {\text{Deff}}>1} , then inference from the data collected is not as accurate as it could have been if people were picked randomly. When researchers use complicated methods to pick their sample, they use the design effect to check and adjust their results. It may also be used when planning a study in order to determine the sample size. == Introduction == In survey methodology, the design effect (generally denoted as Deff {\displaystyle {\text{Deff}}} , D eff {\displaystyle D_{\text{eff}}} , or D eft 2 {\displaystyle D_{\text{eft}}^{2}} ) is a measure of the expected impact of a sampling


id: design-effect-20260505-1
file: data/en.wikipedia.org/wiki/Design_effect-1.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
The numerator represents the actual variance for an estimator of a parameter ( θ ^ w {\displaystyle {\hat {\theta }}_{w}} ) under a given sampling design p {\displaystyle p} ; The denominator represents the variance assuming the same sample size, but if the sample were obtained using the estimator for simple random sampling without replacement ( θ ^ S R S W O R {\displaystyle {\hat {\theta }}_{SRSWOR}} ). So that: Deff p ( θ ^ ) = v a r ( θ ^ w ) v a r ( θ ^ S R S W O R ) {\displaystyle {\text{Deff}}_{p}({\hat {\theta }})={\frac {var({\hat {\theta }}_{w})}{var({\hat {\theta }}_{SRSWOR})}}} In other words, Deff {\displaystyle {\text{Deff}}} measures the extent to which the variance has increased (or, in some cases, decreased) because the sample was drawn and adjusted to a specific sampling design (e.g., using weights or other measures) compared to if the sample was from a simple random sample (without replacement). Notice how the definition of Deff {\displaystyle {\text{Deff}}} is based on parameters of the population that are often unknown, and that are hard to estimate directly. Specifically, the definition involves the variances of estimators under two different sampling designs, even though


id: design-effect-20260505-2
file: data/en.wikipedia.org/wiki/Design_effect-2.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
This quantity reflects what would be the sample size that is needed to achieve the current variance of the estimator (for some parameter) with the existing design, if the sample design (and its relevant parameter estimator) were based on a simple random sample. A related quantity is the effective sample size ratio (ESSR), which can be calculated by simply taking the inverse of Deff {\displaystyle {\text{Deff}}} (i.e., n eff n = 1 Deff {\displaystyle {\frac {n_{\text{eff}}}{n}}={\frac {1}{\text{Deff}}}} ). For example, let the design effect, for estimating the population mean based on some sampling design, be 2. If the sample size is 1,000, then the effective sample size will be 500. It means that the variance of the weighted mean based on 1,000 samples will be the same as that of a simple mean based on 500 samples obtained using a simple random sample. == The design effect for well-known sampling designs == === The design effect depends on sampling design and statistical adjustments === Different sampling designs and statistical adjustments may have substantially different impact on the bias and variance of estimators (such as the mean). An example of a design which can lead to estimation efficiency, compared to simple


id: design-effect-20260505-3
file: data/en.wikipedia.org/wiki/Design_effect-3.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
Disproportional sampling due to selection frame or procedure. This happens when a researcher deliberately over- or under-samples specific sub-populations or clusters. For example: In stratified sampling when units from some strata are known to have a larger variance than other strata. In such cases, the intention of the researcher may be to use this prior knowledge about the variance between strata in order to reduce the overall variance of an estimator of some population level parameter of interest (e.g., the mean). This can be achieved by a strategy known as optimum allocation, in which a stratum h {\displaystyle h} is over sampled proportional to higher standard deviation and lower sampling cost (i.e., f h ∝ S h C h {\displaystyle f_{h}\propto {\frac {S_{h}}{\sqrt {C_{h}}}}} , where S h {\displaystyle S_{h}} is the standard deviation of the outcome in h {\displaystyle h} , and C h {\displaystyle C_{h}} relates to the cost of recruiting one element from h {\displaystyle h} ). An example of an optimum allocation is Neyman's optimal allocation which, when cost is fixed for recruiting people from each stratum, the sample size is: n h = n W h S U h ∑ h W h S U


id: design-effect-20260505-4
file: data/en.wikipedia.org/wiki/Design_effect-4.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
Alternatively, when the sampling design is fully known (leading to some p h {\displaystyle p_{h}} probability of selection for some element from stratum h), and the non-response is measurable (i.e., we know that only r h {\displaystyle r_{h}} observations answered in stratum h), then an exactly known inverse probability weight can be calculated for each element i from stratum h using: w i = 1 p h r h {\displaystyle w_{i}={\frac {1}{p_{h}r_{h}}}} . Sometimes a statistical adjustment, such as post-stratification or raking, is used for estimating the selection probability. E.g., when comparing the sample we have with same target population, also known as matching to controls. The estimation process may be focused only on adjusting the existing population to an alternative population (for example, if trying to extrapolate from a panel drawn from several regions to an entire country). In such a case, the adjustment might be focused on some calibration factor c i {\displaystyle c_{i}} and the weights be calculated as w i = c i p h r h {\displaystyle w_{i}={\frac {c_{i}}{p_{h}r_{h}}}} . However, in other cases, both the under-coverage and non-response are all modeled as part of the statistical adjustment, which leads to an estimation of the


id: design-effect-20260505-5
file: data/en.wikipedia.org/wiki/Design_effect-5.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
==== "Design based" vs "model based" for describing properties of estimators ==== Adjusting for unequal probability selection through "individual case weights" (e.g. inverse probability weighting), yields various types of estimators for quantities of interest. Estimators such as Horvitz–Thompson estimator yield unbiased estimators (if the selection probabilities are indeed known, or approximately known), for total and the mean of the population. Deville and Särndal (1992) coined the term "calibration estimator" for estimators using weights such that they satisfy some condition, such as having the sum of weights equal the population size. And more generally, that the weighted sum of weights is equal some quantity of an auxiliary variable: ∑ w i x i = X {\displaystyle \sum w_{i}x_{i}=X} (e.g., that the sum of weighted ages of the respondents is equal to the population size in each age group). The two primary ways to argue about the properties of calibration estimators are: randomization based (or, sampling design based) - in this case, the weights ( w i {\displaystyle w_{i}} ) and values of the outcome of interest y i {\displaystyle y_{i}} that are measured in the sample are all treated as known. In this framework, there is variability in the (known) values


id: design-effect-20260505-6
file: data/en.wikipedia.org/wiki/Design_effect-6.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
Frequency weights are a basic type of weighting presented in introductory statistics courses. With these, each weight is an integer number that indicates the absolute frequency of an item in the sample. These are also sometimes termed repeat (or occurrence) weights. The specific value has an absolute meaning that is lost if the weights are transformed, such as when scaling. For example: if we have the numbers 10 and 20 with the frequency weights values of 2 and 3, then when "spreading" our data it is: 10,10, 20, 20, 20 (with weights of 1 to each of these items). Frequency weights includes the amount of information contained in a dataset, and thus allows things like creating unbiased weighted variance estimation using Bessel's correction. Notice that such weights are often random variables, since the specific number of items we will see from each value in the dataset is random. inverse-variance weighting, also known as analytic weights, is when each element is assigned a weight that is the inverse of its (known) variance. When all elements have the same expectancy, using such weights for calculating weighted averages has the least variance among all weighted averages. In the common formulation, these weights are


id: design-effect-20260505-7
file: data/en.wikipedia.org/wiki/Design_effect-7.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
Deff = n ∑ i = 1 n w i 2 ( ∑ i = 1 n w i ) 2 = 1 n ∑ i = 1 n w i 2 ( 1 n ∑ i = 1 n w i ) 2 = w 2 ¯ w ¯ 2 {\displaystyle {\text{Deff}}={\frac {n\sum _{i=1}^{n}w_{i}^{2}}{(\sum _{i=1}^{n}w_{i})^{2}}}={\frac {{\frac {1}{n}}\sum _{i=1}^{n}w_{i}^{2}}{\left({\frac {1}{n}}\sum _{i=1}^{n}w_{i}\right)^{2}}}={\frac {\overline {w^{2}}}{{\overline {w}}^{2}}}} This version of the formula is valid when one stratum had several observations taken from it (i.e., each having the same weight), or when there are just many strata were each one had one observation taken from it, but several of them had the same probability of selection. While the interpretation is slightly different, the calculation of the two scenarios comes out to be the same. When using Kish's design effect for unequal weights, you may use the following simplified formula for "Kish's Effective Sample Size" n eff = ( ∑ i = 1 n w i ) 2 ∑ i = 1 n w i 2 {\displaystyle n_{\text{eff}}={\frac {(\sum _{i=1}^{n}w_{i})^{2}}{\sum _{i=1}^{n}w_{i}^{2}}}} ===== Assumptions and proofs ===== The above formula, by Kish, gives the increase in the variance of the weighted mean based on "haphazard" weights.


id: design-effect-20260505-8
file: data/en.wikipedia.org/wiki/Design_effect-8.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
===== Relation to disproportionate stratified sampling ===== Kish's original definition compared the variance under some sampling design to the variance achieved through a simple random sample. Some literature provide the following alternative definition for Kish's design effect: "the ratio of the variance of the weighted survey mean under disproportionate stratified sampling to the variance under proportionate stratified sampling when all stratum unit variances are equal". Reflecting on this, Park and Lee (2006) stated that "The rationale behind [...][Kish's] derivation is that the loss in precision of [the weighted mean] due to haphazard unequal weighting can be approximated by the ratio of the variance under disproportionate stratified sampling to that under the proportionate stratified sampling". Note that this alternative definition only approximated since if the denominator is based on "proportionate stratified sampling" (achieved via stratified sampling) then such a selection will yield a reduced variance as compared with simple random sample. This is since stratified sampling removes some of the variability in the specific number of elements per stratum, as occurs under SRS. Relatedly, Cochran (1977) provides a formula for the proportional increase in variance due to deviation from optimum allocation (what, in Kish's formulas, would be called L). ===== Alternative


id: design-effect-20260505-9
file: data/en.wikipedia.org/wiki/Design_effect-9.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
σ ^ y {\displaystyle {\hat {\sigma }}_{y}} estimates the population variance σ y {\displaystyle \sigma _{y}} , and L is the relvariance of the weights, as defined in Kish's formula: L = c v w 2 = relvar ( w ) = V ( w ) w ¯ 2 {\displaystyle L=cv_{w}^{2}={\text{relvar}}(w)={\frac {V(w)}{{\bar {w}}^{2}}}} . This assumes that the regression model fits well so that the probability of selection and the residuals are independent, since it leads to the residuals, and the square residuals, to be uncorrelated with the weights, i.e., that ρ ϵ , W = 0 {\displaystyle \rho _{\epsilon ,W}=0} and also ρ ϵ 2 , W = 0 {\displaystyle \rho _{\epsilon ^{2},W}=0} . When the population size (N) is very large, the formula can be written as: Deff S p e n c e r = ( 1 − ρ ^ y , P 2 ) ( 1 + c v w 2 ) + ( 1 c v Y 2 ) 2 c v w 2 {\displaystyle {\text{Deff}}_{Spencer}=(1-{\hat {\rho }}_{y,P}^{2})(1+cv_{w}^{2})+\left({\frac {1}{cv_{Y}^{2}}}\right)^{2}cv_{w}^{2}} (since α = Y ¯ − β × P ¯ = Y ¯ − β × 1 N ≈ Y ¯ {\displaystyle \alpha ={\bar {Y}}-\beta \times


id: design-effect-20260505-10
file: data/en.wikipedia.org/wiki/Design_effect-10.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
=== The design effect for complex designs === ==== Unequal selection probabilities times Cluster sampling ==== In a 1987 paper, Kish proposed a combined design effect that incorporates both the effects due to weighting that accounts for unequal selection probabilities and cluster sampling: Deff Kish = n ∑ h = 1 H ( n h w h 2 ) ( ∑ h = 1 H n h w h ) 2 ( 1 + ( n ∗ − 1 ) ρ ) = Deff k × Deff C {\displaystyle {\text{Deff}}_{\text{Kish}}={\frac {n\sum \limits _{h=1}^{H}(n_{h}w_{h}^{2})}{\left(\sum \limits _{h=1}^{H}n_{h}w_{h}\right)^{2}}}\left(1+(n^{*}-1)\rho \right)={\text{Deff}}_{k}\times {\text{Deff}}_{C}} The above uses notations similar to what is used in this article (the original 1987 publication used different notation). A model based justification for this formula was provided by Gabler et al. ==== Stratified sampling times unequal selection probabilities times Cluster sampling ==== In 2000, Liu and Aragon proposed a decomposition of unequal selection probabilities design effect for different strata in stratified sampling. In 2002, Liu et al. extended that work to account for stratified samples, where within each stratum is a set of unequal selection probability weights. The cluster sampling is either global or per stratum. Similar work was done also by


id: design-effect-20260505-11
file: data/en.wikipedia.org/wiki/Design_effect-11.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
When planning a future data collection - D e f f {\displaystyle Deff} may be used to evaluate the sampling efficiency. E.g. if there is potentially "too much" increase in variance due to some sampling design decision, or if some alternative (economically feasible) design is more efficient. This also influences the sample size (overall, per stratum, per cluster, etc.). When planning the sample size, work may be done to correct the design effect so as to separate the interviewer effect (measurement error) from the effects of the sampling design on the sampling variance. As a diagnostic tool - D e f f {\displaystyle Deff} may help in evaluating potential problems with a post-hoc weighting analysis (e.g. from non-response adjustments). For example, if the D e f f {\displaystyle Deff} value is especially high, then it might indicate an issue with the sampling or weighting scheme. This can also assist when performing some manipulation on the weights (e.g., weight trimming), the design effect could be used to evaluate the influence of the manipulation on the effective sample size. And also in identifying glaring issues with the data or its analysis (e.g., ranging from mistakes to the presence of Outliers). Although some


id: design-matrix-20260505-0
file: data/en.wikipedia.org/wiki/Design_matrix-0.md
category: reference
title: Design matrix
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_matrix
date_saved: 2026-05-05T09:49:58.034133+00:00
instance: kb-cron
parent: design-matrix-20260505-0
summary:
In statistics and in particular in regression analysis, a design matrix, also known as model matrix or regressor matrix and often denoted by X, is a matrix of values of explanatory variables of a set of objects. Each row represents an individual object, with the successive columns corresponding to the variables and their specific values for that object. The design matrix is used in certain statistical models, e.g., the general linear model. It can contain indicator variables (ones and zeros) that indicate group membership in an ANOVA, or it can contain values of continuous variables. The design matrix contains data on the independent variables (also called explanatory variables), in a statistical model that is intended to explain observed data on a response variable (often called a dependent variable). The theory relating to such models uses the design matrix as input to some linear algebra : see for example linear regression. A notable feature of the concept of a design matrix is that it is able to represent a number of different experimental designs and statistical models, e.g., ANOVA, ANCOVA, and linear regression. == Definition == The design matrix is defined to be a matrix X {\displaystyle X} such that X


id: design-matrix-20260505-1
file: data/en.wikipedia.org/wiki/Design_matrix-1.md
category: reference
title: Design matrix
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_matrix
date_saved: 2026-05-05T09:49:58.034133+00:00
instance: kb-cron
parent: design-matrix-20260505-0
summary:
[ y 1 y 2 y 3 y 4 y 5 y 6 y 7 ] = [ 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 ] [ μ 1 μ 2 μ 3 ] + [ ε 1 ε 2 ε 3 ε 4 ε 5 ε 6 ε 7 ] {\displaystyle {\begin{bmatrix}y_{1}\\y_{2}\\y_{3}\\y_{4}\\y_{5}\\y_{6}\\y_{7}\end{bmatrix}}={\begin{bmatrix}1&0&0\\1&0&0\\1&0&0\\0&1&0\\0&1&0\\0&0&1\\0&0&1\end{bmatrix}}{\begin{bmatrix}\mu _{1}\\\mu _{2}\\\mu _{3}\end{bmatrix}}+{\begin{bmatrix}\varepsilon _{1}\\\varepsilon _{2}\\\varepsilon _{3}\\\varepsilon _{4}\\\varepsilon _{5}\\\varepsilon _{6}\\\varepsilon _{7}\end{bmatrix}}} In this model μ i {\displaystyle \mu _{i}} represents the mean of the i {\displaystyle i} th group. === One-way ANOVA (offset from reference group) === The ANOVA model could be equivalently written as each group parameter τ i {\displaystyle \tau _{i}} being an offset from some overall reference. Typically this reference point is taken to be one of the groups under consideration. This makes sense in the context of comparing multiple treatment groups to a control group and the control group is considered the "reference". In this example, group 1 was chosen to be the reference group. As such the model to be fit is y i j = μ + τ i + ε i j {\displaystyle y_{ij}=\mu +\tau _{i}+\varepsilon _{ij}}


id: design-space-exploration-20260505-0
file: data/en.wikipedia.org/wiki/Design_space_exploration-0.md
category: reference
title: Design space exploration
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_space_exploration
date_saved: 2026-05-05T09:49:59.275013+00:00
instance: kb-cron
parent: design-space-exploration-20260505-0
summary:
Design Space Exploration (DSE) refers to systematic analysis and pruning of unwanted design points based on parameters of interest. While the term DSE can apply to any kind of system, we refer to electronic and embedded system design in this article. Given the complex specification of electronic systems and the plethora of design choices ranging from the choice of components, number of components, operating modes of each of the components, connections between the components, choice of algorithm, etc.; design decisions need to be based on a systematic exploration process. However, the exploration process is complex because of a variety of ways in which the same functionality can be implemented. A tradeoff analysis between each of the implementation options based on a certain parameter of interest forms the basis of DSE. The parameter of interest could vary across systems, but the commonly used parameters are power, performance, and cost. Additional factors like size, shape, weight, etc. can be important for some handheld systems like cellphone and tablets. With growing usage of mobile devices, energy is also becoming a mainstream optimization parameter along with power and performance. Owing to the complexity of the exploration process, researchers have proposed automated DSE where the


id: design-expert-20260505-0
file: data/en.wikipedia.org/wiki/Design–Expert-0.md
category: reference
title: Design–Expert
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design–Expert
date_saved: 2026-05-05T09:50:00.505639+00:00
instance: kb-cron
parent: design-expert-20260505-0
summary:
Design–Expert is a statistical software package from Stat-Ease Inc. that is specifically dedicated to performing design of experiments (DOE). Design–Expert offers comparative tests, screening, characterization, optimization, robust parameter design, mixture designs and combined designs. Design–Expert provides test matrices for screening up to 50 factors. Statistical significance of these factors is established with analysis of variance (ANOVA). Graphical tools help identify the impact of each factor on the desired outcomes and reveal abnormalities in the data. == History == Stat-Ease released its first version of Design–Expert in 1988. In 1996 the firm released version 5 which was the first version of the software designed for Microsoft Windows. Version 6.0 moved to a full 32-bit architecture and fuller compliance with Windows visual convention and also allowed up to 256 runs for two-level blocked designs. Version 7.0 added 3D surface plots for category factors and a t-value effects Pareto chart among many other functional additions. This version also includes the ability to type in variable constraints directly to the design in ratio form. Version 9 incorporates split-plot factorial designs including two-level full and fractional factorials, general factorials and optimal factorials. == Features == Design–Expert offers test matrices for screening up to 50 factors.


id: designated-member-review-20260505-0
file: data/en.wikipedia.org/wiki/Designated_Member_Review-0.md
category: reference
title: Designated Member Review
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Designated_Member_Review
date_saved: 2026-05-05T09:50:01.851591+00:00
instance: kb-cron
parent: designated-member-review-20260505-0
summary:
A Designated Member Review (DMR) or Designated Subcommittee Review (DSR), also known as Designated Review, is a review of a protocol where a committee designates one or more members of the committee to review a decisionmaking process or a protocol or procedure, a review which would ordinarily require the full committee's review. Typically this pertains to IACUCs. In protocols of the National Institutes of Health (NIH) in the United States, 'Correct Conduct of Full-Committee and Designated-Member Protocol Reviews', there are two ways a procedure or protocol can be reviewed, according to PHS policy. Sometimes a protocol or amendment to policies is submitted, which may not need to be considered at a full meeting. If everyone on the committee agrees, then the chair or the committee can assign a person of knowledge and selected other member(s) to review the protocol and approve it or send it back to the full committee for discussion. A first step in such a process is for the chair to poll committee members to determine agreement for the DMR. If they agree, the DMR proceeds; if they do not agree, the DMR does not occur and it should be considered at a convened meeting by the


id: difference-in-differences-20260505-0
file: data/en.wikipedia.org/wiki/Difference_in_differences-0.md
category: reference
title: Difference in differences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Difference_in_differences
date_saved: 2026-05-05T09:50:03.034225+00:00
instance: kb-cron
parent: difference-in-differences-20260505-0
summary:
Difference in differences (DID or DD) is a quasi-experimental statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differential effect of a treatment on a "treatment group" versus a "control group" in a natural experiment. It calculates the effect of a treatment (i.e., an explanatory variable or an independent variable) on an outcome (i.e., a response variable or dependent variable) by comparing the average change over time in the outcome variable for the treatment group to the average change over time for the control group. Although it is intended to mitigate the effects of extraneous factors and selection bias, depending on how the treatment group is chosen, this method may still be subject to certain biases (e.g., mean regression, reverse causality and omitted variable bias). In contrast to a time-series estimate of the treatment effect on subjects (which analyzes differences over time) or a cross-section estimate of the treatment effect (which measures the difference between treatment and control groups), the difference in differences uses panel data to measure the differences, between the treatment and control group, of the changes in the outcome


id: difference-in-differences-20260505-1
file: data/en.wikipedia.org/wiki/Difference_in_differences-1.md
category: reference
title: Difference in differences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Difference_in_differences
date_saved: 2026-05-05T09:50:03.034225+00:00
instance: kb-cron
parent: difference-in-differences-20260505-0
summary:
δ ( D 11 − D 12 ) + δ ( D 22 − D 21 ) + ε ¯ 11 − ε ¯ 12 + ε ¯ 22 − ε ¯ 21 . {\displaystyle {\begin{aligned}&({\overline {y}}_{11}-{\overline {y}}_{12})-({\overline {y}}_{21}-{\overline {y}}_{22})\\[6pt]={}&{\big [}(\gamma _{1}+\lambda _{1}+\delta D_{11}+{\overline {\varepsilon }}_{11})-(\gamma _{1}+\lambda _{2}+\delta D_{12}+{\overline {\varepsilon }}_{12}){\big ]}\\&\qquad {}-{\big [}(\gamma _{2}+\lambda _{1}+\delta D_{21}+{\overline {\varepsilon }}_{21})-(\gamma _{2}+\lambda _{2}+\delta D_{22}+{\overline {\varepsilon }}_{22}){\big ]}\\[6pt]={}&\delta (D_{11}-D_{12})+\delta (D_{22}-D_{21})+{\overline {\varepsilon }}_{11}-{\overline {\varepsilon }}_{12}+{\overline {\varepsilon }}_{22}-{\overline {\varepsilon }}_{21}.\end{aligned}}} The strict exogeneity assumption then implies that E ⁡ [ ( y ¯ 11 − y ¯ 12 ) − ( y ¯ 21 − y ¯ 22 ) ] = δ ( D 11 − D 12 ) + δ ( D 22 − D 21 ) . {\displaystyle \operatorname {E} \left[({\overline {y}}_{11}-{\overline {y}}_{12})-({\overline {y}}_{21}-{\overline {y}}_{22})\right]~=~\delta (D_{11}-D_{12})+\delta (D_{22}-D_{21}).} Without loss of generality, assume that s = 2 {\displaystyle s=2} is the treatment group, and t = 2 {\displaystyle t=2} is the after period, then D 22 = 1 {\displaystyle D_{22}=1} and D 11 = D 12 = D 21 = 0 {\displaystyle D_{11}=D_{12}=D_{21}=0} , giving the DID estimator δ ^ = ( y ¯ 11 − y ¯ 12 ) − ( y ¯


id: difference-in-differences-20260505-2
file: data/en.wikipedia.org/wiki/Difference_in_differences-2.md
category: reference
title: Difference in differences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Difference_in_differences
date_saved: 2026-05-05T09:50:03.034225+00:00
instance: kb-cron
parent: difference-in-differences-20260505-0
summary:
where E ^ ( ⋯ ∣ … ) {\displaystyle {\widehat {E}}(\dots \mid \dots )} stands for conditional averages computed on the sample, for example, T = 1 {\displaystyle T=1} is the indicator for the after period, S = 0 {\displaystyle S=0} is an indicator for the control group. Note that β ^ 1 {\displaystyle {\hat {\beta }}_{1}} is an estimate of the counterfactual rather than the impact of the control group. The control group is often used as a proxy for the counterfactual (see, Synthetic control method for a deeper understanding of this point). Thereby, β ^ 1 {\displaystyle {\hat {\beta }}_{1}} can be interpreted as the impact of both the control group and the intervention's (treatment's) counterfactual. Similarly, β ^ 2 {\displaystyle {\hat {\beta }}_{2}} , due to the parallel trend assumption, is also the same differential between the treatment and control group in T = 1 {\displaystyle T=1} . The above descriptions should not be construed to imply the (average) effect of only the control group, for β ^ 1 {\displaystyle {\hat {\beta }}_{1}} , or only the difference of the treatment and control groups in the pre-period, for β ^ 2 {\displaystyle {\hat {\beta }}_{2}} . As


id: difference-in-differences-20260505-3
file: data/en.wikipedia.org/wiki/Difference_in_differences-3.md
category: reference
title: Difference in differences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Difference_in_differences
date_saved: 2026-05-05T09:50:03.034225+00:00
instance: kb-cron
parent: difference-in-differences-20260505-0
summary:
=== In economic history === Difference-in-differences has also been applied to the study of historical events, particularly in the field of economic history, where researchers rely on natural experiments to investigate long-run outcomes. By comparing regions or groups that were differentially exposed to shocks such as disease, institutional change, or wartime destruction, scholars have used the method to identify causal effects that cannot be observed directly. In 2021, Elena Esposito used DID to examine how the arrival of malaria influenced the expansion of African slavery in the United States. She compared counties that were more ecologically suitable for malaria transmission with those that were less suitable, before and after the introduction of the disease in the late seventeenth century. Results showed that malaria-prone counties experienced a much greater increase in the share of enslaved Africans after the disease became endemic. In addition, enslaved individuals from parts of Africa with high malaria prevalence sold at higher prices in Louisiana slave markets, suggesting that buyers placed a premium on resistance to malaria. This application demonstrated how DID can be used to link environmental shocks with institutional development over the long run. González, Marshall, and Naidu in 2017 used DID to analyze how


id: drug-design-20260505-0
file: data/en.wikipedia.org/wiki/Drug_design-0.md
category: reference
title: Drug design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Drug_design
date_saved: 2026-05-05T09:50:04.282020+00:00
instance: kb-cron
parent: drug-design-20260505-0
summary:
Drug design, often referred to as rational drug design or simply rational design, is the inventive process of finding new medications based on the knowledge of a biological target. The drug is most commonly an organic small molecule that activates or inhibits the function of a biomolecule such as a protein, which in turn results in a therapeutic benefit to the patient. In the most basic sense, drug design involves the design of molecules that are complementary in shape and charge to the biomolecular target with which they interact and therefore will bind to it. Drug design frequently but not necessarily relies on computer modeling techniques. This type of modeling is sometimes referred to as computer-aided drug design. Finally, drug design that relies on the knowledge of the three-dimensional structure of the biomolecular target is known as structure-based drug design. In addition to small molecules, biopharmaceuticals including peptides and especially therapeutic antibodies are an increasingly important class of drugs and computational methods for improving the affinity, selectivity, and stability of these protein-based therapeutics have also been developed. == Definition == The phrase "drug design" is similar to ligand design (i.e., design of a molecule that will bind tightly to its


id: drug-design-20260505-1
file: data/en.wikipedia.org/wiki/Drug_design-1.md
category: reference
title: Drug design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Drug_design
date_saved: 2026-05-05T09:50:04.282020+00:00
instance: kb-cron
parent: drug-design-20260505-0
summary:
==== Rational drug discovery ==== Rational drug design (also called reverse pharmacology) begins with a hypothesis that modulation of a specific biological target may have therapeutic value. In order for a biomolecule to be selected as a drug target, two essential pieces of information are required. The first is evidence that modulation of the target will be disease modifying. This knowledge may come from, for example, disease linkage studies that show an association between mutations in the biological target and certain disease states. The second is that the target is capable of binding to a small molecule and that its activity can be modulated by the small molecule. Once a suitable target has been identified, the target is normally cloned and produced and purified. The purified protein is then used to establish a screening assay. In addition, the three-dimensional structure of the target may be determined. The search for small molecules that bind to the target is begun by screening libraries of potential drug compounds. This may be done by using the screening assay (a "wet screen"). In addition, if the structure of the target is available, a virtual screen may be performed of candidate drugs. Ideally, the candidate drug


id: drug-design-20260505-2
file: data/en.wikipedia.org/wiki/Drug_design-2.md
category: reference
title: Drug design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Drug_design
date_saved: 2026-05-05T09:50:04.282020+00:00
instance: kb-cron
parent: drug-design-20260505-0
summary:
=== Structure-based === Structure-based drug design (or direct drug design) relies on knowledge of the three dimensional structure of the biological target obtained through methods such as x-ray crystallography or NMR spectroscopy. If an experimental structure of a target is not available, it may be possible to create a homology model of the target based on the experimental structure of a related protein. Using the structure of the biological target, candidate drugs that are predicted to bind with high affinity and selectivity to the target may be designed using interactive graphics and the intuition of a medicinal chemist. Alternatively, various automated computational procedures may be used to suggest new drug candidates. Current methods for structure-based drug design can be divided roughly into three main categories. The first method is identification of new ligands for a given receptor by searching large databases of 3D structures of small molecules to find those fitting the binding pocket of the receptor using fast approximate docking programs. This method is known as virtual screening. A second category is de novo design of new ligands. In this method, ligand molecules are built up within the constraints of the binding pocket by assembling small pieces in a


id: drug-design-20260505-3
file: data/en.wikipedia.org/wiki/Drug_design-3.md
category: reference
title: Drug design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Drug_design
date_saved: 2026-05-05T09:50:04.282020+00:00
instance: kb-cron
parent: drug-design-20260505-0
summary:
== Examples == A particular example of rational drug design involves the use of three-dimensional information about biomolecules obtained from such techniques as X-ray crystallography and NMR spectroscopy. Computer-aided drug design in particular becomes much more tractable when there is a high-resolution structure of a target protein bound to a potent ligand. This approach to drug discovery is sometimes referred to as structure-based drug design. The first unequivocal example of the application of structure-based drug design leading to an approved drug is the carbonic anhydrase inhibitor dorzolamide, which was approved in 1995. Another case study in rational drug design is imatinib, a tyrosine kinase inhibitor designed specifically for the bcr-abl fusion protein that is characteristic for Philadelphia chromosome-positive leukemias (chronic myelogenous leukemia and occasionally acute lymphocytic leukemia). Imatinib is substantially different from previous drugs for cancer, as most agents of chemotherapy simply target rapidly dividing cells, not differentiating between cancer cells and other tissues. Additional examples include: == Drug screening == Types of drug screening include phenotypic screening, high-throughput screening, and virtual screening. Phenotypic screening is characterized by the process of screening drugs using cellular or animal disease models to identify compounds that alter the phenotype and produce beneficial disease-related


id: ecological-study-20260505-0
file: data/en.wikipedia.org/wiki/Ecological_study-0.md
category: reference
title: Ecological study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ecological_study
date_saved: 2026-05-05T09:50:05.530567+00:00
instance: kb-cron
parent: ecological-study-20260505-0
summary:
In epidemiology, ecological studies are used to understand the relationship between outcome and exposure at a population level, where 'population' represents a group of individuals with a shared characteristic such as geography, ethnicity, socio-economic status of employment. What differentiates ecological studies from other studies is that the unit analysis being studied is the group, therefore inferences cannot be made about individual study participants. On the other hand, details of outcome and exposure can be generalized to the population being studied. Examples of such studies include investigating associations between units of grouped data, such as electoral wards, regions, or even whole countries. == Study design == Generally, three different designs can be used to conduct ecological studies depending on the situation. Such studies may compare populations or groups using a multiple-group design, periods of time using a time-trend design, or groups and time using a mixed design. == Notable examples == === Cholera study === The study by John Snow regarding a cholera outbreak in London is considered the first ecological study to solve a health issue. He used a map of deaths from cholera to determine that the source of the cholera was a pump on Broad Street. He had


id: experimental-factor-ontology-20260505-0
file: data/en.wikipedia.org/wiki/Experimental_factor_ontology-0.md
category: reference
title: Experimental factor ontology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Experimental_factor_ontology
date_saved: 2026-05-05T09:50:06.784380+00:00
instance: kb-cron
parent: experimental-factor-ontology-20260505-0
summary:
Experimental factor ontology, also known as EFO, is an open-access ontology of experimental variables particularly those used in molecular biology. The ontology covers variables which include aspects of disease, anatomy, cell type, cell lines, chemical compounds and assay information. EFO is developed and maintained at the EMBL-EBI as a cross-cutting resource for the purposes of curation, querying and data integration in resources such as Ensembl, ChEMBL and Expression Atlas. == Scope and access == The original aim of EFO was to describe experimental variables in the EBI's Expression Atlas resource. This consisted primarily of disease, anatomical regions and cell types. By December 2013 the scope had grown to include several other EMBL-EBI resources and several external projects including CellFinder, cell lines from the ENCODE project and phenotype to SNP information in the NHGRI's Catalog of Published Genome-Wide Association Studies. EFO makes use of existing biomedical ontologies from the Open Biomedical Ontologies collection in order to improve interoperability with other resources which may also use these same ontologies, such as ChEBI and the Ontology for Biomedical Investigations. All data in the database is non-proprietary or is derived from a non-proprietary source. It is thus freely accessible and available to anyone. In


id: ethics-committee-20260505-0
file: data/en.wikipedia.org/wiki/Ethics_committee-0.md
category: reference
title: Ethics committee
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ethics_committee
date_saved: 2026-05-05T09:50:08.036049+00:00
instance: kb-cron
parent: ethics-committee-20260505-0
summary:
An ethics committee is a body responsible for ensuring that medical experimentation and human subject research are carried out in an ethical manner in accordance with national and international law. == By jurisdiction == === European Union === An ethics committee in the European Union is a body responsible for oversight of medical or human research studies in EU member states. Local terms for a European ethics committee include: A Research Ethics Committee (REC) in the United Kingdom A Medical Research Ethics Committee (MREC) in the Netherlands. A Comité de Protection des Personnes (CPP) in France. === United States === In the United States, an ethics committee is usually known as an institutional review board (IRB) or research ethics board (REB) and is dedicated to overseeing the rights and well-being of research subjects participating in scientific studies in the US. Similarly in Canada, the committee is called a Research Ethics Board (REB). === Australia === In Australia, an ethics committee in medical research refers to a Human Research Ethics Committee (HREC). === New Zealand === Aotearoa New Zealand's ethics committee is Kāhui Matatika o te Motu, also known as the National Ethics Advisory Committee (NEAC). They outline the standards for


id: experimental-benchmarking-20260505-0
file: data/en.wikipedia.org/wiki/Experimental_benchmarking-0.md
category: reference
title: Experimental benchmarking
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Experimental_benchmarking
date_saved: 2026-05-05T09:50:10.509258+00:00
instance: kb-cron
parent: experimental-benchmarking-20260505-0
summary:
Experimental benchmarking allows researchers to learn about the accuracy of non-experimental research designs. Specifically, one can compare observational results to experimental findings to calibrate bias. Under ordinary conditions, carrying out an experiment gives the researchers an unbiased estimate of their parameter of interest. This estimate can then be compared to the findings of observational research. Note that benchmarking is an attempt to calibrate non-statistical uncertainty (flaws in underlying assumptions). When combined with meta-analysis this method can be used to understand the scope of bias associated with a specific area of research. == History == The start of experimental benchmarking in social science is often attributed to Robert LaLonde. In 1986 he found that findings of econometric procedures assessing the effect of an employment program on trainee earnings did not recover the experimental findings. Experimental benchmarking is often conducted in medical research, such as Schnell‐Inderst et al. (2017) and Burden et al. (2017). == Procedural Considerations == The most instructive experimental benchmarking designs are done on a large scale. They also compare experimental and non-experimental work that looks at the same outcome and the same population. == Observational Designs That Can Be Assessed with Benchmarking == Non-experimental, or observational, research designs


id: exploratory-thought-20260505-0
file: data/en.wikipedia.org/wiki/Exploratory_thought-0.md
category: reference
title: Exploratory thought
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Exploratory_thought
date_saved: 2026-05-05T09:50:11.728800+00:00
instance: kb-cron
parent: exploratory-thought-20260505-0
summary:
Exploratory thought is an academic term used in the field of psychology to describe reasoning that neutrally considers multiple points of view and tries to anticipate all possible objections to, or flaws in, a particular position, with the goal of seeking truth. The opposite of exploratory thought is confirmatory thought, which is reasoning designed to construct justification supporting a specific point of view. Both terms were coined by social psychologist Jennifer Lerner and psychology professor Philip Tetlock in the 2002 book Emerging Perspectives in Judgment and Decision Making. The authors argue that most people, most of the time, make decisions based on gut feelings and poor logic, and reason through issues primarily to provide justification, to themselves and to others, of what they already believe. Lerner and Tetlock say that when people expect to need to justify their position to external parties, and they already know those parties' views, they will tend to adopt a similar position to theirs, and then engage in confirmatory thought with the goal of bolstering their own credibility rather than reaching a good conclusion. However, if the external parties are overly aggressive or critical, people will disengage from thought altogether, and simply assert their personal


id: factorial-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Factorial_experiment-0.md
category: reference
title: Factorial experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Factorial_experiment
date_saved: 2026-05-05T09:50:13.140941+00:00
instance: kb-cron
parent: factorial-experiment-20260505-0
summary:
In statistics, a factorial experiment (also known as full factorial experiment) investigates how multiple factors influence a specific outcome, called the response variable. Each factor is tested at distinct values, or levels, and the experiment includes every possible combination of these levels across all factors. This comprehensive approach lets researchers see not only how each factor individually affects the response, but also how the factors interact and influence each other. Often, factorial experiments simplify things by using just two levels for each factor. A 2x2 factorial design, for instance, has two factors, each with two levels, leading to four unique combinations to test. The interaction between these factors is often the most crucial finding, even when the individual factors also have an effect. If a full factorial design becomes too complex due to the sheer number of combinations, researchers can use a fractional factorial design. This method strategically omits some combinations (usually at least half) to make the experiment more manageable. These combinations of factor levels are sometimes called runs (of an experiment), points (viewing the combinations as vertices of a graph), and cells (arising as intersections of rows and columns). == History == Factorial designs were used in the


id: factorial-experiment-20260505-1
file: data/en.wikipedia.org/wiki/Factorial_experiment-1.md
category: reference
title: Factorial experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Factorial_experiment
date_saved: 2026-05-05T09:50:13.140941+00:00
instance: kb-cron
parent: factorial-experiment-20260505-0
summary:
== Example == The simplest factorial experiment contains two levels for each of two factors. Suppose an engineer wishes to study the total power used by each of two different motors, A and B, running at each of two different speeds, 2000 or 3000 RPM. The factorial experiment would consist of four experimental units: motor A at 2000 RPM, motor B at 2000 RPM, motor A at 3000 RPM, and motor B at 3000 RPM. Each combination of a single level selected from every factor is present once. This experiment is an example of a 22 (or 2×2) factorial experiment, so named because it considers two levels (the base) for each of two factors (the power or superscript), or #levels#factors, producing 22=4 factorial points. Designs can involve many independent variables. As a further example, the effects of three input variables can be evaluated in eight experimental conditions shown as the corners of a cube. This can be conducted with or without replication, depending on its intended purpose and available resources. It will provide the effects of the three independent variables on the dependent variable and possible interactions. == Notation == Factorial experiments are described by two things: the number of


id: factorial-experiment-20260505-2
file: data/en.wikipedia.org/wiki/Factorial_experiment-2.md
category: reference
title: Factorial experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Factorial_experiment
date_saved: 2026-05-05T09:50:13.140941+00:00
instance: kb-cron
parent: factorial-experiment-20260505-0
summary:
A contrast vector belongs to the main effect of a particular factor if the values of its components depend only on the level of that factor. A contrast vector belongs to the interaction of two factors, say A and B, if (i) the values of its components depend only on the levels of A and B, and (ii) it is orthogonal (perpendicular) to the contrast vectors representing the main effects of A and B. Similar definitions hold for interactions of more than two factors. In the 2 × 3 example, for instance, the pattern of the A column follows the pattern of the levels of factor A, indicated by the first component of each cell. Similarly, the pattern of the B columns follows the levels of factor B (sorting on B makes this easier to see). The number of columns needed to specify each effect is the degrees of freedom for the effect, and is an essential quantity in the analysis of variance. The formula is as follows: A main effect for a factor with s levels has s−1 degrees of freedom. The interaction of two factors with s1 and s2 levels, respectively, has (s1−1)(s2−1) degrees of freedom. The formula


id: factorial-experiment-20260505-3
file: data/en.wikipedia.org/wiki/Factorial_experiment-3.md
category: reference
title: Factorial experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Factorial_experiment
date_saved: 2026-05-05T09:50:13.140941+00:00
instance: kb-cron
parent: factorial-experiment-20260505-0
summary:
== Implementation == For more than two factors, a 2k factorial experiment can usually be recursively designed from a 2k−1 factorial experiment by replicating the 2k−1 experiment, assigning the first replicate to the first (or low) level of the new factor, and the second replicate to the second (or high) level. This framework can be generalized to, e.g., designing three replicates for three level factors, etc. A factorial experiment allows for estimation of experimental error in two ways. The experiment can be replicated, or the sparsity-of-effects principle can often be exploited. Replication is more common for small experiments and is a very reliable way of assessing experimental error. When the number of factors is large (typically more than about 5 factors, but this does vary by application), replication of the design can become operationally difficult. In these cases, it is common to only run a single replicate of the design, and to assume that factor interactions of more than a certain order (say, between three or more factors) are negligible. Under this assumption, estimates of such high order interactions are estimates of an exact zero, thus really an estimate of experimental error. When there are many factors, many experimental runs


id: field-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Field_experiment-0.md
category: reference
title: Field experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Field_experiment
date_saved: 2026-05-05T09:50:14.421917+00:00
instance: kb-cron
parent: field-experiment-20260505-0
summary:
Field experiments are experiments carried out outside of laboratory settings. They are different from others in that they are conducted in real-world settings often unobtrusively and control not only the subject pool but selection and overtness, as defined by leaders such as John A. List. This is in contrast to laboratory experiments, which enforce scientific control by testing a hypothesis in the artificial and highly controlled setting of a laboratory. Field experiments have some contextual differences as well from naturally occurring experiments and quasi-experiments. While naturally occurring experiments rely on an external force (e.g. a government, nonprofit, etc.) controlling the randomization treatment assignment and implementation, field experiments require researchers to retain control over randomization and implementation. Quasi-experiments occur when treatments are administered as-if randomly (e.g. U.S. Congressional districts where candidates win with slim margins, weather patterns, natural disasters, etc.). In a field experiment, researchers randomly assign subjects (or other sampling units) to either treatment or control groups to test claims of causal relationships. Random assignment helps establish the comparability of the treatment and control group so that any differences between them that emerge after the treatment has been administered plausibly reflect the influence of the treatment rather than preexisting differences


id: field-experiment-20260505-1
file: data/en.wikipedia.org/wiki/Field_experiment-1.md
category: reference
title: Field experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Field_experiment
date_saved: 2026-05-05T09:50:14.421917+00:00
instance: kb-cron
parent: field-experiment-20260505-0
summary:
== Limitations == There are limitations of and arguments against using field experiments in place of other research designs (e.g. lab experiments, survey experiments, observational studies, etc.). Given that field experiments necessarily take place in a specific geographic and political setting, there is a concern about extrapolating outcomes to formulate a general theory regarding the population of interest. However, researchers have begun to find strategies to effectively generalize causal effects outside of the sample by comparing the environments of the treated population and external population, accessing information from larger sample size, and accounting and modeling for treatment effects heterogeneity within the sample. Others have used covariate blocking techniques to generalize from field experiment populations to external populations. Noncompliance issues affecting field experiments (both one-sided and two-sided noncompliance) can occur when subjects who are assigned to a certain group never receive their assigned intervention. Other problems to data collection include attrition (where subjects who are treated do not provide outcome data) which, under certain conditions, will bias the collected data. These problems can lead to imprecise data analysis; however, researchers who use field experiments can use statistical methods in calculating useful information even when these difficulties occur. Using field experiments can


id: fisher-information-20260505-0
file: data/en.wikipedia.org/wiki/Fisher_information-0.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
In mathematical statistics, the Fisher information is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized and explored by the statistician Sir Ronald Fisher (following some initial results by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys' rule. It also appears as the large-sample covariance of the posterior distribution, provided that the prior is sufficiently smooth (a result known as Bernstein–von Mises theorem, which was anticipated by Laplace for exponential families). The same result is used when approximating the posterior with Laplace's approximation, where the Fisher information appears as the covariance of the fitted Gaussian. Statistical systems of a scientific nature (physical, biological, etc.) whose likelihood functions


id: fisher-information-20260505-1
file: data/en.wikipedia.org/wiki/Fisher_information-1.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
The partial derivative of f(X; θ) with respect to θ exists almost everywhere. (It can fail to exist on a null set, as long as this set does not depend on θ.) The integral of f(X; θ) can be differentiated under the integral sign with respect to θ. The support of f(X; θ) does not depend on θ. If θ is a vector then the regularity conditions must hold for every component of θ. It is easy to find an example of a density that does not satisfy the regularity conditions: The density of a Uniform(0, θ) variable fails to satisfy conditions 1 and 3. In this case, even though the Fisher information can be computed from the definition, it will not have the properties it is typically assumed to have. === In terms of likelihood === Because the likelihood of θ given X is always proportional to the probability f(X; θ), their logarithms necessarily differ by a constant that is independent of θ, and the derivatives of these logarithms with respect to θ are necessarily equal. Thus one can substitute in a log-likelihood l(θ; X) instead of log f(X; θ) in the definitions of Fisher Information. === Samples of


id: fisher-information-20260505-2
file: data/en.wikipedia.org/wiki/Fisher_information-2.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
In other words, the precision to which we can estimate θ is fundamentally limited by the Fisher information of the likelihood function. Alternatively, the same conclusion can be obtained directly from the Cauchy–Schwarz inequality for random variables, | Cov ⁡ ( A , B ) | 2 ≤ Var ⁡ ( A ) Var ⁡ ( B ) {\displaystyle |\operatorname {Cov} (A,B)|^{2}\leq \operatorname {Var} (A)\operatorname {Var} (B)} , applied to the random variables θ ^ ( X ) {\displaystyle {\hat {\theta }}(X)} and ∂ θ log ⁡ f ( X ; θ ) {\displaystyle \partial _{\theta }\log f(X;\theta )} , and observing that for unbiased estimators we have Cov ⁡ [ θ ^ ( X ) , ∂ θ log ⁡ f ( X ; θ ) ] = ∫ θ ^ ( x ) ∂ θ f ( x ; θ ) d x = ∂ θ E ⁡ [ θ ^ ] = 1. {\displaystyle \operatorname {Cov} [{\hat {\theta }}(X),\partial _{\theta }\log f(X;\theta )]=\int {\hat {\theta }}(x)\,\partial _{\theta }f(x;\theta )\,dx=\partial _{\theta }\operatorname {E} [{\hat {\theta }}]=1.} == Examples == === Single-parameter Bernoulli experiment === A Bernoulli trial is a random variable with two possible outcomes, 0 and 1,


id: fisher-information-20260505-3
file: data/en.wikipedia.org/wiki/Fisher_information-3.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
=== Estimate θ from X ~ Bern (√θ) === As another toy example consider a random variable X {\displaystyle X} with possible outcomes 0 and 1, with probabilities p 0 = 1 − θ {\displaystyle p_{0}=1-{\sqrt {\theta }}} and p 1 = θ {\displaystyle p_{1}={\sqrt {\theta }}} , respectively, for some θ ∈ [ 0 , 1 ] {\displaystyle \theta \in [0,1]} . Our goal is estimating θ {\displaystyle \theta } from observations of X {\displaystyle X} . The Fisher information reads in this case I ( θ ) = E [ ( ∂ ∂ θ log ⁡ f ( X ; θ ) ) 2 | θ ] = ( 1 − θ ) ( − 1 2 θ ( 1 − θ ) ) 2 + θ ( 1 2 θ ) 2 = 1 4 θ ( 1 1 − θ + 1 θ ) . {\displaystyle {\begin{aligned}{\mathcal {I}}(\theta )&=\mathrm {E} \left[\left({\frac {\partial }{\partial \theta }}\log f(X;\theta )\right)^{2}{\Bigg |}\,\theta \right]\\&=(1-{\sqrt {\theta }})\left({\frac {-1}{2{\sqrt {\theta }}(1-{\sqrt {\theta }})}}\right)^{2}+{\sqrt {\theta }}\left({\frac {1}{2\theta }}\right)^{2}\\&={\frac {1}{4\theta }}\left({\frac {1}{1-{\sqrt {\theta }}}}+{\frac {1}{\sqrt {\theta }}}\right)\end{aligned}}.} This expression can also be derived directly from the change of reparametrization formula given below. More generally, for


id: fisher-information-20260505-4
file: data/en.wikipedia.org/wiki/Fisher_information-4.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
=== Multivariate normal distribution === The FIM for a N-variate multivariate normal distribution, X ∼ N ( μ ( θ ) , Σ ( θ ) ) {\displaystyle \,X\sim N\left(\mu (\theta ),\,\Sigma (\theta )\right)} has a special form. Let the K-dimensional vector of parameters be θ = [ θ 1 … θ K ] T {\displaystyle \theta ={\begin{bmatrix}\theta _{1}&\dots &\theta _{K}\end{bmatrix}}^{\textsf {T}}} and the vector of normal random variables be X = [ X 1 … X N ] T {\displaystyle X={\begin{bmatrix}X_{1}&\dots &X_{N}\end{bmatrix}}^{\textsf {T}}} . Assume that the mean values of these random variables are μ ( θ ) = [ μ 1 ( θ ) … μ N ( θ ) ] T {\displaystyle \,\mu (\theta )={\begin{bmatrix}\mu _{1}(\theta )&\dots &\mu _{N}(\theta )\end{bmatrix}}^{\textsf {T}}} , and let Σ ( θ ) {\displaystyle \,\Sigma (\theta )} be the covariance matrix. Then, for 1 ≤ m , n ≤ K {\displaystyle 1\leq m,\,n\leq K} , the (m, n) entry of the FIM is: I m , n = ∂ μ T ∂ θ m Σ − 1 ∂ μ ∂ θ n + 1 2 tr ⁡ ( Σ − 1 ∂ Σ ∂ θ m Σ − 1 ∂ Σ ∂


id: fisher-information-20260505-5
file: data/en.wikipedia.org/wiki/Fisher_information-5.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
Given a convex function f : [ 0 , ∞ ) → ( − ∞ , ∞ ] {\displaystyle f:[0,\infty )\to (-\infty ,\infty ]} that f ( x ) {\displaystyle f(x)} is finite for all x > 0 {\displaystyle x>0} , f ( 1 ) = 0 {\displaystyle f(1)=0} , and f ( 0 ) = lim t → 0 + f ( t ) {\displaystyle f(0)=\lim _{t\to 0^{+}}f(t)} , (which could be infinite), it defines an f-divergence D f {\displaystyle D_{f}} . Then if f {\displaystyle f} is strictly convex at 1 {\displaystyle 1} , then locally at θ ∈ Θ {\displaystyle \theta \in \Theta } , the Fisher information matrix is a metric, in the sense that ( δ θ ) T I ( θ ) ( δ θ ) = 1 f ″ ( 1 ) D f ( P θ + δ θ ∥ P θ ) {\displaystyle (\delta \theta )^{T}I(\theta )(\delta \theta )={\frac {1}{f''(1)}}D_{f}(P_{\theta +\delta \theta }\parallel P_{\theta })} where P θ {\displaystyle P_{\theta }} is the distribution parametrized by θ {\displaystyle \theta } . That is, it's the distribution with pdf f ( x ; θ ) {\displaystyle f(x;\theta )} . In this form,


id: fisher-information-20260505-6
file: data/en.wikipedia.org/wiki/Fisher_information-6.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
where Z ε {\displaystyle Z_{\varepsilon }} is a Gaussian variable with covariance matrix ε I {\displaystyle \varepsilon I} . The name "surface area" is apt because the entropy power e H ( X ) {\displaystyle e^{H(X)}} is the volume of the "effective support set", so S ( X ) {\displaystyle S(X)} is the "derivative" of the volume of the effective support set, much like the Minkowski-Steiner formula. The remainder of the proof uses the entropy power inequality, which is like the Brunn–Minkowski inequality. The trace of the Fisher information matrix is found to be a factor of S ( X ) {\displaystyle S(X)} . == Applications == === Optimal design of experiments === Fisher information is widely used in optimal experimental design. Because of the reciprocity of estimator-variance and Fisher information, minimizing the variance corresponds to maximizing the information. When the linear (or linearized) statistical model has several parameters, the mean of the parameter estimator is a vector and its variance is a matrix. The inverse of the variance matrix is called the "information matrix". Because the variance of the estimator of a parameter vector is a matrix, the problem of "minimizing the variance" is complicated. Using statistical theory, statisticians


id: fisher-information-20260505-7
file: data/en.wikipedia.org/wiki/Fisher_information-7.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
Thus the Fisher information represents the curvature of the relative entropy of a conditional distribution with respect to its parameters. == History == The Fisher information was discussed by several early statisticians, notably F. Y. Edgeworth. For example, Savage says: "In it [Fisher information], he [Fisher] was to some extent anticipated (Edgeworth 1908–9 esp. 502, 507–8, 662, 677–8, 82–5 and references he [Edgeworth] cites including Pearson and Filon 1898 [. . .])." There are a number of early historical sources and a number of reviews of this early work. == See also == Efficiency (statistics) Observed information Fisher information metric Formation matrix Information geometry Jeffreys prior Cramér–Rao bound Minimum Fisher information Quantum Fisher information White information matrix test Other measures employed in information theory: Entropy (information theory) Kullback–Leibler divergence Self-information == Notes == == References == Cramér, Harald (1946). Mathematical methods of statistics. Princeton mathematical series. Princeton: Princeton University Press. ISBN 0-691-08004-6. {{cite book}}: ISBN / Date incompatibility (help) Edgeworth, F. Y. (Jun 1908). "On the Probable Errors of Frequency-Constants". Journal of the Royal Statistical Society. 71 (2): 381–397. doi:10.2307/2339461. JSTOR 2339461. Edgeworth, F. Y. (Sep 1908). "On the Probable Errors of Frequency-Constants (Contd.)". Journal of the Royal Statistical Society.


id: fisher-s-inequality-20260505-0
file: data/en.wikipedia.org/wiki/Fisher's_inequality-0.md
category: reference
title: Fisher's inequality
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher's_inequality
date_saved: 2026-05-05T09:50:16.972104+00:00
instance: kb-cron
parent: fisher-s-inequality-20260505-0
summary:
Fisher's inequality is a necessary condition for the existence of a balanced incomplete block design, that is, a system of subsets that satisfy certain prescribed conditions in combinatorial mathematics. Outlined by Ronald Fisher, a population geneticist and statistician, who was concerned with the design of experiments such as studying the differences among several different varieties of plants, under each of a number of different growing conditions, called blocks. Let: v be the number of varieties of plants; b be the number of blocks. To be a balanced incomplete block design it is required that: k different varieties are in each block, 1 ≤ k < v; no variety occurs twice in any one block; any two varieties occur together in exactly λ blocks; each variety occurs in exactly r blocks. Fisher's inequality states simply that b ≥ v. == Proof == Let the incidence matrix M be a v × b matrix defined so that Mi,j is 1 if element i is in block j and 0 otherwise. Then B = MMT is a v × v matrix such that Bi,i = r and Bi,j = λ for i ≠ j. Since r ≠ λ, det(B) ≠ 0, so rank(B)


id: fractional-factorial-design-20260505-0
file: data/en.wikipedia.org/wiki/Fractional_factorial_design-0.md
category: reference
title: Fractional factorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fractional_factorial_design
date_saved: 2026-05-05T09:50:18.197962+00:00
instance: kb-cron
parent: fractional-factorial-design-20260505-0
summary:
In statistics, a fractional factorial design is a way to conduct experiments with fewer experimental runs than a full factorial design. Instead of testing every single combination of factors, it tests only a carefully selected portion. This "fraction" of the full design is chosen to reveal the most important information about the system being studied (sparsity-of-effects principle), while significantly reducing the number of runs required. It is based on the idea that many tests in a full factorial design can be redundant. However, this reduction in runs comes at the cost of potentially more complex analysis, as some effects can become intertwined, making it impossible to isolate their individual influences. Therefore, choosing which combinations to test in a fractional factorial design must be done carefully. == History == Fractional factorial design was introduced by British statistician David John Finney in 1945, extending previous work by Ronald Fisher on the full factorial experiment at Rothamsted Experimental Station. Developed originally for agricultural applications, it has since been applied to other areas of engineering, science, and business. == Basic working principle == Similar to a full factorial experiment, a fractional factorial experiment investigates the effects of independent variables, known as factors, on a


id: fractional-factorial-design-20260505-1
file: data/en.wikipedia.org/wiki/Fractional_factorial_design-1.md
category: reference
title: Fractional factorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fractional_factorial_design
date_saved: 2026-05-05T09:50:18.197962+00:00
instance: kb-cron
parent: fractional-factorial-design-20260505-0
summary:
== Generation == In practice, experimenters typically rely on statistical reference books to supply the "standard" fractional factorial designs, consisting of the principal fraction. The principal fraction is the set of treatment combinations for which the generators evaluate to + under the treatment combination algebra. However, in some situations, experimenters may take it upon themselves to generate their own fractional design. A fractional factorial experiment is generated from a full factorial experiment by choosing an alias structure. The alias structure determines which effects are confounded with each other. For example, the five-factor 25 − 2 can be generated by using a full three-factor factorial experiment involving three factors (say A, B, and C) and then choosing to confound the two remaining factors D and E with interactions generated by D = A*B and E = A*C. These two expressions are called the generators of the design. So for example, when the experiment is run and the experimenter estimates the effects for factor D, what is really being estimated is a combination of the main effect of D and the two-factor interaction involving A and B. An important characteristic of a fractional design is the defining relation, which gives the set


id: generalized-randomized-block-design-20260505-0
file: data/en.wikipedia.org/wiki/Generalized_randomized_block_design-0.md
category: reference
title: Generalized randomized block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Generalized_randomized_block_design
date_saved: 2026-05-05T09:50:19.398918+00:00
instance: kb-cron
parent: generalized-randomized-block-design-20260505-0
summary:
In randomized statistical experiments, generalized randomized block designs (GRBDs) are used to study the interaction between blocks and treatments. For a GRBD, each treatment is replicated at least two times in each block; this replication allows the estimation and testing of an interaction term in the linear model (without making parametric assumptions about a normal distribution for the error). == Univariate response == === GRBDs versus RCBDs: Replication and interaction === Like a randomized complete block design (RCBD), a GRBD is randomized. Within each block, treatments are randomly assigned to experimental units: this randomization is also independent between blocks. In a (classic) RCBD, however, there is no replication of treatments within blocks. === Two-way linear model: Blocks and treatments === The experimental design guides the formulation of an appropriate linear model. Without replication, the (classic) RCBD has a two-way linear-model with treatment- and block-effects but without a block-treatment interaction. Without replicates, this two-way linear-model that may be estimated and tested without making parametric assumptions (by using the randomization distribution, without using a normal distribution for the error). In the RCBD, the block-treatment interaction cannot be estimated using the randomization distribution; a fortiori there exists no "valid" (i.e. randomization-based) test for


id: gittins-index-20260505-0
file: data/en.wikipedia.org/wiki/Gittins_index-0.md
category: reference
title: Gittins index
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gittins_index
date_saved: 2026-05-05T09:50:20.644914+00:00
instance: kb-cron
parent: gittins-index-20260505-0
summary:
The Gittins index is a measure of the reward that can be achieved through a given stochastic process with certain properties, namely: the process has an ultimate termination state and evolves with an option, at each intermediate state, of terminating. Upon terminating at a given state, the reward achieved is the sum of the probabilistic expected rewards associated with every state from the actual terminating state to the ultimate terminal state, inclusive. The index is a real scalar. == Terminology == To illustrate the theory we can take two examples from a developing sector, such as from electricity generating technologies: wind power and wave power. If we are presented with the two technologies when they are both proposed as ideas we cannot say which will be better in the long run as we have no data, as yet, to base our judgments on. It would be easy to say that wave power would be too problematic to develop as it seems easier to put up many wind turbines than to make the long floating generators, tow them out to sea and lay the cables necessary. If we were to make a judgment call at that early time in development we


id: gittins-index-20260505-1
file: data/en.wikipedia.org/wiki/Gittins_index-1.md
category: reference
title: Gittins index
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gittins_index
date_saved: 2026-05-05T09:50:20.644914+00:00
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parent: gittins-index-20260505-0
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== History == Questions about the optimal stopping policies in the context of clinical trials have been open from the 1940s and in the 1960s a few authors analyzed simple models leading to optimal index policies, but it was only in the 1970s that Gittins and his collaborators demonstrated in a Markovian framework that the optimal solution of the general case is an index policy whose "dynamic allocation index" is computable in principle for every state of each project as a function of the single project's dynamics. In parallel to Gittins, Martin Weitzman established the same result in the economics literature. Soon after the seminal paper of Gittins, Peter Whittle demonstrated that the index emerges as a Lagrange multiplier from a dynamic programming formulation of the problem called retirement process and conjectured that the same index would be a good heuristic in a more general setup named Restless bandit. The question of how to actually calculate the index for Markov chains was first addressed by Varaiya and his collaborators with an algorithm that computes the indexes from the largest first down to the smallest and by Chen and Katehakis who showed that standard LP could be used to calculate the


id: gittins-index-20260505-2
file: data/en.wikipedia.org/wiki/Gittins_index-2.md
category: reference
title: Gittins index
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gittins_index
date_saved: 2026-05-05T09:50:20.644914+00:00
instance: kb-cron
parent: gittins-index-20260505-0
summary:
=== Generalized index === If the probability of survival β ( i ) {\displaystyle \beta (i)} depends on the state i {\displaystyle i} , a generalization introduced by Sonin (2008) defines the Gittins index α ( i ) {\displaystyle \alpha (i)} as the maximum discounted total reward per chance of termination. α ( i ) = sup τ > 0 R τ ( i ) Q τ ( i ) {\displaystyle \alpha (i)=\sup _{\tau >0}{\frac {R^{\tau }(i)}{Q^{\tau }(i)}}} where R τ ( i ) = ⟨ ∑ t = 0 τ − 1 R [ Z ( t ) ] ⟩ Z ( 0 ) = i {\displaystyle R^{\tau }(i)=\left\langle \sum _{t=0}^{\tau -1}R[Z(t)]\right\rangle _{Z(0)=i}} Q τ ( i ) = ⟨ 1 − ∏ t = 0 τ − 1 β [ Z ( t ) ] ⟩ Z ( 0 ) = i {\displaystyle Q^{\tau }(i)=\left\langle 1-\prod _{t=0}^{\tau -1}\beta [Z(t)]\right\rangle _{Z(0)=i}} If β t {\displaystyle \beta ^{t}} is replaced by ∏ j = 0 t − 1 β [ Z ( j ) ] {\displaystyle \prod _{j=0}^{t-1}\beta [Z(j)]} in the definitions of ν ( i ) {\displaystyle \nu (i)} , w ( i ) {\displaystyle w(i)} and h (


id: glossary-of-experimental-design-20260505-0
file: data/en.wikipedia.org/wiki/Glossary_of_experimental_design-0.md
category: reference
title: Glossary of experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Glossary_of_experimental_design
date_saved: 2026-05-05T09:50:21.948791+00:00
instance: kb-cron
parent: glossary-of-experimental-design-20260505-0
summary:
A glossary of terms used in experimental research. == Concerned fields == Statistics Experimental design Estimation theory


id: glossary-of-experimental-design-20260505-1
file: data/en.wikipedia.org/wiki/Glossary_of_experimental_design-1.md
category: reference
title: Glossary of experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Glossary_of_experimental_design
date_saved: 2026-05-05T09:50:21.948791+00:00
instance: kb-cron
parent: glossary-of-experimental-design-20260505-0
summary:
== Glossary == Alias: When the estimate of an effect also includes the influence of one or more other effects (usually high order interactions) the effects are said to be aliased (see confounding). For example, if the estimate of effect D in a four factor experiment actually estimates (D + ABC), then the main effect D is aliased with the 3-way interaction ABC. Note: This causes no difficulty when the higher order interaction is either non-existent or insignificant. Analysis of variance (ANOVA): A mathematical process for separating the variability of a group of observations into assignable causes and setting up various significance tests. Balanced design: An experimental design where all cells (i.e. treatment combinations) have the same number of observations. Blocking: A schedule for conducting treatment combinations in an experimental study such that any effects on the experimental results due to a known change in raw materials, operators, machines, etc., become concentrated in the levels of the blocking variable. Note: the reason for blocking is to isolate a systematic effect and prevent it from obscuring the main effects. Blocking is achieved by restricting randomization. Center Points: Points at the center value of all factor ranges. Coding Factor Levels: Transforming the


id: glossary-of-experimental-design-20260505-2
file: data/en.wikipedia.org/wiki/Glossary_of_experimental_design-2.md
category: reference
title: Glossary of experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Glossary_of_experimental_design
date_saved: 2026-05-05T09:50:21.948791+00:00
instance: kb-cron
parent: glossary-of-experimental-design-20260505-0
summary:
Lack of fit error: Error that occurs when the analysis omits one or more important terms or factors from the process model. Note: Including replication in a designed experiment allows separation of experimental error into its components: lack of fit and random (pure) error. Model: Mathematical relationship which relates changes in a given response to changes in one or more factors. Nested Factors: See factors above. Orthogonality: Two vectors of the same length are orthogonal if the sum of the products of their corresponding elements is 0. Note: An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors. Paradigm: a model created given the basic design, the hypothesis and the particular conditions for the experiment. Random effect: An effect associated with input variables chosen at random from a population having a large or infinite number of possible values. Random error: Error that occurs due to natural variation in the process. Note: Random error is typically assumed to be normally distributed with zero mean and a constant variance. Note: Random error is also called experimental error. Randomization: A schedule for allocating treatment material and for conducting treatment combinations


id: group-testing-20260505-0
file: data/en.wikipedia.org/wiki/Group_testing-0.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
In statistics and combinatorial mathematics, group testing is any procedure that breaks up the task of identifying objects into tests on groups of items, rather than testing each item individually. First studied by Robert Dorfman in 1943, group testing is a relatively new field of mathematics that can be applied to a wide range of practical applications and is an active area of research today. A familiar example of group testing involves a string of light bulbs connected in series, where exactly one of the bulbs is known to be broken. The objective is to find the broken bulb using the smallest number of tests (where a test is when some of the bulbs are connected to a power supply). A simple approach is to test each bulb individually. However, when there are a large number of bulbs it would be much more efficient to pool the bulbs into groups. For example, by connecting the first half of the bulbs at once, it can be determined which half the broken bulb is in, ruling out half of the bulbs in just one test. Schemes for carrying out group testing can be simple or complex and the tests involved at each


id: group-testing-20260505-1
file: data/en.wikipedia.org/wiki/Group_testing-1.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
=== Variations and extensions === There are many ways to extend the problem of group testing. One of the most important is called noisy group testing, and deals with a big assumption of the original problem: that testing is error-free. A group-testing problem is called noisy when there is some chance that the result of a group test is erroneous (e.g. comes out positive when the test contained no defectives). The Bernoulli noise model assumes this probability is some constant, q {\displaystyle q} , but in general it can depend on the true number of defectives in the test and the number of items tested. For example, the effect of dilution can be modelled by saying a positive result is more likely when there are more defectives (or more defectives as a fraction of the number tested), present in the test. A noisy algorithm will always have a non-zero probability of making an error (that is, mislabeling an item). Group testing can be extended by considering scenarios in which there are more than two possible outcomes of a test. For example, a test may have the outcomes 0 , 1 {\displaystyle 0,1} and 2 + {\displaystyle 2^{+}} , corresponding to


id: group-testing-20260505-2
file: data/en.wikipedia.org/wiki/Group_testing-2.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
=== Combinatorial group testing === Group testing was first studied in the combinatorial context by Li in 1962, with the introduction of Li’s s {\displaystyle s} -stage algorithm. Li proposed an extension of Dorfman's '2-stage algorithm' to an arbitrary number of stages that required no more than t = e log 2 ⁡ ( e ) d log 2 ⁡ ( n ) {\textstyle t={\frac {e}{\log _{2}(e)}}d\log _{2}(n)} tests to be guaranteed to find d {\displaystyle d} or fewer defectives among n {\displaystyle n} items. The idea was to remove all the items in negative tests, and divide the remaining items into groups as was done with the initial pool. This was to be done s − 1 {\displaystyle s-1} times before performing individual testing. Combinatorial group testing in general was later studied more fully by Katona in 1973. Katona introduced the matrix representation of non-adaptive group-testing and produced a procedure for finding the defective in the non-adaptive 1-defective case in no more than t = ⌈ log 2 ⁡ ( n ) ⌉ {\displaystyle t=\lceil \log _{2}(n)\rceil } tests, which he also proved to be optimal. In general, finding optimal algorithms for adaptive combinatorial group testing is difficult, and


id: group-testing-20260505-3
file: data/en.wikipedia.org/wiki/Group_testing-3.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
x {\displaystyle \mathbf {x} } is intended to describe the (unknown) set of defective items. The key property of x {\displaystyle \mathbf {x} } is that it is an implicit input. That is to say, there is no direct knowledge of what the entries of x {\displaystyle \mathbf {x} } are, other than that which can be inferred via some series of 'tests'. This leads on to the next definition. Let x {\displaystyle \mathbf {x} } be an input vector. A set, S ⊆ { 1 , 2 , … , n } {\displaystyle S\subseteq \{1,2,\dots ,n\}} is called a test. When testing is noiseless, the result of a test is positive when there exists j ∈ S {\displaystyle j\in S} such that x j = 1 {\displaystyle x_{j}=1} , and the result is negative otherwise. Therefore, the goal of group testing is to come up with a method for choosing a 'short' series of tests that allow x {\displaystyle \mathbf {x} } to be determined, either exactly or with a high degree of certainty. A group-testing algorithm is said to make an error if it incorrectly labels an item (that is, labels any defective item as non-defective or vice


id: group-testing-20260505-4
file: data/en.wikipedia.org/wiki/Group_testing-4.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
Suppose a non-adaptive group testing procedure for n {\displaystyle n} items consists of the tests S 1 , S 2 , … , S t {\displaystyle S_{1},S_{2},\dots ,S_{t}} for some t ∈ N ≥ 0 {\displaystyle t\in \mathbb {N} _{\geq 0}} . The testing matrix for this scheme is the t × n {\displaystyle t\times n} binary matrix, M {\displaystyle M} , where ( M ) i j = 1 {\displaystyle (M)_{ij}=1} if and only if j ∈ S i {\displaystyle j\in S_{i}} (and is zero otherwise). Thus each column of M {\displaystyle M} represents an item and each row represents a test, with a 1 {\displaystyle 1} in the ( i , j ) -th {\displaystyle (i,j){\textrm {-th}}} entry indicating that the i -th {\displaystyle i{\textrm {-th}}} test included the j -th {\displaystyle j{\textrm {-th}}} item and a 0 {\displaystyle 0} indicating otherwise. As well as the vector x {\displaystyle \mathbf {x} } (of length n {\displaystyle n} ) that describes the unknown defective set, it is common to introduce the result vector, which describes the results of each test. Let t {\displaystyle t} be the number of tests performed by a non-adaptive algorithm. The result vector, y =


id: group-testing-20260505-5
file: data/en.wikipedia.org/wiki/Group_testing-5.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
If n ≤ 2 d − 2 {\displaystyle n\leq 2d-2} , test the n {\displaystyle n} items individually. Otherwise, set l = n − d + 1 {\displaystyle l=n-d+1} and α = ⌊ log 2 ⁡ l / d ⌋ {\displaystyle \alpha =\lfloor \log _{2}{l/d}\rfloor } . Test a group of size 2 α {\displaystyle 2^{\alpha }} . If the outcome is negative, every item in the group is declared to be non-defective; set n := n − 2 α {\displaystyle n:=n-2^{\alpha }} and go to step 1. Otherwise, use a binary search to identify one defective and an unspecified number, called x {\displaystyle x} , of non-defective items; set n := n − 1 − x {\displaystyle n:=n-1-x} and d := d − 1 {\displaystyle d:=d-1} . Go to step 1. The generalised binary-splitting algorithm requires no more than T {\displaystyle T} tests where T = { n n ≤ 2 d − 2 ( α + 2 ) d + p − 1 n ≥ 2 d − 1 {\displaystyle T={\begin{cases}n&n\leq 2d-2\\(\alpha +2)d+p-1&n\geq 2d-1\end{cases}}} . For n / d {\displaystyle n/d} large, it can be shown that T → d log 2 ⁡ ( n / d )


id: group-testing-20260505-6
file: data/en.wikipedia.org/wiki/Group_testing-6.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
=== Sequential COMP (SCOMP) === SCOMP (Sequential COMP) is an algorithm that makes use of the fact that DD makes no mistakes until the last step, where it is assumed that the remaining items are non-defective. Let the set of declared defectives be K {\displaystyle K} . A positive test is called explained by K {\displaystyle K} if it contains at least one item in K {\displaystyle K} . The key observation with SCOMP is that the set of defectives found by DD may not explain every positive test, and that every unexplained test must contain a hidden defective. The algorithm proceeds as follows. Carry out steps 1 and 2 of the DD algorithm to obtain K {\displaystyle K} , an initial estimate for the set of defectives. If K {\displaystyle K} explains every positive test, terminate the algorithm: K {\displaystyle K} is the final estimate for the set of defectives. If there are any unexplained tests, find the "possible defective" that appears in the largest number of unexplained tests, and declare it to be defective (that is, add it to the set K {\displaystyle K} ). Go to step 2. In simulations, SCOMP has been shown to perform close


id: group-testing-20260505-7
file: data/en.wikipedia.org/wiki/Group_testing-7.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
This method uses q ( c − 1 ) ( d + 1 ) {\displaystyle q(c-1)(d+1)} tests to exactly identify up to d {\displaystyle d} positives among n = q c {\displaystyle n=q^{c}} samples. Because of this PP is particularly effective for large sample sizes, since the number of tests grows only linearly with respect to c {\displaystyle c} while the samples grow exponentially with this parameter. However PP can also be effective for small sample sizes. == Example applications == The generality of the theory of group testing lends it to many diverse applications, including clone screening, locating electrical shorts; high speed computer networks; medical examination, quantity searching, statistics; machine learning, DNA sequencing; cryptography; and data forensics. This section provides a brief overview of a small selection of these applications. === Multiaccess channels === A multiaccess channel is a communication channel that connects many users at once. Every user can listen and transmit on the channel, but if more than one user transmits at the same time, the signals collide, and are reduced to unintelligible noise. Multiaccess channels are important for various real-world applications, notably wireless computer networks and phone networks. A prominent problem with multiaccess channels is how


id: group-testing-20260505-8
file: data/en.wikipedia.org/wiki/Group_testing-8.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
=== Machine learning and compressed sensing === Machine learning is a field of computer science that has many software applications such as DNA classification, fraud detection and targeted advertising. One of the main subfields of machine learning is the 'learning by examples' problem, where the task is to approximate some unknown function when given its value at a number of specific points. As outlined in this section, this function learning problem can be tackled with a group-testing approach. In a simple version of the problem, there is some unknown function, f : { 0 , 1 } N → { 0 , 1 } {\displaystyle f:\{0,1\}^{N}\to \{0,1\}} where f ( x ) = a ⋅ x {\displaystyle f({\textbf {x}})={\textbf {a}}\cdot {\textbf {x}}} , and a ∈ { 0 , 1 } N {\displaystyle {\textbf {a}}\in \{0,1\}^{N}} (using logical arithmetic: addition is logical OR and multiplication is logical AND). Here a {\displaystyle {\textbf {a}}} is ' d {\displaystyle d} sparse', which means that at most d ≪ N {\displaystyle d\ll N} of its entries are 1 {\displaystyle 1} . The aim is to construct an approximation to f {\displaystyle f} using t {\displaystyle t} point evaluations, where t {\displaystyle t} is


id: group-testing-20260505-9
file: data/en.wikipedia.org/wiki/Group_testing-9.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
=== Data forensics === Data forensics is a field dedicated to finding methods for compiling digital evidence of a crime. Such crimes typically involve an adversary modifying the data, documents or databases of a victim, with examples including the altering of tax records, a virus hiding its presence, or an identity thief modifying personal data. A common tool in data forensics is the one-way cryptographic hash. This is a function that takes the data, and through a difficult-to-reverse procedure, produces a unique number called a hash. Hashes, which are often much shorter than the data, allow us to check if the data has been changed without having to wastefully store complete copies of the information: the hash for the current data can be compared with a past hash to determine if any changes have occurred. An unfortunate property of this method is that, although it is easy to tell if the data has been modified, there is no way of determining how: that is, it is impossible to recover which part of the data has changed. One way to get around this limitation is to store more hashes – now of subsets of the data structure – to narrow down


id: ignorability-20260505-0
file: data/en.wikipedia.org/wiki/Ignorability-0.md
category: reference
title: Ignorability
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ignorability
date_saved: 2026-05-05T09:50:24.772348+00:00
instance: kb-cron
parent: ignorability-20260505-0
summary:
In statistics, ignorability is a feature of an experiment design whereby the method of data collection (and the nature of missing data) does not depend on the missing data. A missing data mechanism such as a treatment assignment or survey sampling strategy is "ignorable" if the missing data matrix, which indicates which variables are observed or missing, is independent of the missing data conditional on the observed data. It has also been called unconfoundedness, selection on the observables, or no omitted variable bias. This idea is part of the Rubin Causal Inference Model, developed by Donald Rubin in collaboration with Paul Rosenbaum in the early 1970s. The exact definition differs between their articles in that period. In a 1978 article, Rubin discusses ignorable assignment mechanisms, which can be understood as the way individuals are assigned to treatment groups being irrelevant for the data analysis, given everything that is recorded about that individual. In a 1983 paper on propensity score matching, Rubin and Rosenbaum define the stronger condition of a treatment assignment being strongly ignorable, mathematically formulated as ( r 1 , r 0 ) ⊥ ⊥ z ∣ v , 0 < pr ⁡ ( z = 1 ) <


id: institutional-review-board-20260505-0
file: data/en.wikipedia.org/wiki/Institutional_review_board-0.md
category: reference
title: Institutional review board
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Institutional_review_board
date_saved: 2026-05-05T09:50:26.001945+00:00
instance: kb-cron
parent: institutional-review-board-20260505-0
summary:
An institutional review board (IRB), also known as an independent ethics committee (IEC), ethical review board (ERB), or research ethics board (REB), is a committee at an institution that applies research ethics by reviewing the methods proposed for research involving human subjects, to ensure that the projects are ethical. The main goal of IRB reviews is to ensure that study participants are not harmed (or that harms are minimal and outweighed by research benefits). Such boards are formally designated to approve (or reject), monitor, and review biomedical and behavioral research involving humans, and they are legally required in some countries under certain specified circumstances. Most countries use some form of IRB to safeguard ethical conduct of research so that it complies with national and international norms, regulations or codes. The purpose of the IRB is to assure that appropriate steps are taken to protect the rights and welfare of people participating in a research study. A key goal of IRBs is to protect human subjects from physical or psychological harm, which they attempt to do by reviewing research protocols and related materials. The protocol review assesses the ethics of the research and its methods, promotes fully informed and voluntary participation


id: institutional-review-board-20260505-1
file: data/en.wikipedia.org/wiki/Institutional_review_board-1.md
category: reference
title: Institutional review board
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Institutional_review_board
date_saved: 2026-05-05T09:50:26.001945+00:00
instance: kb-cron
parent: institutional-review-board-20260505-0
summary:
Research in conventional educational settings, such as those involving the study of instructional strategies or effectiveness of various techniques, curricula, or classroom management methods. In the case of studies involving the use of educational tests, there are specific provisions in the exemption to ensure that subjects cannot be identified or exposed to risks or liabilities. Research involving the analysis of existing data and other materials, where the data is either already publicly available or will be analyzed such that individual subjects cannot be identified. Studies intended to assess the performance or effectiveness of public benefit or service programs, or to evaluate food taste, quality, or consumer acceptance. Generally, human research ethics guidelines require that decisions about exemption are made by an IRB representative, not by the investigators themselves. Additionally, research projects conducted outside of a federal government agency or government-funded institution, such as a citizen science project conducted by a private individual or a group of private individuals, are generally not required to be approved by any institutional review board, unless the project is funded by the US federal government. == International ethics review committees == Numerous other countries have equivalent regulations or guidelines governing human subject studies and the


id: institutional-review-board-20260505-2
file: data/en.wikipedia.org/wiki/Institutional_review_board-2.md
category: reference
title: Institutional review board
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Institutional_review_board
date_saved: 2026-05-05T09:50:26.001945+00:00
instance: kb-cron
parent: institutional-review-board-20260505-0
summary:
Safeguard the rights, safety, and well-being of all trial subjects. Special attention should be paid to trials that may include vulnerable subjects, such as pregnant women, children, prisoners, the elderly, or persons with diminished comprehension. Obtain trial protocol(s)/amendment(s), written Informed Consent Form(s) (ICFs) and consent form updates the investigator proposes for use in the trial, subject recruitment procedures (e.g., advertisements), written information to be provided to subjects, investigator's brochure, available safety information, information about payments and compensation available to subjects, the investigator's current curriculum vitae and/or other documentation evidencing qualifications, and any other documents the IRB may need to fulfill its responsibilities. Review both the amount and method of payment to subjects to assure neither presents problems of coercion or undue influence on the trial subjects. Payments to a subject should be prorated and not wholly contingent on completion of the trial by the subject. Information regarding payment to subjects, including the methods, amounts, and schedule of payment to trial subjects, should be set forth in the written informed consent form and any other written information to be provided to subjects. The way payment will be prorated should be specified. Ensure that the proposed trial is reviewed within a reasonable


id: institutional-review-board-20260505-3
file: data/en.wikipedia.org/wiki/Institutional_review_board-3.md
category: reference
title: Institutional review board
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Institutional_review_board
date_saved: 2026-05-05T09:50:26.001945+00:00
instance: kb-cron
parent: institutional-review-board-20260505-0
summary:
== Relationship with citizen science == Generally speaking, citizen science, whether conducted by a single private individual or a group of individuals, is not required to follow the IRB process. This is true even if some of the individuals involved are professional researchers or are also employed at institutions that normally review all research conducted by the institution. However, many academic journals require proof of IRB approval for all human-subject research, even when it is not legally required, which means that citizen scientists may be unable to publish scientific papers describing their findings. Citizen scientists who expect to need IRB approval for publication or to comply with the terms of a research grant can pay a commercial IRB company. In the US, a standard initial review often costs a few thousand dollars; a review to determine that the project is less expensive. The IRB-based approach to ethics assumes that human-subject research is conducted by an institution employing researchers, and that the institution and researchers have far more power and knowledge than the participants. The researchers and the participants are seen as distinct groups, and the concern is to prevent the researchers from exploiting the participants as a means to an


id: interaction-statistics-20260505-0
file: data/en.wikipedia.org/wiki/Interaction_(statistics)-0.md
category: reference
title: Interaction (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Interaction_(statistics)
date_saved: 2026-05-05T09:50:27.222240+00:00
instance: kb-cron
parent: interaction-statistics-20260505-0
summary:
In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive). Although commonly thought of in terms of causal relationships, the concept of an interaction can also describe non-causal associations (then also called moderation or effect modification). Interactions are often considered in the context of regression analyses or factorial experiments. The presence of interactions can have important implications for the interpretation of statistical models. If two variables of interest interact, the relationship between each of the interacting variables and a third "dependent variable" depends on the value of the other interacting variable. In practice, this makes it more difficult to predict the consequences of changing the value of a variable, particularly if the variables it interacts with are hard to measure or difficult to control. The notion of "interaction" is closely related to that of moderation that is common in social and health science research: the interaction between an explanatory variable and an environmental variable suggests that the effect of the


id: interaction-statistics-20260505-1
file: data/en.wikipedia.org/wiki/Interaction_(statistics)-1.md
category: reference
title: Interaction (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Interaction_(statistics)
date_saved: 2026-05-05T09:50:27.222240+00:00
instance: kb-cron
parent: interaction-statistics-20260505-0
summary:
The distinction between qualitative and quantitative interactions depends on the order in which the variables are considered (in contrast, the property of additivity is invariant to the order of the variables). In the following table, if we focus on the effect of treatment A, there is a quantitative interaction — giving treatment A will improve the outcome on average regardless of whether treatment B is or is not already being given (although the benefit is greater if treatment A is given alone). However, if we focus on the effect of treatment B, there is a qualitative interaction — giving treatment B to a subject who is already receiving treatment A will (on average) make things worse, whereas giving treatment B to a subject who is not receiving treatment A will improve the outcome on average. === Unit treatment additivity === In its simplest form, the assumption of treatment unit additivity states that the observed response yij from experimental unit i when receiving treatment j can be written as the sum yij = yi + tj. The assumption of unit treatment additivity implies that every treatment has exactly the same additive effect on each experimental unit. Since any given experimental unit


id: interaction-statistics-20260505-2
file: data/en.wikipedia.org/wiki/Interaction_(statistics)-2.md
category: reference
title: Interaction (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Interaction_(statistics)
date_saved: 2026-05-05T09:50:27.222240+00:00
instance: kb-cron
parent: interaction-statistics-20260505-0
summary:
=== In regression === The most general approach to modeling interaction effects involves regression, starting from the elementary version given above: Y = c + a x 1 + b x 2 + d ( x 1 × x 2 ) + error {\displaystyle Y=c+ax_{1}+bx_{2}+d(x_{1}\times x_{2})+{\text{error}}\,} where the interaction term ( x 1 × x 2 ) {\displaystyle (x_{1}\times x_{2})} could be formed explicitly by multiplying two (or more) variables, or implicitly using factorial notation in modern statistical packages such as Stata. The components x1 and x2 might be measurements or {0,1} dummy variables in any combination. Interactions involving a dummy variable multiplied by a measurement variable are termed slope dummy variables, because they estimate and test the difference in slopes between groups 0 and 1. When measurement variables are employed in interactions, it is often desirable to work with centered versions, where the variable's mean (or some other reasonably central value) is set as zero. Centering can make the main effects in interaction models more interpretable, as it reduces the multicollinearity between the interaction term and the main effects. The coefficient a in the equation above, for example, represents the effect of x1 when x2 equals zero. Regression approaches


id: interaction-statistics-20260505-3
file: data/en.wikipedia.org/wiki/Interaction_(statistics)-3.md
category: reference
title: Interaction (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Interaction_(statistics)
date_saved: 2026-05-05T09:50:27.222240+00:00
instance: kb-cron
parent: interaction-statistics-20260505-0
summary:
Interaction between adding sugar to coffee and stirring the coffee. Neither of the two individual variables has much effect on sweetness but a combination of the two does. Interaction between adding carbon to steel and quenching. Neither of the two individually has much effect on strength but a combination of the two has a dramatic effect. Interaction between smoking and inhaling asbestos fibres: Both raise lung carcinoma risk, but exposure to asbestos multiplies the cancer risk in smokers and non-smokers. Here, the joint effect of inhaling asbestos and smoking is higher than the sum of both effects. Interaction between genetic risk factors for type 2 diabetes and diet (specifically, a "western" dietary pattern). The western dietary pattern was shown to increase diabetes risk for subjects with a high "genetic risk score", but not for other subjects. Interaction between education and political orientation, affecting general-public perceptions about climate change. For example, US surveys often find that acceptance of the reality of anthropogenic climate change rises with education among moderate or liberal survey respondents, but declines with education among the most conservative. Similar interactions have been observed to affect some non-climate science or environmental perceptions, and to operate with science literacy or


id: interrupted-time-series-20260505-0
file: data/en.wikipedia.org/wiki/Interrupted_time_series-0.md
category: reference
title: Interrupted time series
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Interrupted_time_series
date_saved: 2026-05-05T09:50:28.536522+00:00
instance: kb-cron
parent: interrupted-time-series-20260505-0
summary:
Interrupted time series analysis (ITS), sometimes known as quasi-experimental time series analysis, is a method of statistical analysis involving tracking a long-term period before and after a point of intervention to assess the intervention's effects. The time series refers to the data over the period, while the interruption is the intervention, which is a controlled external influence or set of influences. Effects of the intervention are evaluated by changes in the level and slope of the time series and statistical significance of the intervention parameters. Interrupted time series design is the design of experiments based on the interrupted time series approach. The method is used in various areas of research, such as: political science: impact of changes in laws on the behavior of people; (e.g., Effectiveness of sex offender registration policies in the United States) economics: impact of changes in credit controls on borrowing behavior; sociology: impact of experiments in income maintenance on the behavior of participants in welfare programs; history: impact of major historical events on the behavior of those affected by the events; psychology: impact of expressing emotional experiences on online content; medicine: in medical research, medical treatment is an intervention whose effect are to be studied; marketing


id: jadad-scale-20260505-0
file: data/en.wikipedia.org/wiki/Jadad_scale-0.md
category: reference
title: Jadad scale
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Jadad_scale
date_saved: 2026-05-05T09:50:29.828460+00:00
instance: kb-cron
parent: jadad-scale-20260505-0
summary:
The Jadad scale, sometimes known as Jadad scoring or the Oxford quality scoring system, is a procedure to assess the methodological quality of a clinical trial by objective criteria. It is named after Canadian-Colombian physician Alex Jadad who in 1996 described a system for allocating such trials a score of between zero (very poor) and five (rigorous). It is the most widely used such assessment in the world, and as of May 2024, its seminal paper has been cited in over 25,000 scientific works. == Description == The Jadad scale independently assesses the methodological quality of a clinical trial judging the effectiveness of blinding. Alejandro "Alex" Jadad Bechara, a Colombian physician who worked as a Research Fellow at the Oxford Pain Relief Unit, Nuffield Department of Anaesthetics at the University of Oxford described the allocating trials a score of between zero (very poor) and five (rigorous) in an appendix to a 1996 paper. In a 2007 book, Jadad described the randomised controlled trial as "one of the simplest, most powerful and revolutionary forms of research". == Background == Clinical trials are conducted for the purpose of collecting data on the efficacy of medical treatments. The treatment might be, for example,


id: lack-of-fit-sum-of-squares-20260505-0
file: data/en.wikipedia.org/wiki/Lack-of-fit_sum_of_squares-0.md
category: reference
title: Lack-of-fit sum of squares
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lack-of-fit_sum_of_squares
date_saved: 2026-05-05T09:50:31.030292+00:00
instance: kb-cron
parent: lack-of-fit-sum-of-squares-20260505-0
summary:
In statistics, a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well. The other component is the pure-error sum of squares. The pure-error sum of squares is the sum of squared deviations of each value of the dependent variable from the average value over all observations sharing its independent variable value(s). These are errors that could never be avoided by any predictive equation that assigned a predicted value for the dependent variable as a function of the value(s) of the independent variable(s). The remainder of the residual sum of squares is attributed to lack of fit of the model since it would be mathematically possible to eliminate these errors entirely. == Principle == In order for the lack-of-fit sum of squares to differ from the sum of squares of residuals, there must be more than one value of the response variable for at least one of the values of the set of predictor variables.


id: lack-of-fit-sum-of-squares-20260505-1
file: data/en.wikipedia.org/wiki/Lack-of-fit_sum_of_squares-1.md
category: reference
title: Lack-of-fit sum of squares
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lack-of-fit_sum_of_squares
date_saved: 2026-05-05T09:50:31.030292+00:00
instance: kb-cron
parent: lack-of-fit-sum-of-squares-20260505-0
summary:
=== Sums of squares === Suppose the error terms ε i j are independent and normally distributed with expected value 0 and variance σ2. We treat x i as constant rather than random. Then the response variables Y i j are random only because the errors ε i j are random. It can be shown to follow that if the straight-line model is correct, then the sum of squares due to error divided by the error variance, 1 σ 2 ∑ i = 1 n ∑ j = 1 n i ε ^ i j 2 {\displaystyle {\frac {1}{\sigma ^{2}}}\sum _{i=1}^{n}\sum _{j=1}^{n_{i}}{\widehat {\varepsilon }}_{ij}^{\,2}} has a chi-squared distribution with N − 2 degrees of freedom. Moreover, given the total number of observations N, the number of levels of the independent variable n, and the number of parameters in the model p: The sum of squares due to pure error, divided by the error variance σ2, has a chi-squared distribution with N − n degrees of freedom; The sum of squares due to lack of fit, divided by the error variance σ2, has a chi-squared distribution with n − p degrees of freedom (here p = 2 as there are two


id: latin-hypercube-sampling-20260505-0
file: data/en.wikipedia.org/wiki/Latin_hypercube_sampling-0.md
category: reference
title: Latin hypercube sampling
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Latin_hypercube_sampling
date_saved: 2026-05-05T09:50:33.795501+00:00
instance: kb-cron
parent: latin-hypercube-sampling-20260505-0
summary:
Latin hypercube sampling (LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution. The sampling method is often used to construct computer experiments or for Monte Carlo integration. LHS was described by Michael McKay of Los Alamos National Laboratory in 1979. An equivalent technique was independently proposed by Vilnis Eglājs in 1977. It was further elaborated by Ronald L. Iman and coauthors in 1981. Detailed computer codes and manuals were later published. In the context of statistical sampling, a square grid containing sample positions is a Latin square if (and only if) there is only one sample in each row and each column. A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned hyperplane containing it. When sampling a function of N {\displaystyle N} variables, the range of each variable is divided into M {\displaystyle M} equally probable intervals. M {\displaystyle M} sample points are then placed to satisfy the Latin hypercube requirements; this forces the number of divisions, M {\displaystyle M} , to be equal for each variable. This sampling scheme does not require more samples for


id: latin-rectangle-20260505-0
file: data/en.wikipedia.org/wiki/Latin_rectangle-0.md
category: reference
title: Latin rectangle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Latin_rectangle
date_saved: 2026-05-05T09:50:34.999456+00:00
instance: kb-cron
parent: latin-rectangle-20260505-0
summary:
In combinatorial mathematics, a Latin rectangle is an r × n matrix (where r ≤ n), using n symbols, usually the numbers 1, 2, 3, ..., n or 0, 1, ..., n − 1 as its entries, with no number occurring more than once in any row or column. An n × n Latin rectangle is called a Latin square. Latin rectangles and Latin squares may also be described as the optimal colorings of rook's graphs, or as optimal edge colorings of complete bipartite graphs. An example of a 3 × 5 Latin rectangle is: == Normalization == A Latin rectangle is called normalized (or reduced) if its first row is in natural order and so is its first column. The example above is not normalized. == Enumeration == Let L(k, n) denote the number of normalized k × n Latin rectangles. Then the total number of k × n Latin rectangles is n ! ( n − 1 ) ! L ( k , n ) ( n − k ) ! . {\displaystyle {\frac {n!(n-1)!L(k,n)}{(n-k)!}}.} A 2 × n Latin rectangle corresponds to a permutation with no fixed points. Such permutations have been called discordant permutations. An enumeration


id: latin-square-20260505-0
file: data/en.wikipedia.org/wiki/Latin_square-0.md
category: reference
title: Latin square
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Latin_square
date_saved: 2026-05-05T09:50:36.263147+00:00
instance: kb-cron
parent: latin-square-20260505-0
summary:
In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3 × 3 Latin square is The name "Latin square" was inspired by mathematical papers by Leonhard Euler (1707–1783), who used Latin characters as symbols, but any set of symbols can be used: in the above example, the alphabetic sequence A, B, C can be replaced by the integer sequence 1, 2, 3. Euler began the general theory of Latin squares. == History == The Korean mathematician Choi Seok-jeong was the first to publish an example of Latin squares of order nine, in order to construct a magic square in 1700, predating Leonhard Euler by 67 years. === Counting === This account follows McKay, Meynert & Myrvold (2007, p. 100). The counting of Latin squares has a long history, but the published accounts contain many errors. Euler in 1782, and Cayley in 1890, both knew the number of reduced Latin squares up to order five. In 1915, MacMahon approached the problem in a different way, but initially obtained the wrong value for order


id: latin-square-20260505-1
file: data/en.wikipedia.org/wiki/Latin_square-1.md
category: reference
title: Latin square
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Latin_square
date_saved: 2026-05-05T09:50:36.263147+00:00
instance: kb-cron
parent: latin-square-20260505-0
summary:
Many operations on a Latin square produce another Latin square (for example, turning it upside down). If we permute the rows, permute the columns, or permute the names of the symbols of a Latin square, we obtain a new Latin square said to be isotopic to the first. Isotopism is an equivalence relation, so the set of all Latin squares is divided into subsets, called isotopy classes, such that two squares in the same class are isotopic and two squares in different classes are not isotopic. A stronger form of equivalence exists. Two Latin squares L1 and L2 of side n with common symbol set S that is also the index set for the rows and columns of each square are isomorphic if there is a bijection g: S → S such that g(L1(i, j)) = L2(g(i), g(j)) for all i, j in S. An alternate way to define isomorphic Latin squares is to say that a pair of isotopic Latin squares are isomorphic if the three bijections used to show that they are isotopic are, in fact, equal. Isomorphism is also an equivalence relation and its equivalence classes are called isomorphism classes. Another type of operation is easiest to


id: latin-square-20260505-2
file: data/en.wikipedia.org/wiki/Latin_square-2.md
category: reference
title: Latin square
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Latin_square
date_saved: 2026-05-05T09:50:36.263147+00:00
instance: kb-cron
parent: latin-square-20260505-0
summary:
A transversal in a Latin square is a choice of n cells, where each row contains one cell, each column contains one cell, and there is one cell containing each symbol. One can consider a Latin square as a complete bipartite graph in which the rows are vertices of one part, the columns are vertices of the other part, each cell is an edge (between its row and its column), and the symbols are colors. The rules of the Latin squares imply that this is a proper edge coloring. With this definition, a Latin transversal is a matching in which each edge has a different color; such a matching is called a rainbow matching. Therefore, many results on Latin squares/rectangles are contained in papers with the term "rainbow matching" in their title, and vice versa. Some Latin squares have no transversal. For example, when n is even, an n-by-n Latin square in which the value of cell i,j is (i+j) mod n has no transversal. Here are two examples: [ 1 2 2 1 ] [ 1 2 3 4 2 3 4 1 3 4 1 2 4 1 2 3 ] {\displaystyle {\begin{bmatrix}1&2\\2&1\end{bmatrix}}\quad {\begin{bmatrix}1&2&3&4\\2&3&4&1\\3&4&1&2\\4&1&2&3\end{bmatrix}}} In 1967, H. J.


id: latin-square-20260505-3
file: data/en.wikipedia.org/wiki/Latin_square-3.md
category: reference
title: Latin square
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Latin_square
date_saved: 2026-05-05T09:50:36.263147+00:00
instance: kb-cron
parent: latin-square-20260505-0
summary:
A Latin rectangle is a generalization of a Latin square in which there are n columns and n possible values, but the number of rows may be smaller than n. Each value still appears at most once in each row and column. A Graeco-Latin square is a pair of two Latin squares such that, when one is laid on top of the other, each ordered pair of symbols appears exactly once. A Latin hypercube is a generalization of a Latin square from two dimensions to multiple dimensions. == See also == Block design Combinatorial design Eight queens puzzle Futoshiki Magic square Problems in Latin squares Rook's graph, a graph that has Latin squares as its colorings Sator Square Vedic square Word square == Notes == == References == Bailey, R.A. (2008). "6 Row-Column designs and 9 More about Latin squares". Design of Comparative Experiments. Cambridge University Press. ISBN 978-0-521-68357-9. MR 2422352. Dénes, J.; Keedwell, A. D. (1974). Latin squares and their applications. New York-London: Academic Press. p. 547. ISBN 0-12-209350-X. MR 0351850. Shah, Kirti R.; Sinha, Bikas K. (1989). "4 Row-Column Designs". Theory of Optimal Designs. Lecture Notes in Statistics. Vol. 54. Springer-Verlag. pp. 66–84. ISBN 0-387-96991-8. MR 1016151. van


id: limited-dependent-variable-20260505-0
file: data/en.wikipedia.org/wiki/Limited_dependent_variable-0.md
category: reference
title: Limited dependent variable
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Limited_dependent_variable
date_saved: 2026-05-05T09:50:37.460068+00:00
instance: kb-cron
parent: limited-dependent-variable-20260505-0
summary:
A limited dependent variable is a variable whose range of possible values is "restricted in some important way." In econometrics, the term is often used when estimation of the relationship between the limited dependent variable of interest and other variables requires methods that take this restriction into account. For example, this may arise when the variable of interest is constrained to lie between zero and one, as in the case of a probability, or is constrained to be positive, as in the case of wages or hours worked. Limited dependent variable models include: Censoring, where for some individuals in a data set, some data are missing but other data are present; Truncation, where some individuals are systematically excluded from observation (failure to take this phenomenon into account can result in selection bias); Discrete outcomes, such as binary decisions or qualitative data restricted to a small number of categories. Discrete choice models may have either unordered or ordered alternatives; ordered alternatives may take the form of count data or ordered rating responses (such as a Likert scale). == See also == Logit, logit model, ordered logit Multivariate probit models Probit, probit model, ordered probit Tobit model == See also == Censored


id: list-of-countries-implementing-pool-testing-strategy-against-covid-19-20260505-0
category: reference
title: List of countries implementing pool testing strategy against COVID-19
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_countries_implementing_pool_testing_strategy_against_COVID-19
date_saved: 2026-05-05T09:50:38.731783+00:00
instance: kb-cron
parent: list-of-countries-implementing-pool-testing-strategy-against-covid-19-20260505-0
file:
data/en.wikipedia.org/wiki/List_of_countries_implementing_pool_testing_strategy_against_COVID-19-0.md

summary:
If not otherwise stated, the virological status of sample pools is evaluated through PCR tests. == Screening strategies == === General population === === Campus screening strategies === SUNY campuses are implementing a pool testing strategy based on saliva samples, including Cornell, SUNY Fredonia or SUNY Oneonta. The University of Tennessee is also implementing a saliva pool testing strategy. Researchers from Yale University, Georgia Augusta University, the University of Illinois, are also considering or implementing pool testing strategies. == Small-scale screening or experimental protocols == == References == == See also == Group testing COVID-19 testing


id: manipulation-check-20260505-0
file: data/en.wikipedia.org/wiki/Manipulation_check-0.md
category: reference
title: Manipulation check
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Manipulation_check
date_saved: 2026-05-05T09:50:41.099667+00:00
instance: kb-cron
parent: manipulation-check-20260505-0
summary:
Manipulation check is a term in experimental research in the social sciences which refers to certain kinds of secondary evaluations of an experiment. == Overview == Manipulation checks are measured variables that show what the manipulated variables concurrently affect besides the dependent variable of interest. In experiments, an experimenter manipulates some aspect of a process or task and randomly assigns subjects to different levels of the manipulation ("experimental conditions"). The experimenter then observes whether variation in the manipulated variables cause differences in the dependent variable. Manipulation checks are targeted at variables beside the dependent variable of interest. Manipulations are not intended to verify that the manipulated factor caused variation in the dependent variable. This is verified by random assignment, manipulation before measurement of the dependent variable, and statistical tests of effect of the manipulated variable on the dependent variable. Thus, a failed manipulation check does not refute the hypothesis that the manipulation caused variation in the dependent variable. In contrast, a successful manipulation check can help an experimenter rule out reasons that a manipulation may have failed to influence a dependent variable. When a manipulation creates significant differences between experimental conditions in both (1) the dependent variable and (2) the


id: matching-statistics-20260505-0
file: data/en.wikipedia.org/wiki/Matching_(statistics)-0.md
category: reference
title: Matching (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Matching_(statistics)
date_saved: 2026-05-05T09:50:42.337218+00:00
instance: kb-cron
parent: matching-statistics-20260505-0
summary:
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned). The goal of matching is to reduce bias for the estimated treatment effect in an observational-data study, by finding, for every treated unit, one (or more) non-treated unit(s) with similar observable characteristics against which the covariates are balanced out (similar to the K-nearest neighbors algorithm). By matching treated units to similar non-treated units, matching enables a comparison of outcomes among treated and non-treated units to estimate the effect of the treatment reducing bias due to confounding. Propensity score matching, an early matching technique, was developed as part of the Rubin causal model, but has been shown to increase model dependence, bias, inefficiency, and power and is no longer recommended compared to other matching methods. A simple, easy-to-understand, and statistically powerful method of matching is known as Coarsened Exact Matching or CEM. Matching has been promoted by Donald Rubin. It was prominently criticized in economics by Robert LaLonde (1986), who compared estimates of treatment effects from an experiment to comparable estimates produced with matching methods and showed


id: minimisation-clinical-trials-20260505-0
file: data/en.wikipedia.org/wiki/Minimisation_(clinical_trials)-0.md
category: reference
title: Minimisation (clinical trials)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Minimisation_(clinical_trials)
date_saved: 2026-05-05T09:50:43.477942+00:00
instance: kb-cron
parent: minimisation-clinical-trials-20260505-0
summary:
Minimisation is a method of adaptive stratified sampling that is used in clinical trials, as described by Pocock and Simon. The aim of minimisation is to minimise the imbalance between the number of patients in each treatment group over a number of factors. Normally patients would be allocated to a treatment group randomly and while this maintains a good overall balance, it can lead to imbalances within sub-groups. For example, if a majority of the patients who were receiving the active drug happened to be male, or smokers, the statistical usefulness of the study would be reduced. The traditional method to avoid this problem, known as blocked randomisation, is to stratify patients according to a number of factors (e.g. male and female, or smokers and non-smokers) and to use a separate randomisation list for each group. Each randomisation list would be created such that after every block of x patients, there would be an equal number in each treatment group. The problem with this method is that the number of lists increases exponentially with the number of stratification factors. Minimisation addresses this problem by calculating the imbalance within each factor should the patient be allocated to a particular treatment group.


id: multi-attribute-global-inference-of-quality-20260505-0
file: data/en.wikipedia.org/wiki/Multi-attribute_global_inference_of_quality-0.md
category: reference
title: Multi-attribute global inference of quality
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multi-attribute_global_inference_of_quality
date_saved: 2026-05-05T09:50:44.654885+00:00
instance: kb-cron
parent: multi-attribute-global-inference-of-quality-20260505-0
summary:
Multi-attribute global inference of quality (MAGIQ) is a multi-criteria decision analysis technique. MAGIQ is based on a hierarchical decomposition of comparison attributes and rating assignment using rank order centroids. == Description == The MAGIQ technique is used to assign a single, overall measure of quality to each member of a set of systems where each system has an arbitrary number of comparison attributes. The MAGIQ technique has features similar to the analytic hierarchy process and the simple multi-attribute rating technique exploiting ranks (SMARTER) technique. The MAGIQ technique was first published by James D. McCaffrey. The MAGIQ process begins with an evaluator determining which system attributes are to be used as the basis for system comparison. These attributes are ranked by importance to the particular problem domain, and the ranks are converted to ratings using rank order centroids. Each system under analysis is ranked against each comparison attribute and the ranks are transformed into rank order centroids. The final overall quality metric for each system is the weighted (by comparison attribute importance) sum of each attribute rating. The references provide specific examples of the process. There is little direct research on the theoretical soundness and effectiveness of the MAGIQ technique as


id: multicollinearity-20260505-0
file: data/en.wikipedia.org/wiki/Multicollinearity-0.md
category: reference
title: Multicollinearity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multicollinearity
date_saved: 2026-05-05T09:50:45.853835+00:00
instance: kb-cron
parent: multicollinearity-20260505-0
summary:
In statistics, multicollinearity or collinearity is a situation where the predictors in a regression model are linearly dependent. Perfect multicollinearity refers to a situation where the predictive variables have an exact linear relationship. When there is perfect collinearity, the design matrix X {\displaystyle X} has less than full rank, and therefore the moment matrix X T X {\displaystyle X^{\mathsf {T}}X} cannot be inverted. In this situation, the parameter estimates of the regression are not well-defined, as the system of equations has infinitely many solutions. Imperfect multicollinearity refers to a situation where the predictive variables have a nearly exact linear relationship. The Gauss–Markov theorem assumes absence of perfect multicollinearity. The adverse effect of highly correlated variables is widely known and proven many times. To address the high collinearity of a dataset, variance inflation factor can be used to identify the collinearity of the predictor variables. == Perfect multicollinearity == Perfect multicollinearity refers to a situation where the predictors are linearly dependent (one can be written as an exact linear function of the others). Ordinary least squares requires inverting the matrix X T X {\displaystyle X^{\mathsf {T}}X} , where X = [ 1 X 11 ⋯ X k 1 ⋮ ⋮ ⋮


id: multicollinearity-20260505-1
file: data/en.wikipedia.org/wiki/Multicollinearity-1.md
category: reference
title: Multicollinearity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multicollinearity
date_saved: 2026-05-05T09:50:45.853835+00:00
instance: kb-cron
parent: multicollinearity-20260505-0
summary:
Using prior information or theory. For example, if we notice Alice never steps in puddles, we can reasonably argue puddles are not why she wears boots, as she does not need the boots to avoid puddles. Collecting more data. If we observe Alice enough times, we will eventually see her on days where there are puddles but not rain (e.g. because the rain stops before she leaves home). This confounding becomes substantially worse when researchers attempt to ignore or suppress it by excluding these variables from the regression (see #Misuse). Excluding multicollinear variables from regressions will invalidate causal inference and produce worse estimates by removing important confounders. Multicollinearity can significantly affect the stability and interpretability of regression models. When predictor variables are highly correlated, the variance of the estimated regression coefficients increases, which may lead to large standard errors and unreliable statistical inference. As a result, coefficients may appear statistically insignificant even when the overall model has strong explanatory power. This issue does not necessarily reduce predictive performance, but it complicates the interpretation of individual predictors. === Remedies === There are many ways to prevent multicollinearity from affecting results by planning ahead of time. However, these methods all require a


id: multicollinearity-20260505-2
file: data/en.wikipedia.org/wiki/Multicollinearity-2.md
category: reference
title: Multicollinearity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multicollinearity
date_saved: 2026-05-05T09:50:45.853835+00:00
instance: kb-cron
parent: multicollinearity-20260505-0
summary:
== Further reading == Belsley, David A.; Kuh, Edwin; Welsch, Roy E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: Wiley. ISBN 978-0-471-05856-4. Goldberger, Arthur S. (1991). "Multicollinearity". A Course in Econometrics. Cambridge: Harvard University Press. pp. 245–53. ISBN 9780674175440. Hill, R. Carter; Adkins, Lee C. (2001). "Collinearity". In Baltagi, Badi H. (ed.). A Companion to Theoretical Econometrics. Blackwell. pp. 256–278. doi:10.1002/9780470996249.ch13. ISBN 978-0-631-21254-6. Johnston, John (1972). Econometric Methods (Second ed.). New York: McGraw-Hill. pp. 159–168. ISBN 9780070326798. Kalnins, Arturs (2022). "When does multicollinearity bias coefficients and cause type 1 errors? A reconciliation of Lindner, Puck, and Verbeke (2020) with Kalnins (2018)". Journal of International Business Studies. 53 (7): 1536–1548. doi:10.1057/s41267-022-00531-9. S2CID 249323519. Kmenta, Jan (1986). Elements of Econometrics (Second ed.). New York: Macmillan. pp. 430–442. ISBN 978-0-02-365070-3. Maddala, G. S.; Lahiri, Kajal (2009). Introduction to Econometrics (Fourth ed.). Chichester: Wiley. pp. 279–312. ISBN 978-0-470-01512-4. Tomaschek, Fabian; Hendrix, Peter; Baayen, R. Harald (2018). "Strategies for addressing collinearity in multivariate linguistic data". Journal of Phonetics. 71: 249–267. doi:10.1016/j.wocn.2018.09.004. == External links == Thoma, Mark (2 March 2011). "Econometrics Lecture (topic: multicollinearity)". University of Oregon. Archived from the original on 12 December 2021 – via YouTube. Earliest Uses:


id: multifactor-design-of-experiments-software-20260505-0
file: data/en.wikipedia.org/wiki/Multifactor_design_of_experiments_software-0.md
category: reference
title: Multifactor design of experiments software
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multifactor_design_of_experiments_software
date_saved: 2026-05-05T09:50:47.021513+00:00
instance: kb-cron
parent: multifactor-design-of-experiments-software-20260505-0
summary:
Software that is used for designing factorial experiments plays an important role in scientific experiments and represents a route to the implementation of design of experiments procedures that derive from statistical and combinatorial theory. In principle, easy-to-use design of experiments (DOE) software should be available to all experimenters to foster use of DOE. == Background == == Use of software == Factorial experimental design software drastically simplifies previously laborious hand calculations needed before the use of computers. During World War II, a more sophisticated form of DOE, called factorial design, became a big weapon for speeding up industrial development for the Allied forces. These designs can be quite compact, involving as few as two levels of each factor and only a fraction of all the combinations, and yet they are quite powerful for screening purposes. After the war, a statistician at Imperial Chemical, George Box, described how to generate response surfaces for process optimization. From this point forward, DOE took hold in the chemical process industry, where factors such as time, temperature, pressure, concentration, flow rate and agitation are easily manipulated. DOE results, when discovered accurately with DOE software, strengthen the capability to discern truths about sample populations being tested:


id: multiple-baseline-design-20260505-0
file: data/en.wikipedia.org/wiki/Multiple_baseline_design-0.md
category: reference
title: Multiple baseline design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multiple_baseline_design
date_saved: 2026-05-05T09:50:48.236349+00:00
instance: kb-cron
parent: multiple-baseline-design-20260505-0
summary:
A multiple baseline design is used in medical, psychological, and biological research. The multiple baseline design was first reported in 1960 as used in basic operant research. It was applied in the late 1960s to human experiments in response to practical and ethical issues that arose in withdrawing apparently successful treatments from human subjects. In it two or more (often three) behaviors, people or settings are plotted in a staggered graph where a change is made to one, but not the other two, and then to the second, but not the third behavior, person or setting. Differential changes that occur to each behavior, person or in each setting help to strengthen what is essentially an AB design with its problematic competing hypotheses. Because treatment is started at different times, changes are attributable to the treatment rather than to a chance factor. By gathering data from many subjects (instances), inferences can be made about the likeliness that the measured trait generalizes to a greater population. In multiple baseline designs, the experimenter starts by measuring a trait of interest, then applies a treatment before measuring that trait again. Treatment does not begin until a stable baseline has been recorded, and does not


id: multiple-treatments-20260505-0
file: data/en.wikipedia.org/wiki/Multiple_treatments-0.md
category: reference
title: Multiple treatments
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multiple_treatments
date_saved: 2026-05-05T09:50:49.491929+00:00
instance: kb-cron
parent: multiple-treatments-20260505-0
summary:
Multiple treatments, like multivalued treatments, generalize the binary treatment effects framework. But rather than focusing on a treatment effect that can take on different values, the focus now is on different types of treatment. One example could be a job training program, where different types of job training are offered to the participants. The case of multiple treatments is relatively difficult to handle, as it can require additional functional form restrictions, especially when addressing the counterfactual or potential outcomes framework. Nevertheless, the general instrumental variable framework used to analyze binary treatment effects has been extended to allow for multiple treatments. There are different approaches available to analyze multiple treatment effects. One can think of treatment effects within this framework as the difference in the counterfactual outcomes that would have been observed if the agent faced different general choice sets, with multinomial choices being a natural way to analyze multiple treatments. More formally, assume there are J options available and the value to the agent of choosing option j is Rj (Zj )=vj (Zj ) -ϵj where εj is some unobserved random shock. Then the agent will choose alternative j such that Rj ≥ Rk for all k≠j. There is a


id: multivalued-treatment-20260505-0
file: data/en.wikipedia.org/wiki/Multivalued_treatment-0.md
category: reference
title: Multivalued treatment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multivalued_treatment
date_saved: 2026-05-05T09:50:50.722035+00:00
instance: kb-cron
parent: multivalued-treatment-20260505-0
summary:
In statistics, in particular in the design of experiments, a multi-valued treatment is a treatment that can take on more than two values. It is related to the dose-response model in the medical literature. == Description == Generally speaking, treatment levels may be finite or infinite as well as ordinal or cardinal, which leads to a large collection of possible treatment effects to be studied in applications. One example is the effect of different levels of program participation (e.g. full-time and part-time) in a job training program. Assume there exists a finite collection of multi-valued treatment status T = { 0 , 1 , 2 , … , J , } {\displaystyle T=\{0,1,2,\ldots ,J,\}} with J some fixed integer. As in the potential outcomes framework, denote Y ( j ) ⊂ R {\displaystyle Y(j)\subset R} the collection of potential outcomes under the treatment J, and Y = ∑ j = 0 J D j Y ( j ) {\displaystyle Y=\textstyle \sum _{j=0}^{J}\displaystyle D_{j}Y(j)} denotes the observed outcome and D j {\displaystyle D_{j}} is an indicator that equals 1 when the treatment equals j and 0 when it does not equal j, leading to a fundamental problem of causal inference. A


id: multivariate-analysis-of-variance-20260505-0
file: data/en.wikipedia.org/wiki/Multivariate_analysis_of_variance-0.md
category: reference
title: Multivariate analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multivariate_analysis_of_variance
date_saved: 2026-05-05T09:50:51.939099+00:00
instance: kb-cron
parent: multivariate-analysis-of-variance-20260505-0
summary:
In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used when there are two or more dependent variables, and is often followed by significance tests involving individual dependent variables separately. Without relation to the image, the dependent variables may be k life satisfactions scores measured at sequential time points and p job satisfaction scores measured at sequential time points. In this case there are k+p dependent variables whose linear combination follows a multivariate normal distribution, multivariate variance-covariance matrix homogeneity, and linear relationship, no multicollinearity, and each without outliers. == Model == Assume n {\textstyle n} q {\textstyle q} -dimensional observations, where the i {\textstyle i} ’th observation y i {\textstyle y_{i}} is assigned to the group g ( i ) ∈ { 1 , … , m } {\textstyle g(i)\in \{1,\dots ,m\}} and is distributed around the group center μ ( g ( i ) ) ∈ R q {\textstyle \mu ^{(g(i))}\in \mathbb {R} ^{q}} with multivariate Gaussian noise: y i = μ ( g ( i ) ) + ε i ε i ∼ i.i.d. N q ( 0 , Σ ) for i = 1 ,


id: n-of-1-trial-20260505-0
file: data/en.wikipedia.org/wiki/N-of-1_trial-0.md
category: reference
title: N-of-1 trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/N-of-1_trial
date_saved: 2026-05-05T09:50:53.125257+00:00
instance: kb-cron
parent: n-of-1-trial-20260505-0
summary:
An N-of-1 (N=1) trial is a multiple crossover clinical trial, conducted in a single patient. A trial in which random allocation is used to determine the order in which an experimental and a control intervention are given to a single patient is an N-of-1 randomized controlled trial. Some N-of-1 trials involve randomized assignment and blinding, but the order of experimental and control interventions can also be fixed by the researcher. This type of study has enabled practitioners to achieve experimental progress without the work of designing a group comparison study. This design, especially if including blinding and wash-out periods, can be effective in confirming causality. N-of-1 trials, if used in clinical practice to inform therapeutic decisions concerned with the patient participating in the trial, can be a source of evidence about individual treatment responses, fulfilling the promise of personalized medicine. == Design == The N-of-1 trials can be designed in many ways. For example, Single-Patient Open Trials (SPOTs) are located somewhere in between the formal (explanatory) N-of-1 trials and the trial and error approach used in clinical practice and are characterized by at least one crossover period with washout in between. One of the most common procedures is the ABA


id: national-research-ethics-service-20260505-0
file: data/en.wikipedia.org/wiki/National_Research_Ethics_Service-0.md
category: reference
title: National Research Ethics Service
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/National_Research_Ethics_Service
date_saved: 2026-05-05T09:50:54.306375+00:00
instance: kb-cron
parent: national-research-ethics-service-20260505-0
summary:
The National Research Ethics Service (NRES) is a UK medical quango which deals with research ethics. Principal Investigators must describe the experiment they intend to pursue to the NRES for its approval, failing which the study is prohibited. == History == The NRES was launched on 1 April 2007. The adjective "National" was omitted from the name at some unknown point in time. == Purpose == In 2009, the NRES issued a leaflet in which it described its purpose: The National Research Ethics Service (NRES) reviews research proposals to protect the rights and safety of research participants and enables ethical research which is of potential benefit to science and society. == Substance of reports == The substance of the NRES reports can be gleaned from an approval obtained in 2011 by Stephanie Taylor, who was then Professor of Public Health and Primary Care at Queen Mary University of London. == References ==


id: nested-case-control-study-20260505-0
file: data/en.wikipedia.org/wiki/Nested_case–control_study-0.md
category: reference
title: Nested case–control study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nested_case–control_study
date_saved: 2026-05-05T09:50:55.486311+00:00
instance: kb-cron
parent: nested-case-control-study-20260505-0
summary:
A nested case–control (NCC) study is a variation of a case–control study in which cases and controls are drawn from the population in a fully enumerated cohort. Usually, the exposure of interest is only measured among the cases and the selected controls. Thus the nested case–control study is more efficient than the full cohort design. The nested case–control study can be analyzed using methods for missing covariates. The NCC design is often used when the exposure of interest is difficult or expensive to obtain and when the outcome is rare. By utilizing data previously collected from a large cohort study, the time and cost of beginning a new case–control study is avoided. By only measuring the covariate in as many participants as necessary, the cost and effort of exposure assessment is reduced. This benefit is pronounced when the covariate of interest is biological, since assessments such as gene expression profiling are expensive, and because the quantity of blood available for such analysis is often limited, making it a valuable resource that should not be used unnecessarily. == Example == As an example, of the 91,523 women in the Nurses' Health Study who did not have cancer at baseline and who


id: null-hypothesis-20260505-0
file: data/en.wikipedia.org/wiki/Null_hypothesis-0.md
category: reference
title: Null hypothesis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Null_hypothesis
date_saved: 2026-05-05T09:50:56.623806+00:00
instance: kb-cron
parent: null-hypothesis-20260505-0
summary:
The null hypothesis (often denoted H 0 {\textstyle H_{0}} ) is the claim in scientific research that the effect being studied does not exist. The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed. If the null hypothesis is true, any experimentally observed effect is due to chance alone, hence the term "null". In contrast with the null hypothesis, an alternative hypothesis (often denoted H A {\displaystyle H_{A}} or H 1 {\displaystyle H_{1}} ) is developed, which claims that a relationship does exist between two variables. == Basic definitions == The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise. The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis, or a statement of 'no effect' or 'no difference'. It is often symbolized as H 0 {\displaystyle H_{0}} . The statement that is being tested against the null hypothesis is the


id: null-hypothesis-20260505-1
file: data/en.wikipedia.org/wiki/Null_hypothesis-1.md
category: reference
title: Null hypothesis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Null_hypothesis
date_saved: 2026-05-05T09:50:56.623806+00:00
instance: kb-cron
parent: null-hypothesis-20260505-0
summary:
== Technical description == The null hypothesis is a default hypothesis that a quantity to be measured is zero (null). Typically, the quantity to be measured is the difference between two situations. For instance, trying to determine if there is a positive proof that an effect has occurred or that samples derive from different batches. The null hypothesis is generally assumed to remain possibly true. Multiple analyses can be performed to show how the hypothesis should either be rejected or excluded e.g. having a high confidence level, thus demonstrating a statistically significant difference. This is demonstrated by showing that zero is outside of the specified confidence interval of the measurement on either side, typically within the real numbers. Failure to exclude the null hypothesis (with any confidence) does not logically confirm or support the (unprovable) null hypothesis. (When it is proven that something is e.g. bigger than x, it does not necessarily imply it is plausible that it is smaller or equal than x; it may instead be a poor quality measurement with low accuracy. Confirming the null hypothesis is two-sided would amount to positively proving it is bigger or equal than 0 and to positively proving it is smaller


id: null-hypothesis-20260505-2
file: data/en.wikipedia.org/wiki/Null_hypothesis-2.md
category: reference
title: Null hypothesis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Null_hypothesis
date_saved: 2026-05-05T09:50:56.623806+00:00
instance: kb-cron
parent: null-hypothesis-20260505-0
summary:
== Principle == Hypothesis testing requires constructing a statistical model of what the data would look like if chance or random processes alone were responsible for the results. The hypothesis that chance alone is responsible for the results is called the null hypothesis. The model of the result of the random process is called the distribution under the null hypothesis. The obtained results are compared with the distribution under the null hypothesis, and the likelihood of finding the obtained results is thereby determined. Hypothesis testing works by collecting data and measuring how likely the particular set of data is (assuming the null hypothesis is true), when the study is on a randomly selected representative sample. The null hypothesis assumes no relationship between variables in the population from which the sample is selected. If the data-set of a randomly selected representative sample is very unlikely relative to the null hypothesis (defined as being part of a class of sets of data that are rarely observed), the experimenter rejects the null hypothesis, concluding it (probably) is false. This class of data-sets is usually specified via a test statistic, which is designed to measure the extent of apparent departure from the null hypothesis.


id: null-hypothesis-20260505-3
file: data/en.wikipedia.org/wiki/Null_hypothesis-3.md
category: reference
title: Null hypothesis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Null_hypothesis
date_saved: 2026-05-05T09:50:56.623806+00:00
instance: kb-cron
parent: null-hypothesis-20260505-0
summary:
== Choice of the null hypothesis == The choice of the null hypothesis is associated with sparse and inconsistent advice. Fisher mentioned few constraints on the choice and stated that many null hypotheses should be considered and that many tests are possible for each. The variety of applications and the diversity of goals suggests that the choice can be complicated. In many applications the formulation of the test is traditional. A familiarity with the range of tests available may suggest a particular null hypothesis and test. Formulating the null hypothesis is not automated (though the calculations of significance testing usually are). David Cox said, "How [the] translation from subject-matter problem to statistical model is done is often the most critical part of an analysis". A statistical significance test is intended to test a hypothesis. If the hypothesis summarizes a set of data, there is no value in testing the hypothesis on that set of data. Example: If a study of last year's weather reports indicates that rain in a region falls primarily on weekends, it is only valid to test that null hypothesis on weather reports from any other year. Testing hypotheses suggested by the data is circular reasoning that


id: null-hypothesis-20260505-4
file: data/en.wikipedia.org/wiki/Null_hypothesis-4.md
category: reference
title: Null hypothesis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Null_hypothesis
date_saved: 2026-05-05T09:50:56.623806+00:00
instance: kb-cron
parent: null-hypothesis-20260505-0
summary:
==== Discussion ==== Fisher said, "the null hypothesis must be exact, that is free of vagueness and ambiguity, because it must supply the basis of the 'problem of distribution,' of which the test of significance is the solution", implying a more restrictive domain for H0. According to this view, the null hypothesis must be numerically exact—it must state that a particular quantity or difference is equal to a particular number. In classical science, it is most typically the statement that there is no effect of a particular treatment; in observations, it is typically that there is no difference between the value of a particular measured variable and that of a prediction. Most statisticians believe that it is valid to state direction as a part of null hypothesis, or as part of a null hypothesis/alternative hypothesis pair. However, the results are not a full description of all the results of an experiment, merely a single result tailored to one particular purpose. For example, consider an H0 that claims the population mean for a new treatment is an improvement on a well-established treatment with population mean = 10 (known from long experience), with the one-tailed alternative being that the new treatment's mean


id: null-hypothesis-20260505-5
file: data/en.wikipedia.org/wiki/Null_hypothesis-5.md
category: reference
title: Null hypothesis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Null_hypothesis
date_saved: 2026-05-05T09:50:56.623806+00:00
instance: kb-cron
parent: null-hypothesis-20260505-0
summary:
Before 1925: There are occasional transient traces of statistical tests in past centuries, which were early examples of null hypotheses. In the late 19th century statistical significance was defined. In the early 20th century important probability distributions were defined. Gossett and Pearson worked on specific cases of significance testing. 1925: Fisher published the first edition of Statistical Methods for Research Workers, which defined the statistical significance test and made it a mainstream method of analysis for much of experimental science. The text was devoid of proofs and weak on explanations, but was filled with real examples. It placed statistical practice in the sciences well in advance of published statistical theory. 1933: In a series of papers (published over a decade starting in 1928) Neyman & Pearson defined the statistical hypothesis test as a proposed improvement on Fisher's test. The papers provided much of the terminology for statistical tests including alternative hypothesis and H0 as a hypothesis to be tested using observational data (with H1, H2... as alternatives). 1935: Fisher published the first edition of the book The Design of Experiments, which introduced the null hypothesis (by example rather than by definition) and carefully explained the rationale for significance tests in


id: null-result-20260505-0
file: data/en.wikipedia.org/wiki/Null_result-0.md
category: reference
title: Null result
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Null_result
date_saved: 2026-05-05T09:50:57.839258+00:00
instance: kb-cron
parent: null-result-20260505-0
summary:
In science, a null result is a result without the expected content: that is, the proposed result is absent. It is an experimental outcome which does not show an otherwise expected effect. This does not imply a result of zero or nothing, simply a result that does not support the hypothesis. In statistical hypothesis testing, a null result occurs when an experimental result is not significantly different from what is to be expected under the null hypothesis; its probability (under the null hypothesis) does not exceed the significance level, i.e., the threshold set prior to testing for rejection of the null hypothesis. The significance level varies, but common choices include 0.10, 0.05, and 0.01. However, a non-significant result does not necessarily mean that an effect is absent. As an example in physics, the results of the Michelson–Morley experiment were of this type, as it did not detect the expected velocity relative to the postulated luminiferous aether. This experiment's famous failed detection, commonly referred to as the null result, contributed to the development of special relativity. The experiment did appear to measure a non-zero "drift", but the value was far too small to account for the theoretically expected results; it is


id: nuremberg-code-20260505-0
file: data/en.wikipedia.org/wiki/Nuremberg_Code-0.md
category: reference
title: Nuremberg Code
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuremberg_Code
date_saved: 2026-05-05T09:50:59.021660+00:00
instance: kb-cron
parent: nuremberg-code-20260505-0
summary:
The Nuremberg Code (German: Nürnberger Kodex) is a set of ethical research principles for human experimentation created by the court in U.S. v Brandt, one of the Subsequent Nuremberg trials that were held after the Second World War. Though it was articulated as part of the court's verdict in the trial, the Code would later become significant beyond its original context; in a review written on the 50th anniversary of the Brandt verdict, Jay Katz writes that "a careful reading of the judgment suggests that [the authors] wrote the Code for the practice of human experimentation whenever it is being conducted." == Background == The origin of the Code began in pre–World War II German politics, particularly during the 1930s and 1940s. Starting in the mid-1920s, German physicians, usually proponents of racial hygiene, were accused by the public and the medical society of unethical medical practices. The use of racial hygiene was supported by the German government in order to promote an Aryan race. Racial hygiene extremists merged with National Socialism to promote the use of biology to accomplish their goals of racial purity, a core concept in the Nationalist ideology. Physicians were attracted to the scientific ideology and aided


id: nuremberg-code-20260505-1
file: data/en.wikipedia.org/wiki/Nuremberg_Code-1.md
category: reference
title: Nuremberg Code
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuremberg_Code
date_saved: 2026-05-05T09:50:59.021660+00:00
instance: kb-cron
parent: nuremberg-code-20260505-0
summary:
The voluntary consent of the human subject is absolutely essential. This means that the person involved should have legal capacity to give consent; should be so situated as to be able to exercise free power of choice, without the intervention of any element of force, fraud, deceit, duress, overreaching, or other ulterior form of constraint or coercion; and should have sufficient knowledge and comprehension of the elements of the subject matter involved as to enable him to make an understanding and enlightened decision. This latter element requires that before the acceptance of an affirmative decision by the experimental subject there should be made known to him the nature, duration, and purpose of the experiment; the method and means by which it is to be conducted; all inconveniences and hazards reasonably to be expected; and the effects upon his health or person which may possibly come from his participation in the experiment. The duty and responsibility for ascertaining the quality of the consent rests upon each individual who initiates, directs, or engages in the experiment. It is a personal duty and responsibility which may not be delegated to another with impunity. The experiment should be such as to yield fruitful results


id: o-brien-fleming-boundary-20260505-0
file: data/en.wikipedia.org/wiki/O'Brien–Fleming_boundary-0.md
category: reference
title: O'Brien–Fleming boundary
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/O'Brien–Fleming_boundary
date_saved: 2026-05-05T09:51:00.170438+00:00
instance: kb-cron
parent: o-brien-fleming-boundary-20260505-0
summary:
The O'Brien–Fleming (OBF) boundary is a set of statistical thresholds used in group-sequential clinical trial designs. It allows analyses (typically by a data monitoring committee) of accumulating data at several pre-specified interim points while still preserving the overall Type I error rate (the chance of a false-positive result) that was specified for the final analysis. The boundary is conservative at early interim analyses—requiring very strong evidence to stop a trial early—and becomes less stringent as the study progresses. At the first interim looks the rule requires a very high test statistic (or equivalently a very low p-value) to declare significance. This protects against premature stopping on random fluctuations. As the trial progresses, the required statistic becomes less extreme. By the final analysis the boundary is essentially the nominal significance level (e.g., 0.05). The method is a special case of the general parameterized method of Wang & Tsiatis. One disadvantage of the OBF boundary is that it requires prespecification of the number of interim analyses and the proportion of total information used at each analysis. More recent methods, such as the boundary method proposed by Lan and DeMets, allow dynamic allocation of the boundary values as the study progresses. Despite this


id: observational-study-20260505-0
file: data/en.wikipedia.org/wiki/Observational_study-0.md
category: reference
title: Observational study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Observational_study
date_saved: 2026-05-05T09:51:01.318282+00:00
instance: kb-cron
parent: observational-study-20260505-0
summary:
In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws conclusions without controlling the independent variable due to ethical or practical limitations. One common example studies the effect of a treatment, where the researcher does not assign subjects to treatment or control group. This is in contrast with experiments, such as randomized controlled trials, where each subject is randomly assigned to a treated group or a control group. Observational studies, for lacking an assignment mechanism, naturally present difficulties for inferential analysis. == Motivation == The independent variable may be beyond the control of the investigator for a variety of reasons: A randomized experiment would violate ethical standards. Suppose one wanted to investigate the abortion – breast cancer hypothesis, which postulates a causal link between induced abortion and the incidence of breast cancer. In a hypothetical controlled experiment, one would start with a large subject pool of pregnant women and divide them randomly into a treatment group (receiving induced abortions) and a control group (not receiving abortions), and then conduct regular cancer screenings for women from both groups. Such an experiment would violate ethical principles. (It would also suffer from various confounds and sources of bias, e.g.


id: observational-study-20260505-1
file: data/en.wikipedia.org/wiki/Observational_study-1.md
category: reference
title: Observational study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Observational_study
date_saved: 2026-05-05T09:51:01.318282+00:00
instance: kb-cron
parent: observational-study-20260505-0
summary:
=== Omitted variable bias === An observer of an uncontrolled experiment (or process) records potential factors and the data output: the goal is to determine the effects of the factors. Sometimes the recorded factors may not be directly causing the differences in the output. There may be more important factors which were not recorded but are, in fact, causal. Also, recorded or unrecorded factors may be correlated which may yield incorrect conclusions. === Selection bias === Another difficulty with observational studies is that researchers may themselves be biased in their observational skills. This would allow for researchers to (either consciously or unconsciously) seek out the information they're looking for while conducting their research. For example, researchers may exaggerate the effect of one variable, or downplay the effect of another: researchers may even select in subjects that fit their conclusions. This selection bias can happen at any stage of the research process. This introduces bias into the data where certain variables are systematically incorrectly measured. == Quality == A 2014 (updated in 2024) Cochrane review concluded that observational studies produce results similar to those conducted as randomized controlled trials. The review reported little evidence for significant effect differences between observational studies


id: observer-expectancy-effect-20260505-0
file: data/en.wikipedia.org/wiki/Observer-expectancy_effect-0.md
category: reference
title: Observer-expectancy effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Observer-expectancy_effect
date_saved: 2026-05-05T09:51:02.509827+00:00
instance: kb-cron
parent: observer-expectancy-effect-20260505-0
summary:
The observer-expectancy effect is a form of reactivity in which a researcher's cognitive bias causes them to subconsciously influence the participants of an experiment. Confirmation bias can lead to the experimenter interpreting results incorrectly because of the tendency to look for information that affirms their hypothesis, and overlook information that conflicts with it. It is a significant threat to a study's internal validity, and is therefore typically controlled using a double-blind experimental design. The observer-expectancy effect is distinct from related phenomena such as the subject-expectancy effect and demand characteristics. In observer-expectancy effects, the researcher’s expectations influence participant behavior or data interpretation through subtle cues, whereas subject-expectancy effects arise from participants’ own beliefs about the study, and demand characteristics refer more broadly to situational cues that signal expected responses. It may include conscious or unconscious influences on subject behavior including creation of demand characteristics that influence subjects, and altered or selective recording of experimental results themselves. == Overview == The experimenter may introduce cognitive bias into a study in several ways‍—‍in the observer-expectancy effect, the experimenter may subtly communicate their expectations for the outcome of the study to the participants, causing them to alter their behavior to conform to those expectations.


id: one-factor-at-a-time-method-20260505-0
file: data/en.wikipedia.org/wiki/One-factor-at-a-time_method-0.md
category: reference
title: One-factor-at-a-time method
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/One-factor-at-a-time_method
date_saved: 2026-05-05T09:51:03.967480+00:00
instance: kb-cron
parent: one-factor-at-a-time-method-20260505-0
summary:
The one-factor-at-a-time method, also known as one-variable-at-a-time, OFAT, OF@T, OFaaT, OVAT, OV@T, OVaaT, or monothetic analysis is a method of designing experiments involving the testing of factors, or causes, one at a time instead of multiple factors simultaneously. == Advantages == OFAT is favored by non-experts, especially in situations where the data is cheap and abundant. There exist cases where the mental effort required to conduct a complex multi-factor analysis exceeds the effort required to acquire extra data, in which case OFAT might make sense. Furthermore, some researchers have shown that OFAT can be more effective than fractional factorials under certain conditions (number of runs is limited, primary goal is to attain improvements in the system, and experimental error is not large compared to factor effects, which must be additive and independent of each other). == Disadvantages == In contrast, in situations where data is precious and must be analyzed with care, it is almost always better to change multiple factors at once. A middle-school-level example illustrating this point is the family of balance puzzles, which includes the Twelve Coins puzzle. At the undergraduate level, one could compare Bevington's GRIDLS versus GRADLS. The latter is far from optimal, but the


id: optimal-experimental-design-20260505-0
file: data/en.wikipedia.org/wiki/Optimal_experimental_design-0.md
category: reference
title: Optimal experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optimal_experimental_design
date_saved: 2026-05-05T09:51:06.413636+00:00
instance: kb-cron
parent: optimal-experimental-design-20260505-0
summary:
In the design of experiments, optimal experimental designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with designing experiments. == Advantages == Optimal designs offer three advantages over sub-optimal experimental designs: Optimal designs reduce the costs of experimentation by allowing statistical models to be estimated with fewer experimental runs. Optimal designs can accommodate multiple types of factors, such as process, mixture, and discrete factors. Designs can be optimized when the design-space is constrained,


id: optimal-experimental-design-20260505-1
file: data/en.wikipedia.org/wiki/Optimal_experimental_design-1.md
category: reference
title: Optimal experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optimal_experimental_design
date_saved: 2026-05-05T09:51:06.413636+00:00
instance: kb-cron
parent: optimal-experimental-design-20260505-0
summary:
==== Flexible optimality criteria and convex analysis ==== High-quality statistical software provide a combination of libraries of optimal designs or iterative methods for constructing approximately optimal designs, depending on the model specified and the optimality criterion. Users may use a standard optimality-criterion or may program a custom-made criterion. All of the traditional optimality-criteria are convex (or concave) functions, and therefore optimal-designs are amenable to the mathematical theory of convex analysis and their computation can use specialized methods of convex minimization. The practitioner need not select exactly one traditional, optimality-criterion, but can specify a custom criterion. In particular, the practitioner can specify a convex criterion using the maxima of convex optimality-criteria and nonnegative combinations of optimality criteria (since these operations preserve convex functions). For convex optimality criteria, the Kiefer-Wolfowitz equivalence theorem allows the practitioner to verify that a given design is globally optimal. The Kiefer-Wolfowitz equivalence theorem is related with the Legendre-Fenchel conjugacy for convex functions. If an optimality-criterion lacks convexity, then finding a global optimum and verifying its optimality often are difficult. === Model uncertainty and Bayesian approaches === ==== Model selection ==== When scientists wish to test several theories, then a statistician can design an experiment that allows optimal


id: optimal-experimental-design-20260505-2
file: data/en.wikipedia.org/wiki/Optimal_experimental_design-2.md
category: reference
title: Optimal experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optimal_experimental_design
date_saved: 2026-05-05T09:51:06.413636+00:00
instance: kb-cron
parent: optimal-experimental-design-20260505-0
summary:
Logic will not undertake to inform you what kind of experiments you ought to make in order best to determine the acceleration of gravity, or the value of the Ohm; but it will tell you how to proceed to form a plan of experimentation. [....] Unfortunately practice generally precedes theory, and it is the usual fate of mankind to get things done in some boggling way first, and find out afterward how they could have been done much more easily and perfectly. Kirstine Smith proposed optimal designs for polynomial models in 1918. (Kirstine Smith had been a student of the Danish statistician Thorvald N. Thiele and was working with Karl Pearson in London.) == See also == == Notes == == References == Atkinson, A. C.; Donev, A. N.; Tobias, R. D. (2007). Optimum experimental designs, with SAS. Oxford University Press. pp. 511+xvi. ISBN 978-0-19-929660-6. Chernoff, Herman (1972). Sequential analysis and optimal design. Society for Industrial and Applied Mathematics. ISBN 978-0-89871-006-9. Fedorov, V. V. (1972). Theory of Optimal Experiments. Academic Press. Fedorov, Valerii V.; Hackl, Peter (1997). Model-Oriented Design of Experiments. Lecture Notes in Statistics. Vol. 125. Springer-Verlag. Goos, Peter (2002). The Optimal Design of Blocked and Split-plot Experiments. Lecture


id: orthogonal-array-20260505-0
file: data/en.wikipedia.org/wiki/Orthogonal_array-0.md
category: reference
title: Orthogonal array
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Orthogonal_array
date_saved: 2026-05-05T09:51:07.576803+00:00
instance: kb-cron
parent: orthogonal-array-20260505-0
summary:
In mathematics, an orthogonal array (more specifically, a fixed-level orthogonal array) is a table ("array") whose entries come from a fixed finite set of symbols (for example, {1,2,...,v}), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t-tuples of the symbols, formed by taking the entries in each row restricted to these columns, appear the same number of times. The number t is called the strength of the orthogonal array. Here are two examples: The example at left is that of an orthogonal array with symbol set {1,2} and strength 2. Notice that the four ordered pairs (2-tuples) formed by the rows restricted to the first and third columns, namely (1,1), (2,1), (1,2) and (2,2), are all the possible ordered pairs of the two element set and each appears exactly once. The second and third columns would give, (1,1), (2,1), (2,2) and (1,2); again, all possible ordered pairs each appearing once. The same statement would hold had the first and second columns been used. This is thus an orthogonal array of strength two. In the example on the right, the rows restricted to the first


id: orthogonal-array-20260505-1
file: data/en.wikipedia.org/wiki/Orthogonal_array-1.md
category: reference
title: Orthogonal array
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Orthogonal_array
date_saved: 2026-05-05T09:51:07.576803+00:00
instance: kb-cron
parent: orthogonal-array-20260505-0
summary:
== Terminology and notation == The terms symmetric and asymmetric are sometimes used for fixed-level and mixed-level. Here symmetry refers to the property that all factors have the same number of levels, not to the "shape" of the array: a symmetric orthogonal array is almost never a symmetric matrix. The notation OA(N, k, v, t) is sometimes contracted so that one may, for example, write simply OA(k, v), as long as the text makes clear the unstated parameter values. In the other direction, it may be expanded for mixed-level arrays. Here one would write OA(N, k, v1···vk, t), where column i has vi levels. This notation is usually shortened when values v are repeated, so that one writes OA(8, 5, 2441, 2) for the example at the end of the last section, rather than OA(8, 5, 2·2·2·2·4, 2). In similar fashion, one may shorten OA(N, k, v, t) to OA(N, vk, t) for fixed-level arrays. This OA notation does not explicitly include the index λ, but λ can be recovered from the other parameters via the relation N = λvt. This is effective when the parameters all have specific numerical values, but less so when a class of orthogonal arrays


id: orthogonal-array-20260505-2
file: data/en.wikipedia.org/wiki/Orthogonal_array-2.md
category: reference
title: Orthogonal array
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Orthogonal_array
date_saved: 2026-05-05T09:51:07.576803+00:00
instance: kb-cron
parent: orthogonal-array-20260505-0
summary:
=== Latin cubes === In the statistics literature, a Latin cube is a three-dimensional n × n × n matrix consisting of n layers, each having n rows and n columns such that the n distinct elements which appear are repeated n2 times and arranged so that in each layer parallel to each of the three pairs of opposite faces of the cube all the n distinct elements appear and each is repeated exactly n times in that layer. Note that with this definition a layer of a Latin cube need not be a Latin square. In fact, no row, column or file (the cells of a particular position in the different layers) need be a permutation of the n symbols. A Latin cube of order n is equivalent to an OA(n3, 4 ,n, 2). Two Latin cubes of order n are orthogonal if, among the n3 pairs of elements chosen from corresponding cells of the two cubes, each distinct ordered pair of the elements occurs exactly n times. A set of k − 3 mutually orthogonal Latin cubes of order n is equivalent to an OA(n3, k, n, 2). An example of a pair of mutually orthogonal Latin cubes


id: orthogonal-array-20260505-3
file: data/en.wikipedia.org/wiki/Orthogonal_array-3.md
category: reference
title: Orthogonal array
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Orthogonal_array
date_saved: 2026-05-05T09:51:07.576803+00:00
instance: kb-cron
parent: orthogonal-array-20260505-0
summary:
A factorial experiment is a statistically structured experiment in which several factors (watering levels, antibiotics, fertilizers, etc.) are applied to each experimental unit at finitely many levels, which may be quantitative or qualitative. In a full factorial experiment all combinations of levels of the factors need to be tested. In a fractional factorial design only a subset of treatment combinations are used. An orthogonal array can be used to design a fractional factorial experiment. The columns represent the various factors and the entries are the levels at which the factors are observed. An experimental run is a row of the orthogonal array, that is, a specific combination of factor levels. The strength of the array determines the resolution of the fractional design. When using one of these designs, the treatment units and trial order should be randomized as much as the design allows. For example, one recommendation is that an appropriately sized orthogonal array be randomly selected from those available, and that the run order then be randomized. Mixed-level designs occur naturally in the statistical setting. === Quality control === Orthogonal arrays played a central role in the development of Taguchi methods by Genichi Taguchi, which took place during his


id: orthogonal-array-testing-20260505-0
file: data/en.wikipedia.org/wiki/Orthogonal_array_testing-0.md
category: reference
title: Orthogonal array testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Orthogonal_array_testing
date_saved: 2026-05-05T09:51:23.219077+00:00
instance: kb-cron
parent: orthogonal-array-testing-20260505-0
summary:
Orthogonal array testing is a systematic and statistically-driven black-box testing technique employed in the field of software testing. This method is particularly valuable in scenarios where the number of inputs to a system is substantial enough to make exhaustive testing impractical. == Overview == Orthogonal array testing works on the premise of selecting a subset of test cases from a large pool of potential inputs. This selection is based on statistical methods to ensure that the chosen subset represents the whole input space. As a result, serious bugs can be identified while the number of tests necessary to do so is greatly reduced. === Benefits === Reduced testing cycle time: By strategically selecting test cases, the testing process becomes more efficient, leading to time savings. Simplified analysis: The structured nature of orthogonal array testing makes analysis straightforward and less complex. Balanced test cases: This technique ensures that test cases are well-balanced, making it easier to isolate defects and assess performance. Cost savings: It offers a significant cost advantage over pair-wise testing, making it an economical choice for testing large-scale software systems. === Cons === Limited applicability: This technique is most effective when the number of inputs is relatively small. In


id: paradigm-experimental-20260505-0
file: data/en.wikipedia.org/wiki/Paradigm_(experimental)-0.md
category: reference
title: Paradigm (experimental)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paradigm_(experimental)
date_saved: 2026-05-05T09:51:25.533610+00:00
instance: kb-cron
parent: paradigm-experimental-20260505-0
summary:
In the behavioural sciences (e.g. psychology, biology, neurosciences), an experimental paradigm is an experimental setup or way of conducting a certain type of experiment (a protocol) that is defined by certain fine-tuned standards, and often has a theoretical background. A paradigm in this technical sense, however, is not a way of thinking as it is in the epistemological meaning (paradigm). In the social sciences empiricist experimentation has independent [and dependent] variables and control conditions...What is the origin of the hypotheses which are studied? Given the basic design, the hypothesis and the particular conditions for the experiment, an experimental paradigm must be made up. The paradigm typically includes factors such as experimental instructions for the subjects, the physical design of the experiment room, and the rules for process of the trial or trials to be carried out. The more paradigms which are attempted, and the more variables within a single paradigm are attempted, with the same results, the more sure one is of the results, that, "the effect is a true one and not merely a product of artifacts engendered by the use of a particular paradigm." The three core factors of paradigm design may be considered: "(a) ...the 'nuts and


id: phases-of-clinical-research-20260505-0
file: data/en.wikipedia.org/wiki/Phases_of_clinical_research-0.md
category: reference
title: Phases of clinical research
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phases_of_clinical_research
date_saved: 2026-05-05T09:51:26.696563+00:00
instance: kb-cron
parent: phases-of-clinical-research-20260505-0
summary:
The phases of clinical research are the stages in which scientists conduct experiments with a health intervention to obtain sufficient evidence for a process considered effective as a medical treatment. For drug development, the clinical phases start with testing for drug safety in a few human subjects, then expand to many study participants (potentially tens of thousands) to determine if the treatment is effective. Clinical research is conducted on drug candidates, vaccine candidates, new medical devices, and new diagnostic assays. == Description == Clinical trials testing potential medical products are commonly classified into four phases. The drug development process will normally proceed through all four phases over many years. When expressed specifically, a clinical trial phase is capitalized both in name and Roman numeral, such as "Phase I" clinical trial. If the drug successfully passes through Phases I, II, and III, it will usually be approved by the national regulatory authority for use in the general population. Phase IV trials are 'post-marketing' or 'surveillance' studies conducted to monitor safety over several years. == Preclinical studies == Before clinical trials are undertaken for a candidate drug, vaccine, medical device, or diagnostic assay, the product candidate is tested extensively in preclinical studies.


id: phases-of-clinical-research-20260505-1
file: data/en.wikipedia.org/wiki/Phases_of_clinical_research-1.md
category: reference
title: Phases of clinical research
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phases_of_clinical_research
date_saved: 2026-05-05T09:51:26.696563+00:00
instance: kb-cron
parent: phases-of-clinical-research-20260505-0
summary:
=== Phase Ia === Single ascending dose (Phase Ia): In single ascending dose studies, small groups of subjects are given a single dose of the drug while they are observed and tested for a period of time to confirm safety. Typically, a small number of participants, usually three, are entered sequentially at a particular dose. If they do not exhibit any adverse side effects, and the pharmacokinetic data are roughly in line with predicted safe values, the dose is escalated, and a new group of subjects is then given a higher dose. If unacceptable toxicity is observed in any of the three participants, an additional number of participants, usually three, are treated at the same dose. This is continued until pre-calculated pharmacokinetic safety levels are reached, or intolerable side effects start showing up (at which point the drug is said to have reached the maximum tolerated dose (MTD)). If an additional unacceptable toxicity is observed, then the dose escalation is terminated and that dose, or perhaps the previous dose, is declared to be the maximally tolerated dose. This particular design assumes that the maximally tolerated dose occurs when approximately one-third of the participants experience unacceptable toxicity. Variations of this design


id: phases-of-clinical-research-20260505-2
file: data/en.wikipedia.org/wiki/Phases_of_clinical_research-2.md
category: reference
title: Phases of clinical research
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phases_of_clinical_research
date_saved: 2026-05-05T09:51:26.696563+00:00
instance: kb-cron
parent: phases-of-clinical-research-20260505-0
summary:
=== Failure rate === Phase I trials historically have experienced the lowest success, having about a 66% failure rate due mainly to adverse effects and other toxicity concerns. A 2022 review found that about 90% of drug candidates fail over the course of Phases I-III, mainly due to absence of therapeutic efficacy, toxicity, non-specific drug properties, poor strategic planning, and recognition that the compound will not succeed commercially. == Phase III == This phase is designed to assess the effectiveness of the new intervention and, thereby, its value in clinical practice. Phase III studies are randomized controlled multicenter trials on large patient groups (300–3,000 or more depending upon the disease/medical condition studied) and are aimed at being the definitive assessment of how effective the drug is, in comparison with current 'gold standard' treatment. Because of their size and comparatively long duration, Phase III trials are the most expensive, time-consuming and difficult trials to design and run, especially in therapies for chronic medical conditions. Phase III trials of chronic conditions or diseases often have a short follow-up period for evaluation, relative to the period of time the intervention might be used in practice. It is common practice that certain Phase III


id: phases-of-clinical-research-20260505-3
file: data/en.wikipedia.org/wiki/Phases_of_clinical_research-3.md
category: reference
title: Phases of clinical research
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phases_of_clinical_research
date_saved: 2026-05-05T09:51:26.696563+00:00
instance: kb-cron
parent: phases-of-clinical-research-20260505-0
summary:
== Phase IV == A Phase IV trial is also known as a postmarketing surveillance trial or drug monitoring trial to assure long-term safety and effectiveness of the drug, vaccine, device or diagnostic test. Phase IV trials involve the safety surveillance (pharmacovigilance) and ongoing technical support of a drug after it receives regulatory approval to be sold. Phase IV studies may be required by regulatory authorities or may be undertaken by the sponsoring company for competitive (finding a new market for the drug) or other reasons (for example, the drug may not have been tested for interactions with other drugs, or on certain population groups such as pregnant women, who are unlikely to subject themselves to trials). The safety surveillance is designed to detect any rare or long-term adverse effects over a much larger patient population and longer time period than was possible during the Phase I-III clinical trials. Harmful effects discovered by Phase IV trials may result in a drug being withdrawn from the market or restricted to certain uses; examples include cerivastatin (brand names Baycol and Lipobay), troglitazone (Rezulin) and rofecoxib (Vioxx). == Overall cost == The entire process of developing a drug from preclinical research to marketing


id: placebo-controlled-study-20260505-0
file: data/en.wikipedia.org/wiki/Placebo-controlled_study-0.md
category: reference
title: Placebo-controlled study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Placebo-controlled_study
date_saved: 2026-05-05T09:51:27.963028+00:00
instance: kb-cron
parent: placebo-controlled-study-20260505-0
summary:
Placebo-controlled studies are a way of testing a medical therapy in which, in addition to a group of subjects that receives the treatment to be evaluated, a separate control group receives a sham "placebo" treatment which is specifically designed to have no real effect. Placebos are most commonly used in blinded trials, where subjects do not know whether they are receiving real or placebo treatment. Often, there is also a further "natural history" group that does not receive any treatment at all. The purpose of the placebo group is to account for the placebo effect, that is, effects from treatment that do not depend on the treatment itself. Such factors include knowing one is receiving a treatment, attention from health care professionals, and the expectations of a treatment's effectiveness by those running the research study. Without a placebo group to compare against, it is not possible to know whether the treatment itself had any effect. Patients frequently show improvement even when given a sham or "fake" treatment. Such intentionally inert placebo treatments can take many forms, such as a pill containing only sugar, or a medical device (such as an ultrasound machine) that is not actually turned on. Also, due


id: placebo-controlled-study-20260505-1
file: data/en.wikipedia.org/wiki/Placebo-controlled_study-1.md
category: reference
title: Placebo-controlled study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Placebo-controlled_study
date_saved: 2026-05-05T09:51:27.963028+00:00
instance: kb-cron
parent: placebo-controlled-study-20260505-0
summary:
the degree to which there is a considerably higher level of "placebo response" than one would expect is an index of the degree to which the drug's active ingredient is not efficacious. the degree to which there is a considerably lower level of "placebo response" than one would expect is an index of the degree to which, in some particular way, the placebo is not simulating the active drug in an appropriate way. However, in particular cases such as the use of Cimetidine to treat ulcers, a significant level of placebo response can also prove to be an index of how much the treatment has been directed at a wrong target. == Implementation issues == === Adherence === The Coronary Drug Project was intended to study the safety and effectiveness of drugs for long-term treatment of coronary heart disease in men. Those in the placebo group who adhered to the placebo treatment (took the placebo regularly as instructed) showed nearly half the mortality rate as those who were not adherent. A similar study of women similarly found survival was nearly 2.5 times greater for those who adhered to their placebo. This apparent placebo effect may have occurred because: Adhering to


id: placebo-controlled-study-20260505-2
file: data/en.wikipedia.org/wiki/Placebo-controlled_study-2.md
category: reference
title: Placebo-controlled study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Placebo-controlled_study
date_saved: 2026-05-05T09:51:27.963028+00:00
instance: kb-cron
parent: placebo-controlled-study-20260505-0
summary:
=== Jellinek and headache remedy ingredients === Jellinek in 1946 was asked to test whether or not the headache drug's overall efficacy would be reduced if certain ingredients were removed. In post-World War II 1946, pharmaceutical chemicals were restricted, and one U.S. headache remedy manufacturer sold a drug composed of three ingredients: a, b, and c, and chemical b was in particular short supply. Jellinek set up a complex trial involving 199 subjects, all of whom had "frequent headaches". The subjects were randomly divided into four test groups. He prepared four test drugs, involving various permutations of the three drug constituents, with a placebo as a scientific control. The structure of this trial is significant because, in those days, the only time placebos were ever used "was to express the efficacy or non-efficacy of a drug in terms of "how much better" the drug was than the "placebo". (Note that the trial conducted by Austin Flint is an example of such a drug efficacy vs. placebo efficacy trial.) The four test drugs were identical in shape, size, colour and taste: Drug A: contained a, b, and c. Drug B: contained a and c. Drug C: contained a and b. Drug


id: placebo-controlled-study-20260505-3
file: data/en.wikipedia.org/wiki/Placebo-controlled_study-3.md
category: reference
title: Placebo-controlled study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Placebo-controlled_study
date_saved: 2026-05-05T09:51:27.963028+00:00
instance: kb-cron
parent: placebo-controlled-study-20260505-0
summary:
== Declaration of Helsinki == From the time of the Hippocratic Oath questions of the ethics of medical practice have been widely discussed, and codes of practice have been gradually developed as a response to advances in scientific medicine. The Nuremberg Code, which was issued in August 1947, as a consequence of the so-called Doctors' Trial which examined the human experimentation conducted by Nazi doctors during World War II, offers ten principles for legitimate medical research, including informed consent, absence of coercion, and beneficence towards experiment participants. In 1964, the World Medical Association issued the Declaration of Helsinki, which specifically limited its directives to health research by physicians, and emphasized a number of additional conditions in circumstances where "medical research is combined with medical care". The significant difference between the 1947 Nuremberg Code and the 1964 Declaration of Helsinki is that the first was a set of principles that was suggested to the medical profession by the "Doctors' Trial" judges, whilst the second was imposed by the medical profession upon itself. Paragraph 29 of the Declaration makes specific mention of placebos: 29. The benefits, risks, burdens and effectiveness of a new method should be tested against those of the best


id: plackett-burman-design-20260505-0
file: data/en.wikipedia.org/wiki/Plackett–Burman_design-0.md
category: reference
title: Plackett–Burman design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Plackett–Burman_design
date_saved: 2026-05-05T09:51:29.193177+00:00
instance: kb-cron
parent: plackett-burman-design-20260505-0
summary:
Plackett–Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply. Their goal was to find experimental designs for investigating the dependence of some measured quantity on a number of independent variables (factors), each taking L levels, in such a way as to minimize the variance of the estimates of these dependencies using a limited number of experiments. Interactions between the factors were considered negligible. The solution to this problem is to find an experimental design where each combination of levels for any pair of factors appears the same number of times, throughout all the experimental runs (refer to table). A complete factorial design would satisfy this criterion, but the idea was to find smaller designs. For the case of two levels (L = 2), Plackett and Burman used the method found in 1933 by Raymond Paley for generating orthogonal matrices whose elements are all either 1 or −1 (Hadamard matrices). Paley's method could be used to find such matrices of size N for most N equal to a multiple of 4. In particular, it worked for all such N up to 100 except N = 92.


id: plackett-burman-design-20260505-1
file: data/en.wikipedia.org/wiki/Plackett–Burman_design-1.md
category: reference
title: Plackett–Burman design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Plackett–Burman_design
date_saved: 2026-05-05T09:51:29.193177+00:00
instance: kb-cron
parent: plackett-burman-design-20260505-0
summary:
== 4 to 48 runs, sorted to show half-fractions == P.B.4 + + + + – – – + – – – + P.B.8 + + + + + + + + + – – – – + + – + + – – – + – – – + + – – + + – + – – – + – + – + – – – + – – + + – – – + + – + P.B.12 + + + + + + + + + + + + + + + – – – + – – – + + – – – + – – + – + + – + – + + + – – – – + – – + – – + – + + – + – – – + – – + – + + – + + – – – + – – + + – + – + + + – – – + – – + – – + – + + + – – – – + + + – – – + – + – – + – – + – + +


id: plackett-burman-design-20260505-2
file: data/en.wikipedia.org/wiki/Plackett–Burman_design-2.md
category: reference
title: Plackett–Burman design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Plackett–Burman_design
date_saved: 2026-05-05T09:51:29.193177+00:00
instance: kb-cron
parent: plackett-burman-design-20260505-0
summary:
== References == This article incorporates public domain material from the National Institute of Standards and Technology


id: pocock-boundary-20260505-0
file: data/en.wikipedia.org/wiki/Pocock_boundary-0.md
category: reference
title: Pocock boundary
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pocock_boundary
date_saved: 2026-05-05T09:51:30.364390+00:00
instance: kb-cron
parent: pocock-boundary-20260505-0
summary:
The Pocock boundary is a method for determining whether to stop a clinical trial prematurely. The typical clinical trial compares two groups of patients. One group are given a placebo or conventional treatment, while the other group of patients are given the treatment that is being tested. The investigators running the clinical trial will wish to stop the trial early for ethical reasons if the treatment group clearly shows evidence of benefit. In other words, "when early results proved so promising it was no longer fair to keep patients on the older drugs for comparison, without giving them the opportunity to change." The concept was introduced by the medical statistician Stuart Pocock in 1977. The many reasons underlying when to stop a clinical trial for benefit were discussed in his editorial from 2005. == Details == The Pocock boundary gives a p-value threshold for each interim analysis which guides the data monitoring committee on whether to stop the trial. The boundary used depends on the number of interim analyses. The Pocock boundary is simple to use in that the p-value threshold is the same at each interim analysis. The disadvantages are that the number of interim analyses must be fixed


id: provocation-test-20260505-0
file: data/en.wikipedia.org/wiki/Provocation_test-0.md
category: reference
title: Provocation test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Provocation_test
date_saved: 2026-05-05T09:51:31.547405+00:00
instance: kb-cron
parent: provocation-test-20260505-0
summary:
A provocation test, also called a provocation trial or provocation study, is a form of medical clinical trial whereby participants are exposed to either a substance or "thing" that is claimed to provoke a response, or to a sham substance or device that should provoke no response, or a severe exercise as in Erb's test for low serum calcium . An example of a provocation test, performed on an individual, is a skin allergy test. == See also == Blind experiment Control group == References ==


id: pseudoreplication-20260505-0
file: data/en.wikipedia.org/wiki/Pseudoreplication-0.md
category: reference
title: Pseudoreplication
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pseudoreplication
date_saved: 2026-05-05T09:51:32.728123+00:00
instance: kb-cron
parent: pseudoreplication-20260505-0
summary:
Pseudoreplication (sometimes unit of analysis error) has many definitions. Pseudoreplication was originally defined in 1984 by Stuart H. Hurlbert as the use of inferential statistics to test for treatment effects with data from experiments where either treatments are not replicated (though samples may be) or replicates are not statistically independent. Subsequently, Millar and Anderson identified it as a special case of inadequate specification of random factors where both random and fixed factors are present. It is sometimes narrowly interpreted as an inflation of the number of samples or replicates which are not statistically independent. This definition omits the confounding of unit and treatment effects in a misspecified F-ratio. In practice, incorrect F-ratios for statistical tests of fixed effects often arise from a default F-ratio that is formed over the error rather the mixed term. Lazic defined pseudoreplication as a problem of correlated samples (e.g. from longitudinal studies) where correlation is not taken into account when computing the confidence interval for the sample mean. For the effect of serial or temporal correlation also see Markov chain central limit theorem. The problem of inadequate specification arises when treatments are assigned to units that are subsampled and the treatment F-ratio in an analysis


id: quasi-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Quasi-experiment-0.md
category: reference
title: Quasi-experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quasi-experiment
date_saved: 2026-05-05T09:51:33.934268+00:00
instance: kb-cron
parent: quasi-experiment-20260505-0
summary:
A quasi-experiment is a research design used to estimate the causal impact of an intervention. This research design is aimed at assessing the difference between outcomes (e.g., reading knowledge, depressive symptoms) in a group that experienced an intervention and a group that did not. The intervention is broadly construed such that it could be designed by researchers (e.g., a reading program) or it could be an event affecting a group of people such as disaster (e.g., an earthquake). Quasi-experiments share similarities with experiments and randomized controlled trials, but specifically lack random assignment to intervention and control conditions. Instead, quasi-experimental designs typically compare groups that are either preexisting (e.g., whether someone was exposed to COVID-19) or groups that were created without random assignment (e.g., students attending schools with different reading programs). The causal analysis of quasi-experiments depends on assumptions that render non-randomness irrelevant, for example, the parallel trends assumption for difference-in-differences (DiD) method. Quasi-experiments are subject to concerns about internal validity. In other words, it may be difficult to convincingly demonstrate a causal link between the treatment and control conditions on the observed outcomes in quasi-experimental designs. This is particularly true if there are confounding variables that cannot be controlled or


id: quasi-experiment-20260505-1
file: data/en.wikipedia.org/wiki/Quasi-experiment-1.md
category: reference
title: Quasi-experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quasi-experiment
date_saved: 2026-05-05T09:51:33.934268+00:00
instance: kb-cron
parent: quasi-experiment-20260505-0
summary:
Difference in differences (pre-post with-without comparison) Event study Nonequivalent control groups design no-treatment control group designs nonequivalent dependent variables designs removed treatment group designs repeated treatment designs reversed treatment nonequivalent control groups designs cohort designs post-test only designs regression continuity designs Regression discontinuity design Case-control design time-series designs multiple time series design interrupted time series design instrumental variables Panel analysis Of all of these designs, the regression discontinuity design comes the closest to the experimental design, as the experimenter maintains control of the treatment assignment and it is known to "yield an unbiased estimate of the treatment effects". It does, however, require large numbers of study participants and precise modeling of the functional form between the assignment and the outcome variable, in order to yield the same power as a traditional experimental design. Though quasi-experiments are sometimes shunned by those who consider themselves to be experimental purists (leading Donald T. Campbell to coin the term "queasy experiments" for them), they can be useful in areas where it is not feasible or desirable to conduct an experiment or randomized control trial. Such instances include evaluating the impact of public policy changes, educational interventions or large scale health interventions. The primary drawback


id: quasi-experiment-20260505-2
file: data/en.wikipedia.org/wiki/Quasi-experiment-2.md
category: reference
title: Quasi-experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quasi-experiment
date_saved: 2026-05-05T09:51:33.934268+00:00
instance: kb-cron
parent: quasi-experiment-20260505-0
summary:
== Disadvantages == Quasi-experimental estimates of impact are subject to contamination by confounding variables. In the example above, a variation in the children's response to spanking is plausibly influenced by factors that cannot be easily measured and controlled, for example the child's intrinsic wildness or the parent's irritability. The lack of random assignment in the quasi-experimental design method may allow studies to be more feasible, but this also poses many challenges for the investigator in terms of internal validity. This deficiency in randomization makes it harder to rule out confounding variables and introduces new threats to internal validity. Because randomization is absent, some knowledge about the data can be approximated, but conclusions of causal relationships are difficult to determine due to a variety of extraneous and confounding variables that exist in a social environment. Moreover, even if these threats to internal validity are assessed, causation still cannot be fully established because the experimenter does not have total control over extraneous variables. Disadvantages also include the study groups may provide weaker evidence because of the lack of randomness. Randomness brings a lot of useful information to a study because it broadens results and therefore gives a better representation of the population


id: random-assignment-20260505-0
file: data/en.wikipedia.org/wiki/Random_assignment-0.md
category: reference
title: Random assignment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Random_assignment
date_saved: 2026-05-05T09:51:35.110967+00:00
instance: kb-cron
parent: random-assignment-20260505-0
summary:
Random assignment or random placement is an experimental technique for assigning human participants or animal subjects to different groups in an experiment (e.g., a treatment group versus a control group) using randomization, such as by a chance procedure (e.g., flipping a coin) or a random number generator. This ensures that each participant or subject has an equal chance of being placed in any group. Random assignment of participants helps to ensure that any differences between and within the groups are not systematic at the outset of the experiment. Thus, any differences between groups recorded at the end of the experiment can be more confidently attributed to the experimental procedures or treatment. Random assignment, blinding, and controlling are key aspects of the design of experiments because they help ensure that the results are not spurious or deceptive via confounding. This is why randomized controlled trials are vital in clinical research, especially ones that can be double-blinded and placebo-controlled. Mathematically, there are distinctions between randomization, pseudorandomization, and quasirandomization, as well as between random number generators and pseudorandom number generators. How much these differences matter in experiments (such as clinical trials) is a matter of trial design and statistical rigor, which affect evidence


id: randomization-20260505-0
file: data/en.wikipedia.org/wiki/Randomization-0.md
category: reference
title: Randomization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Randomization
date_saved: 2026-05-05T09:51:37.479553+00:00
instance: kb-cron
parent: randomization-20260505-0
summary:
Randomization is a statistical process in which a random mechanism is employed to select a sample from a population or assign subjects to different groups. The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing selection bias and enhancing the statistical validity. It facilitates the objective comparison of treatment effects in experimental design, as it equates groups statistically by balancing both known and unknown factors at the outset of the study. In statistical terms, it underpins the principle of probabilistic equivalence among groups, allowing for the unbiased estimation of treatment effects and the generalizability of conclusions drawn from sample data to the broader population. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern but follow an evolution described by probability distributions. For example, a random sample of individuals from a population refers to a sample where every individual has a known probability of being sampled. This would be contrasted with nonprobability sampling, where arbitrary individuals are selected. A runs test can be used to determine whether the occurrence of a set of measured values is random. Randomization


id: randomization-20260505-1
file: data/en.wikipedia.org/wiki/Randomization-1.md
category: reference
title: Randomization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Randomization
date_saved: 2026-05-05T09:51:37.479553+00:00
instance: kb-cron
parent: randomization-20260505-0
summary:
== Randomization in statistical analysis == Randomization is a core principle in statistical theory, whose importance was emphasized by Charles S. Peirce in "Illustrations of the Logic of Science" (1877–1878) and "A Theory of Probable Inference" (1883). Its application in statistical methodologies is multifaceted and includes critical processes such as randomized controlled experiments, survey sampling and simulations. === Randomized controlled experiment === In the realm of scientific research, particularly within clinical study designs, constraints such as limited manpower, material resources, financial backing, and time necessitate a selective approach to participant inclusion. Despite the broad spectrum of potential participants who fulfill the inclusion criteria, it is impractical to incorporate every eligible individual in the target population due to these constraints. Therefore, a representative subset of treatment groups is chosen based on the specific requirements of the research. A randomized sampling method is employed to ensure the integrity and representativeness of the study. This method ensures that all qualified subjects within the target population have an equal opportunity to be selected. Such a strategy is pivotal in mirroring the overall characteristics of the target population and in mitigating the risk of selection bias. The selected samples (or continuous non-randomly sampled samples) are


id: randomized-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Randomized_experiment-0.md
category: reference
title: Randomized experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Randomized_experiment
date_saved: 2026-05-05T09:51:39.917852+00:00
instance: kb-cron
parent: randomized-experiment-20260505-0
summary:
In science, randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects. Randomization-based inference is especially important in experimental design and in survey sampling. == Overview == In the statistical theory of design of experiments, randomization involves randomly allocating the experimental units across the treatment groups. For example, if an experiment compares a new drug against a standard drug, then the patients should be allocated to either the new drug or to the standard drug control using randomization. Randomized experimentation is not haphazard. Randomization reduces bias by equalising other factors that have not been explicitly accounted for in the experimental design (according to the law of large numbers). Randomization also produces ignorable designs, which are valuable in model-based statistical inference, especially Bayesian or likelihood-based. In the design of experiments, the simplest design for comparing treatments is the "completely randomized design". Some "restriction on randomization" can occur with blocking and experiments that have hard-to-change factors; additional restrictions on randomization can occur when a full randomization is infeasible or when it is desirable to reduce the variance of estimators of selected effects. Randomization of treatment in clinical trials pose ethical problems. In some cases,


id: regression-discontinuity-design-20260505-0
file: data/en.wikipedia.org/wiki/Regression_discontinuity_design-0.md
category: reference
title: Regression discontinuity design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Regression_discontinuity_design
date_saved: 2026-05-05T09:51:41.067762+00:00
instance: kb-cron
parent: regression-discontinuity-design-20260505-0
summary:
Regression discontinuity designs (RDD) are a quasi-experimental pretest–posttest design that attempts to determine the causal effects of interventions by assigning a cutoff or threshold above or below which an intervention is assigned. By comparing observations lying closely on either side of the threshold, it is possible to estimate the average treatment effect in environments where random assignment to conditions is unfeasible. True causal inference using RDDs is still impossible, because the RDD cannot account for the potentially confounding effects of other variables without randomization. The RDD was originally applied by Donald Thistlethwaite and Donald Campbell (1960) to evaluate the effect of scholarship programs on student career plans. The RDD is used in disciplines like psychology, economics, political science, epidemiology, and other related disciplines. Recent comparisons of randomised controlled trials (RCTs) and RDDs have empirically demonstrated the internal validity of the design. == Example == The intuition behind the RDD is well illustrated using the evaluation of merit-based scholarships. The main problem with estimating the causal effect of such an intervention is the homogeneity of performance to the assignment of treatment (e.g., a scholarship award). Since high-performing students are more likely to be awarded the merit scholarship and continue performing well


id: regression-discontinuity-design-20260505-1
file: data/en.wikipedia.org/wiki/Regression_discontinuity_design-1.md
category: reference
title: Regression discontinuity design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Regression_discontinuity_design
date_saved: 2026-05-05T09:51:41.067762+00:00
instance: kb-cron
parent: regression-discontinuity-design-20260505-0
summary:
== Required assumptions == Regression discontinuity design requires that all potentially relevant variables besides the treatment variable and outcome variable be continuous at the point where the treatment and outcome discontinuities occur. One sufficient, though not necessary, condition is if the treatment assignment is "as good as random" at the threshold for treatment. If this holds, then it guarantees that those who just barely received treatment are comparable to those who just barely did not receive treatment, as treatment status is effectively random. Treatment assignment at the threshold can be "as good as random" if there is randomness in the assignment variable and the agents considered (individuals, firms, etc.) cannot perfectly manipulate their treatment status. For example, suppose the treatment is passing an exam, where a grade of 50% is required. In this case, this example is a valid regression discontinuity design so long as grades are somewhat random, due either to the randomness of grading or randomness of student performance. Students must not also be able to perfectly manipulate their grade so as to determine their treatment status perfectly. Two examples include students being able to convince teachers to "mercy pass" them, or students being allowed to retake the


id: regression-discontinuity-design-20260505-2
file: data/en.wikipedia.org/wiki/Regression_discontinuity_design-2.md
category: reference
title: Regression discontinuity design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Regression_discontinuity_design
date_saved: 2026-05-05T09:51:41.067762+00:00
instance: kb-cron
parent: regression-discontinuity-design-20260505-0
summary:
== Disadvantages == The estimated effects are only unbiased if the functional form of the relationship between the treatment and outcome is correctly modelled. The most popular caveats are non-linear relationships that are mistaken as a discontinuity. Contamination by other treatments. Suppose another treatment occurs at the same cutoff value of the same assignment variable. In that case, the measured discontinuity in the outcome variable may be partially attributed to this other treatment. For example, suppose a researcher wishes to study the impact of legal access to alcohol on mental health using a regression discontinuity design at the minimum legal drinking age. The measured impact could be confused with legal access to gambling, which may occur at the same age. == Extensions == === Fuzzy RDD === The identification of causal effects hinges on the crucial assumption that there is indeed a sharp cut-off, around which there is a discontinuity in the probability of assignment from 0 to 1. In reality, however, cutoffs are often not strictly implemented (e.g. exercised discretion for students who just fell short of passing the threshold) and the estimates will hence be biased. In contrast to the sharp regression discontinuity design, a fuzzy regression discontinuity


id: replication-statistics-20260505-0
file: data/en.wikipedia.org/wiki/Replication_(statistics)-0.md
category: reference
title: Replication (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Replication_(statistics)
date_saved: 2026-05-05T09:51:43.532403+00:00
instance: kb-cron
parent: replication-statistics-20260505-0
summary:
In engineering, science, and statistics, replication is the process of repeating a study or experiment under the same or similar conditions. It is a crucial step to test the original claim and confirm or reject the accuracy of results as well as for identifying and correcting the flaws in the original experiment. ASTM, in standard E1847, defines replication as "... the repetition of the set of all the treatment combinations to be compared in an experiment. Each of the repetitions is called a replicate." For a full factorial design, replicates are multiple experimental runs with the same factor levels. You can replicate combinations of factor levels, groups of factor level combinations, or even entire designs. For instance, consider a scenario with three factors, each having two levels, and an experiment that tests every possible combination of these levels (a full factorial design). One complete replication of this design would comprise 8 runs ( 2 3 {\displaystyle 2^{3}} ). The design can be executed once or with several replicates. There are two main types of replication in statistics. First, there is a type called “exact replication” (also called "direct replication"), which involves repeating the study as closely as possible to the


id: resentful-demoralization-20260505-0
file: data/en.wikipedia.org/wiki/Resentful_demoralization-0.md
category: reference
title: Resentful demoralization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Resentful_demoralization
date_saved: 2026-05-05T09:51:44.708773+00:00
instance: kb-cron
parent: resentful-demoralization-20260505-0
summary:
Resentful demoralization is an issue in controlled experiments in which those in the control group become resentful of not receiving the experimental treatment. Alternatively, the experimental group could be resentful of the control group, if the experimental group perceive its treatment as inferior. They may become angry, depressed, uncooperative, or non-compliant. This may lead to significant systematic differences in the outcome of the control group, obscuring the results of the study and threatening their validity. Resentful demoralization can also make participants less likely to join future studies. If people feel treated unfairly or get upset with their treatment, they might not want to be part of research again. This can lead to fewer participants and affect the quality of future studies. So, it's important to address these feelings to keep participants engaged and ensure good research outcomes. == See also == Clinical trial Randomized controlled trial == External links == Resentful Demoralization in Encyclopedia of Statistics in Behavioral Science. (subscription required)


id: response-surface-methodology-20260505-0
file: data/en.wikipedia.org/wiki/Response_surface_methodology-0.md
category: reference
title: Response surface methodology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Response_surface_methodology
date_saved: 2026-05-05T09:51:45.870436+00:00
instance: kb-cron
parent: response-surface-methodology-20260505-0
summary:
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. RSM is an empirical model which employs the use of mathematical and statistical techniques to relate input variables, otherwise known as factors, to the response. RSM became very useful because other methods available, such as the theoretical model, could be very cumbersome to use, time-consuming, inefficient, error-prone, and unreliable. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process. Statistical approaches such as RSM can be employed to maximize the production of a special substance by optimization of operational factors. Of late, for formulation optimization, the RSM, using proper design of experiments (DoE), has become extensively used. In contrast to conventional methods, the interaction among process variables can be determined by statistical techniques. == Basic


id: restricted-randomization-20260505-0
file: data/en.wikipedia.org/wiki/Restricted_randomization-0.md
category: reference
title: Restricted randomization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Restricted_randomization
date_saved: 2026-05-05T09:51:47.072793+00:00
instance: kb-cron
parent: restricted-randomization-20260505-0
summary:
In statistics, restricted randomization occurs in the design of experiments and in particular in the context of randomized experiments and randomized controlled trials. Restricted randomization allows intuitively poor allocations of treatments to experimental units to be avoided, while retaining the theoretical benefits of randomization. For example, in a clinical trial of a new proposed treatment of obesity compared to a control, an experimenter would want to avoid outcomes of the randomization in which the new treatment was allocated only to the heaviest patients. The concept was introduced by Frank Yates (1948) and William J. Youden (1972) "as a way of avoiding bad spatial patterns of treatments in designed experiments." == Example of nested data == Consider a batch process that uses 7 monitor wafers in each run. The plan further calls for measuring a response variable on each wafer at each of 9 sites. The organization of the sampling plan has a hierarchical or nested structure: the batch run is the topmost level, the second level is an individual wafer, and the third level is the site on the wafer. The total amount of data generated per batch run will be 7 · 9 = 63 observations. One approach to


id: restricted-randomization-20260505-1
file: data/en.wikipedia.org/wiki/Restricted_randomization-1.md
category: reference
title: Restricted randomization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Restricted_randomization
date_saved: 2026-05-05T09:51:47.072793+00:00
instance: kb-cron
parent: restricted-randomization-20260505-0
summary:
==== Example: some factors hard to vary ==== Consider running the experiment under the first condition listed above, with the factor solution concentration of the plating agent (S) being hard to vary. Since this factor is hard to vary, the experimenter would like to randomize the treatment combinations so that the solution concentration factor has a minimal number of changes. In other words, the randomization of the treatment runs is restricted somewhat by the level of the solution concentration factor. As a result, the treatment combinations might be randomized such that those treatment runs corresponding to one level of the concentration (−1) are run first. Each copper strip is individually plated, meaning only one strip at a time is placed in the solution for a given treatment combination. Once the four runs at the low level of solution concentration have been completed, the solution is changed to the high level of concentration (1), and the remaining four runs of the experiment are performed (where again, each strip is individually plated). Once one complete replicate of the experiment has been completed, a second replicate is performed with a set of four copper strips processed for a given level of solution concentration


id: restricted-randomization-20260505-2
file: data/en.wikipedia.org/wiki/Restricted_randomization-2.md
category: reference
title: Restricted randomization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Restricted_randomization
date_saved: 2026-05-05T09:51:47.072793+00:00
instance: kb-cron
parent: restricted-randomization-20260505-0
summary:
==== Example: experimental units processed individually ==== Consider running the experiment under the third scenario listed above. There is only one copper strip in the solution at one time. However, two strips, one at the low current and one at the high current, are processed one right after the other under the same temperature and concentration setting. Once two strips have been processed, the concentration is changed and the temperature is reset to another combination. Two strips are again processed, one after the other, under this temperature and concentration setting. This process is continued until all 16 copper strips have been processed. Running the experiment in this way also results in a split-plot design in which the whole-plot factors are again solution concentration and solution temperature and the subplot factor is current. In this experiment, one size experimental unit is an individual copper strip. The treatment or factor that was applied to the individual strips is current (this factor was changed each time for a different strip within the solution). The other or larger-size experimental unit is a set of two copper strips. The treatments or factors that were applied to a pair of two strips are solution concentration and


id: restricted-randomization-20260505-3
file: data/en.wikipedia.org/wiki/Restricted_randomization-3.md
category: reference
title: Restricted randomization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Restricted_randomization
date_saved: 2026-05-05T09:51:47.072793+00:00
instance: kb-cron
parent: restricted-randomization-20260505-0
summary:
=== Strip-plot example: two steps and three factor variables === Consider the following example from the semiconductor industry. An experiment requires an implant step and an anneal step. At both the anneal and the implant steps there are three factors to test. The implant process accommodates 12 wafers in a batch, and implanting a single wafer under a specified set of conditions is not practical nor does doing so represent economical use of the implanter. The anneal furnace can handle up to 100 wafers. The settings for a two-level factorial design for the three factors in the implant step are denoted (A, B, C), and a two-level factorial design for the three factors in the anneal step are denoted (D, E, F). Also present are interaction effects between the implant factors and the anneal factors. Therefore, this experiment contains three sizes of experimental units, each of which has a unique error term for estimating the significance of effects. To put actual physical meaning to each of the experimental units in the above example, consider each combination of implant and anneal steps as an individual wafer. A batch of eight wafers goes through the implant step first. Treatment combination 3 in


id: riffle-splitter-20260505-0
file: data/en.wikipedia.org/wiki/Riffle_splitter-0.md
category: reference
title: Riffle splitter
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Riffle_splitter
date_saved: 2026-05-05T09:51:48.272622+00:00
instance: kb-cron
parent: riffle-splitter-20260505-0
summary:
The riffle splitter is a device used to divide a bulk sample of material into smaller, representative sub-samples. It can be used in laboratory settings or fieldwork. The device is usually constructed with steel sheet and should be designed to have an even number of opposing inclined chutes (the riffles), with each chute having the same width. The recommended chute width should be at least 2.5× the size of the maximum particle diameter that can be found in the lot to be split. Riffle splitters are typically used in assay and analytical laboratories to reduce the size of samples provided from other sources (crushed rock, soils, powders and so on) to a lot size that is appropriate for the next stage of analytical sample preparation. == Design == There are many different versions of the riffle splitter. However, not all can be considered correct sub-sampling devices, in that the two sub-sample halves are deemed to be representative of the original lot. The issue of correctness of a riffles split sub-sample are function of both the design and the use of the splitter. The design key items are: The splitter should have an even number of riffles so the two sub


id: round-robin-test-20260505-0
file: data/en.wikipedia.org/wiki/Round-robin_test-0.md
category: reference
title: Round-robin test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Round-robin_test
date_saved: 2026-05-05T09:51:49.467773+00:00
instance: kb-cron
parent: round-robin-test-20260505-0
summary:
In experimental methodology, a round-robin test is an interlaboratory test (measurement, analysis, or experiment) performed independently several times. This can involve multiple independent scientists performing the test with the use of the same method in different equipment, or a variety of methods and equipment. In reality it is often a combination of the two, for example if a sample is analysed, or one (or more) of its properties is measured by different laboratories using different methods, or even just by different units of equipment of identical construction. A round-robin program is a measurement systems analysis technique which uses analysis of variance (ANOVA) random effects model to assess a measurement system. == Round-robin tests regarding occupational safety and health == Companies are obliged to determine whether hazardous substances are in the air at the workplace by using appropriate measurements. To maintain the quality parameters for analytic procedures, the quality assurance methods are to be applied that are state-of-the-art. The Institute for Occupational Safety and Health of the German Social Accident Insurance (IFA) provides proficiency testing as support and assistance for the measuring stations worldwide for the purpose of self-examination and for the external presentation of quality standards. The PT schemes are


id: royal-commission-on-animal-magnetism-20260505-0
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-0.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
The Royal Commission on Animal Magnetism involved two entirely separate and independent French Royal Commissions, each appointed by Louis XVI in 1784, that were conducted simultaneously by a committee composed of four physicians from the Paris Faculty of Medicine (Faculté de médecine de Paris) and five scientists from the Royal Academy of Sciences (Académie des sciences) (the "Franklin Commission", named for Benjamin Franklin), and a second committee composed of five physicians from the Royal Society of Medicine (Société Royale de Médecine) (the "Society Commission"). Each Commission took five months to complete its investigations. The "Franklin" Report was presented to the King on 11 August 1784 – and was immediately published and very widely circulated throughout France and neighbouring countries – and the "Society" Report was presented to the King five days later on 16 August 1784. The "Franklin Commission's" investigations are notable as a very early "classic" example of a systematic controlled trial, which not only applied "sham" and "genuine" procedures to patients with "sham" and "genuine" disorders, but, significantly, was the first to use the "blindfolding" of both the investigators and their subjects. The report of the ["Franklin"] Royal Commission of 1784 ... is a masterpiece of its genre,


id: royal-commission-on-animal-magnetism-20260505-1
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-1.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
From the perspective of a given phenomenon, one can look down to the entities and activities composing it. One can look up to the higher-level mechanisms of which it is a component. One can look back to the mechanisms that come before it or by which it developed. One can look forward to what comes after it. [And, finally] one can look around to see the wider context with which it operates. === Tensions within the royal family === Prior to his arrival in Paris in 1777 – with a letter of recommendation from Chancellor von Kaunitz of the Habsburg monarchy to the Austrian Ambassador to France, the Comte de Mercy-Argenteau (who, in turn, introduced Mesmer to Jean-Baptiste Le Roy (1720–1800), the Director of the Academy of Sciences) – Mesmer was already known to Marie Antoinette. At the urging of her two closest friends, Marie-Paule Angélique d’Albert de Luynes (1744–1781), "the Duchesse de Chaulnes" and Marie Thérèse Louise de Savoie-Carignan (1749–1792), "the Princess of Lamballe", both of whom "had benefited from Mesmer's treatment", Marie Antoinette had been able to arrange for both Mesmer and d'Eslon to be officially "interviewed" by (an otherwise unidentified) representative of the King on 14 March


id: royal-commission-on-animal-magnetism-20260505-2
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-2.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
=== Scientific issues === In a prevailing atmosphere of "[an overall] redefinition of frontiers in the legitimacy of knowledge" – and, in relation to Mesmer's claims, a redefinition "which did not necessarily match the public popularity that they attracted" (Zanetti, 2018), p. 59) – the issue of the existence (or not) of a substantial "magnetic fluid" and/or "animal magnetism" required resolution. === Medical issues === At a time when, in relation to "healers and healing", the conglomerate of "physicians, empirics, surgeons, apothecaries, folk healers, and religious personalities all vied with each other (as well as worked together) for medical legitimacy and patients" (Broomhall, 2004, p. 5), Mesmer was not only a "foreign national", but also one that had no affiliation of any kind with any known professional medical association within France (or elsewhere in Europe); and, as a consequence, his professional conduct, his medical practice, his medico-commercial enterprises, and his therapeutic endeavours were not regulated in any way. Moreover, the efficacy of Mesmer's interventions had never been objectively tested, neither the agency nor the (pre- and post-intervention) veracity of his supposed "cures" had ever been objectively verified, and, finally, in relation to the presenting conditions of those with (supposedly) 'real'


id: royal-commission-on-animal-magnetism-20260505-3
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-3.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
The second of the two Royal Commissions, usually referred to as the "Society Commission", was appointed on 5 April 1784. It was composed of five eminent physicians from the Royal Society of Medicine – the physician and one of the first members of the Royal Society, Charles-Louis-François Andry (1741–1829), the physician Claude-Antoine Caille (b. 1743), the botanist Antoine Laurent de Jussieu (1748–1836), the physician, Collège de France professor, one of the original directors of the Royal Society, and committed advocate of the therapeutic applications of electricity, Pierre Jean Claude Mauduyt de La Varenne (1732–1792), and the physician and Professor of chemistry in the Collège de France, Pierre-Isaac Poissonnier (1720–1798) – and, as Pattie remarks (1994, p. 156), "the impression given by [their] report is that the commissioners were busy practitioners who wanted to devote no more time to the project than was necessary". Although the investigations of the "Society Commission" were less thorough and less detailed than those of the "Franklin Commission" they were essentially of the same nature, and it is a matter of fact that neither Commission examined Mesmer's practices – they only examined the practices of d'Eslon. == Franz Mesmer == Franz Anton Mesmer (1734–1815), born in


id: royal-commission-on-animal-magnetism-20260505-4
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-4.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
=== A concept that must not be reified === It is clear from his Mémoire (1799) that Mesmer was very aware of the human propensity – in the normal, conventional use of language (la langue de convention) – to speak of "properties" or "qualities" (i.e., these "metaphysical abstractions", illusions de la méthaphysique), as if they were "substances": in Mesmer's words, "substantivise the properties", substantisia les propriétés (Mesmer 1799, pp. 15–17). – in other words, "reification", in the manner of Whitehead's "fallacy of misplaced concreteness". Mesmer was also well aware of the extent to which, through the "distortion" caused by these "substantive words" (mot substantif) – which inappropriately "personified" (personnifia) these metaphysical abstractions (p. 16) – one is induced to believe in the actual physical existence of the "substance" itself. Given these observations, Mesmer was most emphatic in his continuous warnings that his abstract "principles" should not be "substantivised". It is significant that Mesmer (1799) describes how, once he had formulated the abstract, overarching (metaphorical) construct/concept of "animal magnetism" as the therapeutic agent (a quarter of a century earlier) – and with his hope that this newly described "principle of action" (principe de action), when considered as an agent, "could become


id: royal-commission-on-animal-magnetism-20260505-5
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-5.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
=== Post-Mesmer === In late 1782, and eighteen months before the Royal Commission, d'Eslon had (acrimoniously) parted ways with Mesmer; and, despite a brief reconciliation, the relationship was terminated in late 1783. On 28 December 1783, d'Eslon wrote a letter to the Journal de Paris, which not only described the difficulties he had experienced with Mesmer, but also announced that he was opening his own (entirely independent) clinic. Following his break with Mesmer, d'Eslon not only launched his own clinical operation on his break with Mesmer, d'Eslon took all of the patients he had brought to Mesmer with him – but also began teaching his own theories and practices (i.e., rather than those of Mesmer). According to d'Eslon's own account (d'Eslon, 1784b, pp. 25–26), Mesmer had taught 300 students, 160 of whom were medical men (médecins), and d'Eslon himself had taught 160 medical men (this group included 21 members of the Paris Faculty of Medicine). Given that many of those who had privately paid Mesmer for the details of "the secret" were greatly dissatisfied, and had "[justifiably] accused [Mesmer] of having enunciated a theory which was merely a collection of obscure principles" (Binet & Féré, 1888, p. 13), it seems


id: royal-commission-on-animal-magnetism-20260505-6
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-6.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
[The baquet] is a vat about six to seven feet, more or less, in diameter by eighteen inches in height. There is a double bottom in the interior of this vat, in which fragments of broken bottles, gravel, stones, and sticks of pounded sulfur and iron filings are placed. All of this is filled with water and covered up with a floor nailed into the vat. On the surface of the lid, six inches in from the rim, one makes various holes in order to allow the passage of iron rods which are arranged so that one end penetrates the bottom of the vat and the other is directed, by means of a curve, over the pit of the stomach of the patient or other affected parts of the body. Mesmer specifically stressed the primary importance of the patients' hand-holding as a factor in the "augmentation" of the force/quality of the power of the "animal magnetism". Moreover, and significantly, Mesmer (separately) acknowledged that, if it was ever to come to pass that he had a suitable "establishment" – i.e., one with sufficient space available for all the assembled patients to hold hands – he would "abolish the use of baquets"


id: royal-commission-on-animal-magnetism-20260505-7
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-7.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
In his response to the Reports (d'Eslon, 1784b, pp. 21–22), d'Eslon complained that the Commissioners' emphasis on "convulsions" was not justified: among those who received group treatment during the commission's investigations (i.e., involving "50 to 60 individuals"), he wrote, there were never more than six or seven who displayed "convulsions" to any degree – and, further, of the more than 500 patients he had treated over the preceding three years, only 20 of those had manifested "convulsions" (and almost all of those had been suffering from "convulsions" before presenting for any treatment from d'Eslon). He also rejected the suggestions of any connection between the "convulsions" of epilepsy and those of the "crises", citing the cases of two of his patients, who were epileptic and "frequently had seizures at home", who never had a single "attack" during their treatment at his clinic (p. 23). Joseph Michel Antoine Servan, the one time Advocate-General to the Parlement of Grenoble, who reported (at Servan, 1784, p. 3) that, in "the Provinces" – where the various social classes were not kept apart around "the baquet", as they were in Paris – that, in relation to the concerns that the Commissioners expressed in relation to the


id: royal-commission-on-animal-magnetism-20260505-8
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-8.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
=== The substantial existence of "animal magnetism" and "magnetic fluid" were investigated === Rather than being concerned with the applications, utility, and clinical efficacy of d'Eslon's "animal magnetism", the primary concern of each Commission was the significant, crucial, and exclusive question of whether or not d'Eslon's (supposed) "animal magnetic fluid" actually existed in some substantial physical way – for the simple reason that, as the two sets of Commissioners each noted in their independent reports, "Animal magnetism may well exist without being useful but it cannot be useful if it does not exist." === Mesmer's earlier refusal to have his "magnetic" interventions scrutinized === Already, in his earlier (18 September 1780) interaction with the Paris Faculty of Medicine, Mesmer had refused to have his therapeutic interventions on a set of entirely "new" patients directly scrutinized, claiming that his already-achieved "cures" were an objective matter of record. Mesmer justified his refusal as follows: Here is what I said to M. de Lassonne; however bizarre [it may seem] at first sight it is nevertheless entirely serious and very much applicable to the question. When a thief is convicted of theft he is hanged: when a murderer is convicted of murder he is


id: royal-commission-on-animal-magnetism-20260505-9
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-9.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
it was [their] duty ... to confine themselves to arguments purely physical, that is, to the momentaneous [sic] effects of the fluid upon the animal frame, excluding from these effects all the illusions which might mix with them, and assuring themselves that they could proceed from no other cause than the animal magnetism." === Problems with objectively determining the precise therapeutic action of any supposed "efficacious remedy" === In support of its decision, the "Franklin Commission" produced a cogent, extended argument, consistent with the medical knowledge of the day, that is equally relevant to similar investigations in the present day: The majority of diseases have their seat in the interior part of our frame. The collective experience of a great number of centuries has made us acquainted with the symptoms, which indicate and discriminate them; the same experience has taught the method in which they are to be treated. What is the object of the efforts of the physician in this method? It is not to oppose and to subdue nature, it is to assist her in her operations. Nature, says the father of the medical science [viz., Hippocrates], cures the diseased; but sometimes she encounters obstacles, which constrain her


id: royal-commission-on-animal-magnetism-20260505-10
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-10.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
They saw in the centre of a large apartment a circular box, made of oak, and about a foot or a foot and an [sic] half deep, which is called the bucket [baquet]; the lid of this box is pierced with a number of holes, in which are inserted branches of iron, elbowed and moveable. The patients are arranged in ranks about this [baquet], and each has his branch of iron, which by means of the elbow may be applied immediately to the part affected; a cord passed round their bodies connects them one with the other: sometimes a second means of communication is introduced, by the insertion of the thumb of each patient between the forefinger and thumb of the patient next him; the thumb thus inserted is pressed by the person holding it; the impression received by the left hand of the patient, communicates through his right, and thus passes through the whole circle.A piano forté is placed in one corner of the apartment, and different airs are played with various degrees of rapidity; vocal music is sometimes added to the instrumental.The persons who superintend the process, have each of them an iron rod in his hand, from


id: royal-commission-on-animal-magnetism-20260505-11
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-11.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
==== Immediate publication and dissemination ==== The report was immediately published by the government printer; and at least 20,000 copies were rapidly and very widely circulated throughout France and neighbouring countries. Within four months (16 December 1784), the London publishing house of Joseph Johnson was announcing the publication of a complete English version, translated by William Godwin (i.e., Godwin, 1785), and, in between February and July 1785, four different "periodical abridgements of the Franklin report, each printed multiple times in the Atlantic coast publications" were published in the United States (Ogden, 2012, p. 167); and, in 1837, Godwin's complete translation was published, in Philadelphia, as part of a collected work. ==== Touch, imagination, and imitation ==== Clearly "recogniz[ing] that publicly endorsing the curative effects of a technique that had no demonstrable basis in the science of the late 18th century could lead to a proliferation of medical quackery" (McConkey & Perry, 2002, p. 328) and, based on their own "experiments" and "observations", the Commissioners concluded that "the true causes of the effects attributed to this new agent known by the name of animal magnetism, [and] to this fluid which is said to circulate in the body and to communicate itself


id: royal-commission-on-animal-magnetism-20260505-12
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-12.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
On 4 September 1784, Bailly presented a third, brief (15 page) courtesy report to the Royal Academy of Sciences (Bailly, 1784b) on behalf of himself, Franklin, Le Roy, de Bory, and Lavoisier (i.e., those Commissioners who were also Academy members), which provided their Academy colleagues with a brief account of the commission's proceedings, the rationale behind its investigations, and the results. Noting that all of their investigations were jointly conducted with the four members of the Paris Faculty, and that all nine shared the same "interest in [discovering] the truth", they stressed that all the findings of their combined efforts were unanimous (p. 2). ==== The importance of "the Sciences" ==== Further (p. 4), given that the understanding of the Sciences – "which [collectively] are increased by [establishing] the truth" (qui s'accroissent par les vérités) – is increased by "the suppression of error": i.e., given that "error" is always "a bad leaven that ferments and, in the long run, corrupts the mass into which it has been introduced". By contrast, however, in those cases wherein the "error" has been generated by "The Empire of Science", and has spread to "the multitude" – not only to divide and agitate minds, but


id: royal-commission-on-animal-magnetism-20260505-13
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-13.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
Part One (pp. 2–21), discussing the theories of the practices known as "Animal Magnetism". It commences with d'Eslon's definition of "animal magnetism"; namely that it is "the action which one man exercises on another, either through immediate contact or at a certain distance by the mere pointing of a finger or any kind of conduct", and that "this action", according to d'Eslon, "is the effect of a fluid that is distributed throughout the universe" Part Two (pp. 22–37), discussing the procedures and practices of "Animal Magnetism", as well as addressing the issues of their therapeutic efficacy (or not), and those of whether (or not) the procedures/practices should be admitted to conventional medical practice ("doivent-ils être admis en Médecine!": p. 22). The conclusions drawn (pp. 37–39) were, in brief, that they had found no evidence of d'Eslon's "magnetic fluid", that there were "no grounds for any belief in animal magnetism", that "the effects attributed to it are due to known causes", including not only the influence of "contact", "imagination", and/or "imitation", but also the influence of "the environment of the treatment room with its closed windows, fetid air, dim light, and the sight of other patients [and their responses to their


id: royal-commission-on-animal-magnetism-20260505-14
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-14.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
=== Response of the Paris Faculty of Medicine === Immediately following the release of the reports of the two Commissions, the Paris Faculty of Medicine "pressure[d] its own members to renounce animal magnetism" (Crabtree, 1993, p. 32). The Faculty identified some thirty of its docteurs-régent, including François Louis Thomas d'Onglée and Charles-Louis Varnier, who "openly favored animal magnetism or were suspected of so doing". According to the contemporary account of Thomas d'Onglée (1785, passim), the thirty "magnetic physicians" were subjected to "abuse" and were presented with a declaration, of which it was demanded that they sign. Both Thomas d'Onglée and Varnier, among others, refused to sign the declaration (and were, thereby, immediately expelled). The declaration in question read: No Doctor may declare himself a partisan of animal magnetism, through writings or through practice, under penalty of being removed from the role of docteurs-régents. === D'Eslon's response === D'Eslon immediately published an attack on the commission's reports, in which he criticized their failure to investigate the longer-term effects of his treatments, and their refusal to accept his (alleged) "cures" as proof of the existence of "animal magnetism", as well as noting that, "the commissioners' recommendation that the practice of magnetism should


id: royal-commission-on-animal-magnetism-20260505-15
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-15.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
The "classic" structure of the investigations undertaken by the "Franklin" Commission inspired – among many others over the ensuing years – the (1799) investigations of Chester physician John Haygarth (1740–1827) into the efficacy of Perkins' "tractors". In the process of discussing the experiments he had conducted (with medical colleagues as witnesses) with (dummy) "wooden tractors" on 7 January 1799, and with Perkins' "true metallick tractors" on 8 January 1799, Haygarth emphasized his considerable debt to the (earlier) "Franklin Commission" enterprise: It need not be remarked, how completely the trial illustrates the nature of this popular illusion, which has so wonderfully prevailed, and spread so rapidly; it resembles, in a striking manner, that of Animal Magnetism, which merited the attention of Dr. Franklin, when ambassador from America, and of other philosophers at Paris. If any person would repeat these experiments, they should be performed with due solemnity. During the process, the wonderful cures which this remedy is said to have performed ought to be particularly related. Without these indispensable aids, other trials will not prove as successful as those which are above reported. The whole effect undoubtedly depends upon the impression which can be made upon the patient's Imagination. This method


id: royal-commission-on-animal-magnetism-20260505-16
file: data/en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism-16.md
category: reference
title: Royal Commission on Animal Magnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Royal_Commission_on_Animal_Magnetism
date_saved: 2026-05-05T09:51:50.817218+00:00
instance: kb-cron
parent: royal-commission-on-animal-magnetism-20260505-0
summary:
The noted neurologist and psychoanalyst Sigmund Freud not only studied and wrote about "hypnosis" (e.g., Freud, 1891, and 1966), but he also actively used "hypnosis" in his clinical practice for some time. However the (à la Salpêtrière) "hypnosis" that Freud employed – quite unlike the conventional "hypnotism" of James Braid (that was induced by Braid's standard "upwards and inwards squint") – relied upon an induction process that often involved rubbing the top of a patient's head. This requirement, of course, demanded that Freud sat at the end of the therapeutic couch – in order to gain easy access to his subject's head – a practice that Freud continued to follow for his entire (post-"hypnosis") professional career. Another vestige of phreno-magnetism that demanded that Freud position himself at the patient's head was Freud's application of the "head pressure" technique that he had, in person, observed Hippolyte Bernheim use, on one of his visits to Bernheim's clinic at Nancy in 1899. Freud had discontinued this "head pressure" practice by, at least, 1904 – and, possibly, by 1900. === Mistaken identification of Esdaile's Jhar-Phoonk with d’Eslon's magnetization-by-contact === Due, to a large extent, to the (mistaken) enthusiastic promotion of Esdaile's (otherwise) valuable work


id: sample-ratio-mismatch-20260505-0
file: data/en.wikipedia.org/wiki/Sample_ratio_mismatch-0.md
category: reference
title: Sample ratio mismatch
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sample_ratio_mismatch
date_saved: 2026-05-05T09:51:52.013933+00:00
instance: kb-cron
parent: sample-ratio-mismatch-20260505-0
summary:
In the design of experiments, a sample ratio mismatch (SRM) is a statistically significant difference between the expected and actual ratios of the sizes of treatment and control groups in an experiment. Sample ratio mismatches also known as unbalanced sampling often occur in online controlled experiments due to failures in randomization and instrumentation. Sample ratio mismatches can be detected using a chi-squared test. Using methods to detect SRM can help non-experts avoid making decisions using biased data. If the sample size is large enough, even a small discrepancy between the observed and expected group sizes can invalidate the results of an experiment. == Example == Suppose we run an A/B test in which we randomly assign 1000 users to equally sized treatment and control groups (a 50–50 split). The expected size of each group is 500. However, the actual sizes of the treatment and control groups are 600 and 400. Using Pearson's chi-squared goodness of fit test, we find a sample ratio mismatch with a p-value of 2.54×10−10. In other words, if the assignment of users were truly random, the probability that these treatment and control group sizes would occur by chance is 2.54×10−10. == References ==


id: saturated-array-20260505-0
file: data/en.wikipedia.org/wiki/Saturated_array-0.md
category: reference
title: Saturated array
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Saturated_array
date_saved: 2026-05-05T09:51:53.168008+00:00
instance: kb-cron
parent: saturated-array-20260505-0
summary:
In experiments in which additional factors are not likely to interact with any of the other factors, a saturated array can be used. In a saturated array, a controllable factor is substituted for the interaction of two or more by-products. Using a saturated array, a two-factor test matrix could be used to test three factors. Using the saturated array allows three factors to be tested in four tests rather than in eight, as would be required by a standard orthogonal array.


id: scheirer-ray-hare-test-20260505-0
file: data/en.wikipedia.org/wiki/Scheirer–Ray–Hare_test-0.md
category: reference
title: Scheirer–Ray–Hare test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Scheirer–Ray–Hare_test
date_saved: 2026-05-05T09:51:54.386214+00:00
instance: kb-cron
parent: scheirer-ray-hare-test-20260505-0
summary:
The Scheirer–Ray–Hare (SRH) test is a statistical test that can be used to examine whether a measure is affected by two or more factors. Since it does not require a normal distribution of the data, it is one of the non-parametric methods. It is an extension of the Kruskal–Wallis test, the non-parametric equivalent for one-way analysis of variance (ANOVA), to the application for more than one factor. It is thus a non-parametric alternative to multi-factorial ANOVA analyses. The test is named after James Scheirer, William Ray and Nathan Hare, who published it in 1976. == Test description == The Scheirer–Ray–Hare test is analogous to the parametric multi-factorial ANOVA of investigating the influence of two different factors on a measure for which different samples are available for the factors. As with the parametric analysis of variance, the test can be used to investigate the null hypotheses that the two factors examined in each case have no influence on the positional parameter of the samples and thus on the measure, and that there are no interactions between the two factors. A p-value less than 0.05 for one or more of these three hypotheses leads to their rejection. As with many other non-parametric


id: scientific-protocol-20260505-0
file: data/en.wikipedia.org/wiki/Scientific_protocol-0.md
category: reference
title: Scientific protocol
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Scientific_protocol
date_saved: 2026-05-05T09:51:55.594780+00:00
instance: kb-cron
parent: scientific-protocol-20260505-0
summary:
In natural and social science research, a protocol is most commonly a predefined procedural method in the design and implementation of an experiment. Protocols are written whenever it is desirable to standardize a laboratory method to ensure successful replication of results by others in the same laboratory or by other laboratories. Additionally, and by extension, protocols have the advantage of facilitating the assessment of experimental results through peer review. In addition to detailed procedures, equipment, and instruments, protocols will also contain study objectives, reasoning for experimental design, reasoning for chosen sample sizes, safety precautions, and how results were calculated and reported, including statistical analysis and any rules for predefining and documenting excluded data to avoid bias. Similarly, a protocol may refer to the procedural methods of health organizations, commercial laboratories, manufacturing plants, etc. to ensure their activities (e.g., blood testing at a hospital, testing of certified reference materials at a calibration laboratory, and manufacturing of transmission gears at a facility) are consistent to a specific standard, encouraging safe use and accurate results. Finally, in the field of social science, a protocol may also refer to a "descriptive record" of observed events or a "sequence of behavior" of one or more


id: sealedenvelope-com-20260505-0
file: data/en.wikipedia.org/wiki/Sealedenvelope.com-0.md
category: reference
title: Sealedenvelope.com
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sealedenvelope.com
date_saved: 2026-05-05T09:51:56.773434+00:00
instance: kb-cron
parent: sealedenvelope-com-20260505-0
summary:
Sealedenvelope.com is British collaboration that provides support services for clinical trials. They provide services such as randomization, allocation concealment, code-break services, and case report management through a web-based design. They also perform certain calculations such as power calculations. == References == == External links == Official website


id: self-selection-bias-20260505-0
file: data/en.wikipedia.org/wiki/Self-selection_bias-0.md
category: reference
title: Self-selection bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Self-selection_bias
date_saved: 2026-05-05T09:51:57.984111+00:00
instance: kb-cron
parent: self-selection-bias-20260505-0
summary:
In statistics, self-selection bias arises in any situation in which individuals select themselves into a group, causing a biased sample with nonprobability sampling. It is commonly used to describe situations where the characteristics of the people which cause them to select themselves in the group create abnormal or undesirable conditions in the group. It is closely related to the non-response bias, describing when the group of people responding has different responses than the group of people not responding. Self-selection bias is a major problem in research in sociology, psychology, economics and many other social sciences. In such fields, a poll suffering from such bias is termed a self-selected listener opinion poll or "SLOP". The term is also used in criminology to describe the process by which specific predispositions may lead an offender to choose a criminal career and lifestyle. While the effects of self-selection bias are closely related to those of selection bias, the problem arises for rather different reasons; thus there may be a purposeful intent on the part of respondents leading to self-selection bias whereas other types of selection bias may arise more inadvertently, possibly as the result of mistakes by those designing any given study. == Explanation


id: sequential-analysis-20260505-0
file: data/en.wikipedia.org/wiki/Sequential_analysis-0.md
category: reference
title: Sequential analysis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sequential_analysis
date_saved: 2026-05-05T09:51:59.108535+00:00
instance: kb-cron
parent: sequential-analysis-20260505-0
summary:
In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data is evaluated as it is collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost. == History == The method of sequential analysis is first attributed to Abraham Wald with Jacob Wolfowitz, W. Allen Wallis, and Milton Friedman while at Columbia University's Statistical Research Group as a tool for more efficient industrial quality control during World War II. Its value to the war effort was immediately recognised, and led to its receiving a "restricted" classification. At the same time, George Barnard led a group working on optimal stopping in Great Britain. Another early contribution to the method was made by K.J. Arrow with D. Blackwell and M.A. Girshick. A similar approach was independently developed from first principles at about the same time by Alan Turing, as part of the Banburismus technique used at Bletchley Park, to test hypotheses


id: seriousness-check-20260505-0
file: data/en.wikipedia.org/wiki/Seriousness_check-0.md
category: reference
title: Seriousness check
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Seriousness_check
date_saved: 2026-05-05T09:52:00.364244+00:00
instance: kb-cron
parent: seriousness-check-20260505-0
summary:
The seriousness check is a technique that can be used in online research (also called Internet-based research, Web-based research, Web-based experiments) to improve data quality. Nowadays, many scientific studies with human participants are conducted online and are accessible to a large diversity of participants. Nonetheless, many people just want to look at the different pages of the questionnaire, instead of giving carefully chosen answers to the questions. The seriousness check addresses this problem: In this approach the respondents are asked about the seriousness of their participation or for a probability estimate that they will complete the entire study or experiment. Thus, by using the seriousness check irrelevant data entries can be easily identified and be excluded from the data analysis. == Method == Seriousness checks can be implemented both before and after participation in the study. However, it has been shown that the seriousness check is a good predictor of dropout rates when implemented in the first page of the experiment. There are Web-based tools, e.g. WEXTOR, that implement the seriousness check by default. == Impact == Several studies have shown that performing a seriousness check at the start of a study best predicts motivation and dropout probability. It was


id: set-balancing-20260505-0
file: data/en.wikipedia.org/wiki/Set_balancing-0.md
category: reference
title: Set balancing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Set_balancing
date_saved: 2026-05-05T09:52:01.568529+00:00
instance: kb-cron
parent: set-balancing-20260505-0
summary:
The set balancing problem in mathematics is the problem of dividing a set to two subsets that have roughly the same characteristics. It arises naturally in design of experiments. There is a group of subjects. Each subject has several features, which are considered binary. For example: each subject can be either young or old; either black or white; either tall or short; etc. The goal is to divide the subjects to two sub-groups: treatment group (T) and control group (C), such that for each feature, the number of subjects that have this feature in T is roughly equal to the number of subjects that have this feature in C. E.g., both groups should have roughly the same number of young people, the same number of black people, the same number of tall people, etc. == Matrix representation == Formally, the set balancing problem can be described as follows. m {\displaystyle m} is the number of subjects in the general population. n {\displaystyle n} is the number of potential features. The subjects are described by A {\displaystyle A} , an n × m {\displaystyle n\times m} matrix with entries in 0 , 1 {\displaystyle {0,1}} . Each column represents a subject


id: single-subject-research-20260505-0
file: data/en.wikipedia.org/wiki/Single-subject_research-0.md
category: reference
title: Single-subject research
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Single-subject_research
date_saved: 2026-05-05T09:52:05.128250+00:00
instance: kb-cron
parent: single-subject-research-20260505-0
summary:
Single-subject research is a group of research methods that are used extensively in the experimental analysis of behavior and applied behavior analysis with both human and non-human participants. This research strategy focuses on one participant and tracks their progress in the research topic over a period of time. Single-subject research allows researchers to track changes in an individual over a large stretch of time instead of observing different people at different stages. This type of research can provide critical data in several fields, specifically psychology. It is most commonly used in experimental and applied analysis of behaviors. This research has been heavily debated over the years. Some believe that this research method is not effective at all while others praise the data that can be collected from it. Principal methods in this type of research are: A-B-A-B designs, Multi-element designs, Multiple Baseline designs, Repeated acquisition designs, Brief experimental designs and Combined designs. These methods form the heart of the data collection and analytic code of behavior analysis. Behavior analysis is data driven, inductive, and disinclined to hypothetico-deductive methods. == Experimental questions == Experimental questions are decisive in determining the nature of the experimental design to be selected. There are four


id: solomon-four-group-design-20260505-0
file: data/en.wikipedia.org/wiki/Solomon_four-group_design-0.md
category: reference
title: Solomon four-group design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Solomon_four-group_design
date_saved: 2026-05-05T09:52:06.354013+00:00
instance: kb-cron
parent: solomon-four-group-design-20260505-0
summary:
The Solomon four-group design is a research method developed by Richard Solomon in 1949. It is sometimes used in social science, psychology and medicine. It can be used if there are concerns that the treatment might be sensitized by the pre-test. In addition of the usual two groups (treatment and control), it has a second pair of groups who do not receive a pre-intervention evaluation. == Structure == The structure of the trial is shown in the table : The first two groups receive the evaluation test before and after the study, as in a normal two-group trial. The second groups receive the evaluation only after the study. The effectiveness of the treatment can be evaluated by comparisons between groups 1 and 3 and between groups 2 and 4.. In addition, the effect of the pre-treatment evaluation can be calculated by comparing the control group who received the pre-treatment evaluation with those who did not (groups 2 and 4). Various statistical treatments for the Solomon four-group design have been put forward, including Stouffer's Z and Monte Carlo. == References ==


id: sparsity-of-effects-principle-20260505-0
file: data/en.wikipedia.org/wiki/Sparsity-of-effects_principle-0.md
category: reference
title: Sparsity-of-effects principle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sparsity-of-effects_principle
date_saved: 2026-05-05T09:52:07.517443+00:00
instance: kb-cron
parent: sparsity-of-effects-principle-20260505-0
summary:
In the statistical analysis of the results from factorial experiments, the sparsity-of-effects principle states that a system is usually dominated by main effects and low-order interactions. Thus it is most likely that main (single factor) effects and two-factor interactions are the most significant responses in a factorial experiment. In other words, higher order interactions such as three-factor interactions are very rare. This is sometimes referred to as the hierarchical ordering principle. The sparsity-of-effects principle actually refers to the idea that only a few effects in a factorial experiment will be statistically significant. This principle is only valid on the assumption of a factor space far from a stationary point. == See also == Occam's Razor Pareto principle == References ==


id: spectrum-bias-20260505-0
file: data/en.wikipedia.org/wiki/Spectrum_bias-0.md
category: reference
title: Spectrum bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spectrum_bias
date_saved: 2026-05-05T09:52:08.680162+00:00
instance: kb-cron
parent: spectrum-bias-20260505-0
summary:
In biostatistics, spectrum bias refers to the phenomenon that the performance of a diagnostic test may vary in different clinical settings because each setting has a different mix of patients. Because the performance may be dependent on the mix of patients, performance at one clinic may not be predictive of performance at another clinic. These differences are interpreted as a kind of bias. Mathematically, the spectrum bias is a sampling bias and not a traditional statistical bias; this has led some authors to refer to the phenomenon as spectrum effects, whilst others maintain it is a bias if the true performance of the test differs from that which is 'expected'. Usually the performance of a diagnostic test is measured in terms of its sensitivity and specificity and it is changes in these that are considered when referring to spectrum bias. However, other performance measures such as the likelihood ratios may also be affected by spectrum bias. Generally spectrum bias is considered to have three causes. The first is due to a change in the case-mix of those patients with the target disorder (disease) and this affects the sensitivity. The second is due to a change in the case-mix of those


id: spherical-design-20260505-0
file: data/en.wikipedia.org/wiki/Spherical_design-0.md
category: reference
title: Spherical design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spherical_design
date_saved: 2026-05-05T09:52:09.899202+00:00
instance: kb-cron
parent: spherical-design-20260505-0
summary:
A spherical design, part of combinatorial design theory in mathematics, is a finite set of N points on the d-dimensional unit d-sphere Sd such that the average value of any polynomial f of degree t or less on the set equals the average value of f on the whole sphere (that is, the integral of f over Sd divided by the area or measure of Sd). Such a set is often called a spherical t-design to indicate the value of t, which is a fundamental parameter. The concept of a spherical design is due to Delsarte, Goethals, and Seidel, although these objects were understood as particular examples of cubature formulas earlier. Spherical designs can be of value in approximation theory, in statistics for experimental design, in combinatorics, and in geometry. The main problem is to find examples, given d and t, that are not too large; however, such examples may be hard to come by. Spherical t-designs have also recently been appropriated in quantum mechanics in the form of quantum t-designs with various applications to quantum information theory and quantum computing. == Existence of spherical designs == The existence and structure of spherical designs on the circle were studied in


id: spillover-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Spillover_(experiment)-0.md
category: reference
title: Spillover (experiment)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spillover_(experiment)
date_saved: 2026-05-05T09:52:11.116942+00:00
instance: kb-cron
parent: spillover-experiment-20260505-0
summary:
In experiments, a spillover is an indirect effect on a subject not directly treated by the experiment. These effects are useful for policy analysis but complicate the statistical analysis of experiments. Analysis of spillover effects involves relaxing the non-interference assumption, or SUTVA (Stable Unit Treatment Value Assumption). This assumption requires that subject i's revelation of its potential outcomes depends only on that subject i's own treatment status, and is unaffected by another subject j's treatment status. In ordinary settings where the researcher seeks to estimate the average treatment effect ( A T E ^ {\displaystyle {\widehat {ATE}}} ), violation of the non-interference assumption means that traditional estimators for the ATE, such as difference-in-means, may be biased. However, there are many real-world instances where a unit's revelation of potential outcomes depend on another unit's treatment assignment, and analyzing these effects may be just as important as analyzing the direct effect of treatment. One solution to this problem is to redefine the causal estimand of interest by redefining a subject's potential outcomes in terms of one's own treatment status and related subjects' treatment status. The researcher can then analyze various estimands of interest separately. One important assumption here is that this process


id: spillover-experiment-20260505-1
file: data/en.wikipedia.org/wiki/Spillover_(experiment)-1.md
category: reference
title: Spillover (experiment)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spillover_(experiment)
date_saved: 2026-05-05T09:52:11.116942+00:00
instance: kb-cron
parent: spillover-experiment-20260505-0
summary:
=== Using randomization inference for hypothesis testing === In experimental settings where treatment is randomized, we can use randomization inference to test for the existence of spillover effects. The key advantage of this approach is that randomization inference is finite-sample valid, without requiring correct model specification or normal asymptotics. To be specific, consider the aforementioned example experiment in college dorm rooms, and suppose we want to test: H 0 : Y 0 , 1 = Y 0 , 0 {\displaystyle H_{0}:Y_{0,1}=Y_{0,0}} This hypothesis posits that there is no spillover effect on students who don't receive the information (i.e., students who are in control in the experiment). Rejecting this hypothesis implies that even when students don't receive the information message directly, they still may receive it indirectly from treated roommates; hence, there is a spillover effect. To test a hypothesis like H 0 {\displaystyle H_{0}} we can apply a conditional Fisher randomization test. Let R i j = 1 {\displaystyle R_{ij}=1} be an indicator denoting that students i , j {\displaystyle i,j} are roommates, where we assumed for simplicity that each student has exactly one roommate. Suppose this is a completely randomized design and let D i {\displaystyle D_{i}} denote the


id: spillover-experiment-20260505-2
file: data/en.wikipedia.org/wiki/Spillover_(experiment)-2.md
category: reference
title: Spillover (experiment)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spillover_(experiment)
date_saved: 2026-05-05T09:52:11.116942+00:00
instance: kb-cron
parent: spillover-experiment-20260505-0
summary:
I k P I k ′ = [ π 1 ( d k ) π 12 ( d k ) ⋯ π 1 N ( d k ) π 21 ( d k ) π 2 ( d k ) ⋯ π 2 N ( d k ) ⋮ ⋮ ⋱ π N 1 ( d k ) π N 2 ( d k ) π N ( d k ) ] {\displaystyle \mathbf {I} _{k}\mathbf {P} \mathbf {I} _{k}^{\prime }=\left[{\begin{array}{cccc}{\pi _{1}(d_{k})}&\pi _{12}(d_{k})&\cdots &\pi _{1N}(d_{k})\\\pi _{21}(d_{k})&\pi _{2}(d_{k})&\cdots &\pi _{2N}(d_{k})\\\vdots &\vdots &\ddots &\\\pi _{N1}(d_{k})&\pi _{N2}(d_{k})&{}&\pi _{N}(d_{k})\end{array}}\right]} In a similar fashion, the joint probability of exposure of i being in exposure condition d k {\displaystyle d_{k}} and j being in a different exposure condition d l {\displaystyle d_{l}} can be obtained by calculating I k P I l ′ {\displaystyle \mathbf {I} _{k}\mathbf {P} \mathbf {I} _{l}^{\prime }} : I k P I l ′ = [ 0 π 12 ( d k , d l ) … π 1 N ( d k , d l ) π 21 ( d k , d l ) 0 … π 2 N ( d k , d l ) ⋮ ⋮ ⋱


id: standard-treatment-20260505-0
file: data/en.wikipedia.org/wiki/Standard_treatment-0.md
category: reference
title: Standard treatment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Standard_treatment
date_saved: 2026-05-05T09:52:12.282392+00:00
instance: kb-cron
parent: standard-treatment-20260505-0
summary:
The standard treatment, also known as the standard of care, is the medical treatment that is normally provided to people with a given condition. In many scientific studies, the control group receives the standard treatment rather than a placebo while a treatment group receives the experimental treatment. After the clinical trial, researchers compare the outcomes of the two groups to see if the experimental treatment is better than, as good as or not as beneficial as the standard treatment. == Active (positive) concurrent control == In an active control or positive control trial, subjects are randomly assigned to the test treatment or to an active control treatment. Such clinical trials are usually double-blind, but this is not always possible; many oncology trials, for example, are considered difficult or impossible to blind because of different regimens, different routes of administration, and different toxicities. Active control trials can have two distinct objectives with respect to showing efficacy: (1) to show efficacy of the test treatment by showing it is as good as a known effective treatment or (2) to show efficacy by showing superiority of the test treatment to the active control. They may also be used with the primary objective of


id: statistical-hypothesis-test-20260505-0
file: data/en.wikipedia.org/wiki/Statistical_hypothesis_test-0.md
category: reference
title: Statistical hypothesis test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistical_hypothesis_test
date_saved: 2026-05-05T09:52:13.457599+00:00
instance: kb-cron
parent: statistical-hypothesis-test-20260505-0
summary:
A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a p-value computed from the test statistic. Roughly 100 specialized statistical tests are in use and noteworthy. == History == While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see § Human sex ratio. === Choice of null hypothesis === Paul Meehl has argued that the epistemological importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by theory, a more precise experiment will be a more severe test of the underlying theory. When the null hypothesis defaults to "no difference" or "no effect", a more precise experiment is a less severe test of the theory that motivated performing the experiment. An examination of the origins of the


id: statistical-hypothesis-test-20260505-1
file: data/en.wikipedia.org/wiki/Statistical_hypothesis_test-1.md
category: reference
title: Statistical hypothesis test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistical_hypothesis_test
date_saved: 2026-05-05T09:52:13.457599+00:00
instance: kb-cron
parent: statistical-hypothesis-test-20260505-0
summary:
=== Null hypothesis significance testing (NHST) === The modern version of hypothesis testing is generally called the null hypothesis significance testing (NHST) and is a hybrid of the Fisher approach with the Neyman-Pearson approach. In 2000, Raymond S. Nickerson wrote an article stating that NHST was (at the time) "arguably the most widely used method of analysis of data collected in psychological experiments and has been so for about 70 years" and that it was at the same time "very controversial". This fusion resulted from confusion by writers of statistical textbooks (as predicted by Fisher) beginning in the 1940s (but signal detection, for example, still uses the Neyman/Pearson formulation). Great conceptual differences and many caveats in addition to those mentioned above were ignored. Neyman and Pearson provided the stronger terminology, the more rigorous mathematics and the more consistent philosophy, but the subject taught today in introductory statistics has more similarities with Fisher's method than theirs. Sometime around 1940, authors of statistical text books began combining the two approaches by using the p-value in place of the test statistic (or data) to test against the Neyman–Pearson "significance level". == Philosophy == Hypothesis testing and philosophy intersect. Inferential statistics, which includes hypothesis


id: statistical-hypothesis-test-20260505-2
file: data/en.wikipedia.org/wiki/Statistical_hypothesis_test-2.md
category: reference
title: Statistical hypothesis test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistical_hypothesis_test
date_saved: 2026-05-05T09:52:13.457599+00:00
instance: kb-cron
parent: statistical-hypothesis-test-20260505-0
summary:
"The Geiger-counter reading is 10. The limit is 9. Check the suitcase." "The Geiger-counter reading is high; 97% of safe suitcases have lower readings. The limit is 95%. Check the suitcase." The former report is adequate, the latter gives a more detailed explanation of the data and the reason why the suitcase is being checked. Not rejecting the null hypothesis does not mean the null hypothesis is "accepted" per se (though Neyman and Pearson used that word in their original writings; see the Interpretation section). The processes described here are perfectly adequate for computation. They seriously neglect the design of experiments considerations. It is particularly critical that appropriate sample sizes be estimated before conducting the experiment. The phrase "test of significance" was coined by statistician Ronald Fisher. === Interpretation === When the null hypothesis is true and statistical assumptions are met, the probability that the p-value will be less than or equal to the significance level α {\displaystyle \alpha } is at most α {\displaystyle \alpha } . This ensures that the hypothesis test maintains its specified false positive rate (provided that statistical assumptions are met). The p-value is the probability that a test statistic which is at least as


id: statistical-hypothesis-test-20260505-3
file: data/en.wikipedia.org/wiki/Statistical_hypothesis_test-3.md
category: reference
title: Statistical hypothesis test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistical_hypothesis_test
date_saved: 2026-05-05T09:52:13.457599+00:00
instance: kb-cron
parent: statistical-hypothesis-test-20260505-0
summary:
The following definitions are mainly based on the exposition in the book by Lehmann and Romano: Statistical hypothesis: A statement about the parameters describing a population (not a sample). Test statistic: A value calculated from a sample without any unknown parameters, often to summarize the sample for comparison purposes. Simple hypothesis: Any hypothesis which specifies the population distribution completely. Composite hypothesis: Any hypothesis which does not specify the population distribution completely. Null hypothesis (H0) Positive data: Data that enable the investigator to reject a null hypothesis. Alternative hypothesis (H1) Critical values of a statistical test are the boundaries of the acceptance region of the test. The acceptance region is the set of values of the test statistic for which the null hypothesis is not rejected. Depending on the shape of the acceptance region, there can be one or more than one critical value. Region of rejection / Critical region: The set of values of the test statistic for which the null hypothesis is rejected. Power of a test (1 − β) Size: For simple hypotheses, this is the test's probability of incorrectly rejecting the null hypothesis. The false positive rate. For composite hypotheses this is the supremum of the probability


id: statistical-hypothesis-test-20260505-4
file: data/en.wikipedia.org/wiki/Statistical_hypothesis_test-4.md
category: reference
title: Statistical hypothesis test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistical_hypothesis_test
date_saved: 2026-05-05T09:52:13.457599+00:00
instance: kb-cron
parent: statistical-hypothesis-test-20260505-0
summary:
=== Courtroom trial === A statistical test procedure is comparable to a criminal trial; a defendant is considered not guilty as long as his or her guilt is not proven. The prosecutor tries to prove the guilt of the defendant. Only when there is enough evidence for the prosecution is the defendant convicted. In the start of the procedure, there are two hypotheses H 0 {\displaystyle H_{0}} : "the defendant is not guilty", and H 1 {\displaystyle H_{1}} : "the defendant is guilty". The first one, H 0 {\displaystyle H_{0}} , is called the null hypothesis. The second one, H 1 {\displaystyle H_{1}} , is called the alternative hypothesis. It is the alternative hypothesis that one hopes to support. The hypothesis of innocence is rejected only when an error is very unlikely, because one does not want to convict an innocent defendant. Such an error is called error of the first kind (i.e., the conviction of an innocent person), and the occurrence of this error is controlled to be rare. As a consequence of this asymmetric behaviour, an error of the second kind (acquitting a person who committed the crime), is more common. A criminal trial can be regarded as


id: statistical-hypothesis-test-20260505-5
file: data/en.wikipedia.org/wiki/Statistical_hypothesis_test-5.md
category: reference
title: Statistical hypothesis test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistical_hypothesis_test
date_saved: 2026-05-05T09:52:13.457599+00:00
instance: kb-cron
parent: statistical-hypothesis-test-20260505-0
summary:
== Variations and sub-classes == Statistical hypothesis testing is a key technique of both frequentist inference and Bayesian inference, although the two types of inference have notable differences. Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect. The procedure is based on how likely it would be for a set of observations to occur if the null hypothesis were true. This probability of making an incorrect decision is not the probability that the null hypothesis is true, nor whether any specific alternative hypothesis is true. This contrasts with other possible techniques of decision theory in which the null and alternative hypothesis are treated on a more equal basis. One naïve Bayesian approach to hypothesis testing is to base decisions on the posterior probability, but this fails when comparing point and continuous hypotheses. Other approaches to decision making, such as Bayesian decision theory, attempt to balance the consequences of incorrect decisions across all possibilities, rather than concentrating on a single null hypothesis. A number of other approaches to reaching a decision based on data are available via decision theory and optimal decisions, some of which have desirable properties.


id: statistical-hypothesis-test-20260505-6
file: data/en.wikipedia.org/wiki/Statistical_hypothesis_test-6.md
category: reference
title: Statistical hypothesis test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistical_hypothesis_test
date_saved: 2026-05-05T09:52:13.457599+00:00
instance: kb-cron
parent: statistical-hypothesis-test-20260505-0
summary:
The interpretation of a p-value is dependent upon stopping rule and definition of multiple comparison. The former often changes during the course of a study and the latter is unavoidably ambiguous. (i.e. "p values depend on both the (data) observed and on the other possible (data) that might have been observed but weren't"). Confusion resulting (in part) from combining the methods of Fisher and Neyman–Pearson which are conceptually distinct. Emphasis on statistical significance to the exclusion of estimation and confirmation by repeated experiments. Rigidly requiring statistical significance as a criterion for publication, resulting in publication bias. Most of the criticism is indirect. Rather than being wrong, statistical hypothesis testing is misunderstood, overused and misused. When used to detect whether a difference exists between groups, a paradox arises. As improvements are made to experimental design (e.g. increased precision of measurement and sample size), the test becomes more lenient. Unless one accepts the absurd assumption that all sources of noise in the data cancel out completely, the chance of finding statistical significance in either direction approaches 100%. However, this absurd assumption that the mean difference between two groups cannot be zero implies that the data cannot be independent and identically distributed (i.i.d.)


id: statistical-hypothesis-test-20260505-7
file: data/en.wikipedia.org/wiki/Statistical_hypothesis_test-7.md
category: reference
title: Statistical hypothesis test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Statistical_hypothesis_test
date_saved: 2026-05-05T09:52:13.457599+00:00
instance: kb-cron
parent: statistical-hypothesis-test-20260505-0
summary:
A unifying position of critics is that statistics should not lead to an accept-reject conclusion or decision, but to an estimated value with an interval estimate; this data-analysis philosophy is broadly referred to as estimation statistics. Estimation statistics can be accomplished with either frequentist or Bayesian methods. Critics of significance testing have advocated basing inference less on p-values and more on confidence intervals for effect sizes for importance, prediction intervals for confidence, replications and extensions for replicability, meta-analyses for generality :. But none of these suggested alternatives inherently produces a decision. Lehmann said that hypothesis testing theory can be presented in terms of conclusions/decisions, probabilities, or confidence intervals: "The distinction between the ... approaches is largely one of reporting and interpretation." Bayesian inference is one proposed alternative to significance testing. (Nickerson cited 10 sources suggesting it, including Rozeboom (1960)). For example, Bayesian parameter estimation can provide rich information about the data from which researchers can draw inferences, while using uncertain priors that exert only minimal influence on the results when enough data is available. Psychologist John K. Kruschke has suggested Bayesian estimation as an alternative for the t-test and has also contrasted Bayesian estimation for assessing null values with Bayesian


id: steiner-system-20260505-0
file: data/en.wikipedia.org/wiki/Steiner_system-0.md
category: reference
title: Steiner system
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Steiner_system
date_saved: 2026-05-05T09:52:14.665238+00:00
instance: kb-cron
parent: steiner-system-20260505-0
summary:
In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2. A Steiner system with parameters t, k, n, written S(t,k,n), is an n-element set S together with a set of k-element subsets of S (called blocks) with the property that each t-element subset of S is contained in exactly one block. In an alternative notation for block designs, an S(t,k,n) would be a t-(n,k,1) design. This definition is relatively new. The classical definition of Steiner systems also required that k = t + 1. An S(2,3,n) was (and still is) called a Steiner triple (or triad) system, while an S(3,4,n) is called a Steiner quadruple system, and so on. With the generalization of the definition, this naming system is no longer strictly adhered to. Long-standing problems in design theory were whether there exist any nontrivial Steiner systems (nontrivial meaning t < k < n) with t ≥ 6; also whether infinitely many have t = 4 or 5. Both existences were proved by Peter Keevash in 2014. His proof is non-constructive and, as of 2019, no actual Steiner


id: steiner-system-20260505-1
file: data/en.wikipedia.org/wiki/Steiner_system-1.md
category: reference
title: Steiner system
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Steiner_system
date_saved: 2026-05-05T09:52:14.665238+00:00
instance: kb-cron
parent: steiner-system-20260505-0
summary:
for girls labeled A to O, and constructed each subsequent week's solution from its immediate predecessor by changing A to B, B to C, ... L to M and M back to A, all while leaving N and O unchanged. The Week 13 solution, upon undergoing that relabeling, returns to the Week 1 solution. Denniston reported in his paper that the search he employed took 7 hours on an Elliott 4130 computer at the University of Leicester, and he immediately ended the search on finding the solution above, not looking to establish uniqueness. The number of non-isomorphic solutions to Sylvester's problem remains unknown as of 2021. == Properties == It is clear from the definition of S(t, k, n) that 1 < t < k < n {\displaystyle 1<t<k<n} . (Equalities, while technically possible, lead to trivial systems.) If S(t, k, n) exists, then taking all blocks containing a specific element and discarding that element gives a derived system S(t−1, k−1, n−1). Therefore, the existence of S(t−1, k−1, n−1) is a necessary condition for the existence of S(t, k, n). The number of t-element subsets in S is ( n t ) {\displaystyle {\tbinom {n}{t}}} , while the number of


id: steiner-system-20260505-2
file: data/en.wikipedia.org/wiki/Steiner_system-2.md
category: reference
title: Steiner system
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Steiner_system
date_saved: 2026-05-05T09:52:14.665238+00:00
instance: kb-cron
parent: steiner-system-20260505-0
summary:
a "block" (it contains ∞ together with the 5 nonzero squares in F11). From this block, we obtain the other blocks of the S(5,6,12) system by repeatedly applying the linear fractional transformations: z ′ = f ( z ) = a z + b c z + d , {\displaystyle z'=f(z)={\frac {az+b}{cz+d}},} where a,b,c,d are in F11 and ad − bc = 1. With the usual conventions of defining f (−d/c) = ∞ and f (∞) = a/c, these functions map the set S onto itself. In geometric language, they are projectivities of the projective line. They form a group under composition which is the projective special linear group PSL(2,11) of order 660. There are exactly five elements of this group that leave the starting block fixed setwise, namely those such that b=c=0 and ad=1 so that f(z) = a2 z. So there will be 660/5 = 132 images of that block. As a consequence of the multiply transitive property of this group acting on this set, any subset of five elements of S will appear in exactly one of these 132 images of size six. === Kitten construction === An alternative construction of W12 is obtained by use of


id: steiner-system-20260505-3
file: data/en.wikipedia.org/wiki/Steiner_system-3.md
category: reference
title: Steiner system
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Steiner_system
date_saved: 2026-05-05T09:52:14.665238+00:00
instance: kb-cron
parent: steiner-system-20260505-0
summary:
where a,b,c,d are in F23 and ad − bc = 1. With the usual conventions of defining f (−d/c) = ∞ and f (∞) = a/c, these functions map the set S onto itself. In geometric language, they are projectivities of the projective line. They form a group under composition which is the projective special linear group PSL(2,23) of order 6072. There are exactly 8 elements of this group that leave the initial block fixed setwise. So there will be 6072/8 = 759 images of that block. These form the octads of S(5,8,24). === Construction from the Miracle Octad Generator === The Miracle Octad Generator (MOG) is a tool to generate octads, such as those containing specified subsets. It consists of a 4x6 array with certain weights assigned to the rows. In particular, an 8-subset should obey three rules in order to be an octad of S(5,8,24). First, each of the 6 columns should have the same parity, that is, they should all have an odd number of cells or they should all have an even number of cells. Second, the top row should have the same parity as each of the columns. Third, the rows are respectively multiplied by


id: stepped-wedge-trial-20260505-0
file: data/en.wikipedia.org/wiki/Stepped-wedge_trial-0.md
category: reference
title: Stepped-wedge trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stepped-wedge_trial
date_saved: 2026-05-05T09:52:15.845060+00:00
instance: kb-cron
parent: stepped-wedge-trial-20260505-0
summary:
In medicine, a stepped-wedge trial (or SWT) is a type of randomised controlled trial (RCT). An RCT is a scientific experiment that is designed to reduce bias when testing a new medical treatment, a social intervention, or another testable hypothesis. In a traditional RCT, the researcher randomly divides the experiment participants into two groups at the same time: One group receives the treatment (the "treatment group") The other group does not get the treatment (the "control group"). In a SWT, a logistic constraint typically prevents the simultaneous treatment of some participants, and instead, all or most participants receive the treatment in waves or "steps". For instance, a researcher wants to measure whether teaching college students how to make several meals increased their propensity to cook at home instead of eating out. In a traditional RCT, a sample of students would be selected and some would be trained on how to cook these meals, whereas the others would not. Both groups would be monitored to see how frequently they ate out. In the end, the number of times the treatment group ate out would be compared to the number of times the control group ate out, most likely with a t-test


id: stepped-wedge-trial-20260505-1
file: data/en.wikipedia.org/wiki/Stepped-wedge_trial-1.md
category: reference
title: Stepped-wedge trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stepped-wedge_trial
date_saved: 2026-05-05T09:52:15.845060+00:00
instance: kb-cron
parent: stepped-wedge-trial-20260505-0
summary:
== Model == While there are several other potential methods for modeling outcomes in an SWT, the work of Hussey and Hughes "first described methods to determine statistical power available when using a stepped wedge design." What follows is their design. Suppose there are N {\displaystyle N} samples divided into C {\displaystyle C} clusters. At each time point t = 1 , … , T {\displaystyle t=1,\ldots ,T} , preferably equally spaced in actual time, some number of clusters are treated. Let Z c t {\displaystyle Z_{ct}} be 1 {\displaystyle 1} if cluster c {\displaystyle c} has been treated at time t {\displaystyle t} and 0 {\displaystyle 0} otherwise. In particular, note that if Z c t = 1 {\displaystyle Z_{ct}=1} then Z c , t + 1 = 1 {\displaystyle Z_{c,t+1}=1} . For each participant i {\displaystyle i} in cluster c {\displaystyle c} , measure the outcome to be studied y i c t {\displaystyle y_{ict}} at time t {\displaystyle t} . Note that the notation allows for clustering by including c {\displaystyle c} in the subscript of y i c t {\displaystyle y_{ict}} , α c {\displaystyle \alpha _{c}} , Z c t {\displaystyle Z_{ct}} , and ϵ


id: stepped-wedge-trial-20260505-2
file: data/en.wikipedia.org/wiki/Stepped-wedge_trial-2.md
category: reference
title: Stepped-wedge trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stepped-wedge_trial
date_saved: 2026-05-05T09:52:15.845060+00:00
instance: kb-cron
parent: stepped-wedge-trial-20260505-0
summary:
First, since in SWTs the study period lasts longer and all the subjects eventually receive the treatment, costs may increase significantly. Because the design can be expensive, SWTs may not be the optimal solution when measurement precision and outcome autocorrelation are high. Moreover, since everyone is eventually treated, SWTs do not facilitate downstream analysis. Secondly, in an SWT, more clusters are exposed to the intervention at later than earlier time periods. As such, it is possible that an underlying temporal trend may confound the intervention effect, and so the confounding effect of time must be accounted for in both pre-trial power calculations and post-trial analysis. Specifically, in post-trial analysis, the use of generalized linear mixed models or generalized estimating equations is recommended. Finally, the design and analysis of stepped-wedge trials is therefore more complex than for other types of randomized trials. Previous systematic reviews highlighted the poor reporting of sample size calculations and a lack of consistency in the analysis of such trials. Hussey and Hughes were the first authors to suggest a structure and formula for estimating power in stepped-wedge studies in which data was collected at each and every step. This has now been expanded for designs in


id: stock-sampling-20260505-0
file: data/en.wikipedia.org/wiki/Stock_sampling-0.md
category: reference
title: Stock sampling
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stock_sampling
date_saved: 2026-05-05T09:52:17.002391+00:00
instance: kb-cron
parent: stock-sampling-20260505-0
summary:
Stock sampling is sampling people in a certain state at the time of the survey. This is in contrast to flow sampling, where the relationship of interest deals with duration or survival analysis. In stock sampling, rather than focusing on transitions within a certain time interval, we only have observations at a certain point in time. This can lead to both left and right censoring. Imposing the same model on data that have been generated under the two different sampling regimes can lead to research reaching fundamentally different conclusions if the joint distribution across the flow and stock samples differ sufficiently. Stock sampling essentially leads to a sample selection problem. This selection issue is akin to the truncated regression model where we face selection on the basis of a binary response variable, but the problem has been referred to as length-biased sampling in this specific context. Consider, for example, the figure below that plots some duration data. If a researcher would revert to stock sampling and only sample and survey individuals at the survey dates (i.e. the survey data, 12 months after the survey date, etc.), there is a high likelihood the short duration spells will be omitted from the


id: subgroup-analysis-20260505-0
file: data/en.wikipedia.org/wiki/Subgroup_analysis-0.md
category: reference
title: Subgroup analysis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Subgroup_analysis
date_saved: 2026-05-05T09:52:18.188918+00:00
instance: kb-cron
parent: subgroup-analysis-20260505-0
summary:
Subgroup analysis refers to repeating the analysis of a study within subgroups of subjects defined by a subgrouping variable. For example: smoking status defining two subgroups: smokers and non-smokers. == See also == Post hoc analysis == References ==


id: surrogate-model-20260505-0
file: data/en.wikipedia.org/wiki/Surrogate_model-0.md
category: reference
title: Surrogate model
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Surrogate_model
date_saved: 2026-05-05T09:52:19.376341+00:00
instance: kb-cron
parent: surrogate-model-20260505-0
summary:
A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate mathematical model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (e.g., length, curvature, material, etc.). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and "what-if" analysis become impossible since they require thousands or even millions of simulation evaluations. One way of alleviating this burden is by constructing approximation models, known as surrogate models, metamodels or emulators, that mimic the behavior of the simulation model as closely as possible while being computationally cheaper to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), relying solely on the input-output behavior. A model is


id: surrogate-model-20260505-1
file: data/en.wikipedia.org/wiki/Surrogate_model-1.md
category: reference
title: Surrogate model
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Surrogate_model
date_saved: 2026-05-05T09:52:19.376341+00:00
instance: kb-cron
parent: surrogate-model-20260505-0
summary:
== Surrogate-Assisted Evolutionary Algorithms (SAEAs) == SAEAs are an advanced class of optimization techniques that integrate evolutionary algorithms (EAs) with surrogate models. In traditional EAs, evaluating the fitness of candidate solutions often requires computationally expensive simulations or experiments. SAEAs address this challenge by building a surrogate model, which is a computationally inexpensive approximation of the objective function or constraint functions. The surrogate model serves as a substitute for the actual evaluation process during the evolutionary search. It allows the algorithm to quickly estimate the fitness of new candidate solutions, thereby reducing the number of expensive evaluations needed. This significantly speeds up the optimization process, especially in cases where the objective function evaluations are time-consuming or resource-intensive. SAEAs typically involve three main steps: (1) building the surrogate model using a set of initial sampled data points, (2) performing the evolutionary search using the surrogate model to guide the selection, crossover, and mutation operations, and (3) periodically updating the surrogate model with new data points generated during the evolutionary process to improve its accuracy. By balancing exploration (searching new areas in the solution space) and exploitation (refining known promising areas), SAEAs can efficiently find high-quality solutions to complex optimization problems. They have


