# kb

id: aliasing-factorial-experiments-20260505-3
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-3.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
where the equation is modulo s {\displaystyle s} if s {\displaystyle s} is prime, and is in the finite field G F ( s ) {\displaystyle GF(s)} if s {\displaystyle s} is a power of a prime. Such equations are called defining equations of the fraction. When the defining equation or equations are homogeneous, the fraction is said to be principal. One defining equation yields a fraction of size s k − 1 {\displaystyle s^{k-1}} , two independent equations a fraction of size s k − 2 , {\displaystyle s^{k-2},} and so on. Such fractions are generally denoted as s k − r {\displaystyle s^{k-r}} designs. The half-fractions described above are 2 3 − 1 {\displaystyle 2^{3-1}} designs. The notation often includes the resolution as a subscript, in Roman numerals; the above fractions are thus 2 I I I 3 − 1 {\displaystyle 2_{III}^{3-1}} designs. Associated to each expression a 1 t 1 + ⋯ + a k t k {\displaystyle a_{1}t_{1}+\cdots +a_{k}t_{k}} is another, namely A 1 a 1 ⋯ A k a k {\displaystyle A_{1}^{a_{1}}\cdots A_{k}^{a_{k}}} , which rewrites the coefficients as exponents. Such expressions are called "words", a term borrowed from group theory. (In a particular example


id: aliasing-factorial-experiments-20260505-4
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-4.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
The use of arithmetic modulo 2 explains why the factor levels in such designs are labeled 0 and 1. === Example 2 === In a 3-level design, factor levels are denoted 0, 1 and 2, and arithmetic is modulo 3. If there are four factors, say A , B , C {\displaystyle A,B,C} and D {\displaystyle D} , the effects group G {\displaystyle \mathbb {G} } will have the relations A 3 = B 3 = C 3 = D 3 = I . {\displaystyle A^{3}=B^{3}=C^{3}=D^{3}=I.} From these it follows, for example, that D 4 = D {\displaystyle D^{4}=D} and D 6 = I {\displaystyle D^{6}=I} . A defining equation such as t 1 + t 2 + t 3 + 2 t 4 = 0 ( mod 3 ) {\displaystyle t_{1}+t_{2}+t_{3}+2t^{4}=0{\pmod {3}}} would produce a regular 1/3-fraction of the 81 (= 3 4 {\displaystyle 3^{4}} ) treatment combinations, and the corresponding defining word would be A B C D 2 {\displaystyle ABCD^{2}} . Since its powers are ( A B C D 2 ) 2 = A 2 B 2 C 2 D {\displaystyle (ABCD^{2})^{2}=A^{2}B^{2}C^{2}D} and ( A B C D 2 ) 3 = I {\displaystyle (ABCD^{2})^{3}=I} ,


id: aliasing-factorial-experiments-20260505-5
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-5.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
In the 2 3 − 1 {\displaystyle 2^{3-1}} fraction with defining word A B C {\displaystyle ABC} , the maximum resolution is 3 (the length of that word), while the fraction with defining word A B {\displaystyle AB} has maximum resolution 2. The defining words of the 3 4 − 1 {\displaystyle 3^{4-1}} fraction were A B C D 2 {\displaystyle ABCD^{2}} and A 2 B 2 C 2 D {\displaystyle A^{2}B^{2}C^{2}D} , both of length 4, so that the fraction has maximum resolution 4, as indicated. In the 2 5 − 2 {\displaystyle 2^{5-2}} fraction with defining words A B D , A C E {\displaystyle ABD,ACE} and B C D E {\displaystyle BCDE} , the maximum resolution is 3, which is the shortest "wordlength". One could also construct a 2 5 − 2 {\displaystyle 2^{5-2}} fraction from the defining words A B C D {\displaystyle ABCD} and B C D E {\displaystyle BCDE} , but the defining subgroup H {\displaystyle \mathbb {H} } will also include A E {\displaystyle AE} , their product, and so the fraction will only have resolution 2 (the length of A E {\displaystyle AE} ). This is true starting with any two words


id: aliasing-factorial-experiments-20260505-6
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-6.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
== Partial aliasing == In regular 2 k {\displaystyle 2^{k}} fractions there is no partial aliasing: Each effect is either preserved or completely lost, and effects are either unaliased or completely aliased. The same holds in regular s k {\displaystyle s^{k}} experiments with s > 2 {\displaystyle s>2} if one considers only main effects and components of interaction. However, a limited form of partial aliasing occurs in the latter. For example, in the 3 4 − 1 {\displaystyle 3^{4-1}} design described above the overall A × B × C × D {\displaystyle A\times B\times C\times D} interaction is partly lost since its A B C D 2 {\displaystyle ABCD^{2}} component is completely lost in the fraction while its other components (such as A B 2 C 2 D {\displaystyle AB^{2}C^{2}D} ) are preserved. Similarly, the main effect of A {\displaystyle A} is partly aliased with the B × C × D {\displaystyle B\times C\times D} interaction since A {\displaystyle A} is completely aliased with its B C D 2 {\displaystyle BCD^{2}} component and unaliased with the others. In contrast, partial aliasing is uncontrolled and pervasive in nonregular fractions. In the 12-run Plackett-Burman design described in the previous section, for example,


id: all-pairs-testing-20260505-0
file: data/en.wikipedia.org/wiki/All-pairs_testing-0.md
category: reference
title: All-pairs testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/All-pairs_testing
date_saved: 2026-05-05T09:48:50.876127+00:00
instance: kb-cron
parent: all-pairs-testing-20260505-0
summary:
In computer science, all-pairs testing or pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a system (typically, a software algorithm), tests all possible discrete combinations of those parameters. Using carefully chosen test vectors, this can be done much faster than an exhaustive search of all combinations of all parameters by "parallelizing" the tests of parameter pairs. == Rationale == In most cases, a single input parameter or an interaction between two parameters is what causes a program's bugs. Bugs involving interactions between three or more parameters are both progressively less common and also progressively more expensive to find, such testing has as its limit the testing of all possible inputs. Thus, a combinatorial technique for picking test cases like all-pairs testing is a useful cost-benefit compromise that enables a significant reduction in the number of test cases without drastically compromising functional coverage. More rigorously, if we assume that a test case has N {\displaystyle N} parameters given in a set { P i } = { P 1 , P 2 , . . . , P N } {\displaystyle \{P_{i}\}=\{P_{1},P_{2},...,P_{N}\}} . The range of the parameters are given by R


id: allocation-concealment-20260505-0
file: data/en.wikipedia.org/wiki/Allocation_concealment-0.md
category: reference
title: Allocation concealment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Allocation_concealment
date_saved: 2026-05-05T09:48:52.131762+00:00
instance: kb-cron
parent: allocation-concealment-20260505-0
summary:
In a randomized experiment, allocation concealment hides the sorting of trial participants into treatment groups so that this knowledge cannot be exploited. Adequate allocation concealment serves to prevent study participants from influencing treatment allocations for subjects. Studies with poor allocation concealment (or none at all) are prone to selection bias. Some standard methods of ensuring allocation concealment include sequentially numbered, opaque, sealed envelopes (SNOSE); sequentially numbered containers; pharmacy controlled randomization; and central randomization. CONSORT guidelines recommend that allocation concealment methods be included in a study's protocol, and that the allocation concealment methods be reported in detail in their publication; however, a 2005 study determined that most clinical trials have unclear allocation concealment in their protocols, in their publications, or both. A 2008 study of 146 meta-analyses concluded that the results of randomized controlled trials with inadequate or unclear allocation concealment tended to be biased toward beneficial effects only if the trials' outcomes were subjective as opposed to objective. Allocation concealment is different from blinding. An allocation concealment method prevents influence on the randomization process, while blinding conceals the outcome of the randomization. However, allocation concealment may also be called "randomization blinding". == Impact == Without the use of allocation concealment,


id: analysis-of-variance-20260505-0
file: data/en.wikipedia.org/wiki/Analysis_of_variance-0.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation between the group means to the amount of variation within each group. If the between-group variation is substantially larger than the within-group variation, it suggests that the group means are likely different. This comparison is done using an F-test. The underlying principle of ANOVA is based on the law of total variance, which states that the total variance in a dataset can be broken down into components attributable to different sources. In the case of ANOVA, these sources are the variation between groups and the variation within groups. ANOVA was developed by the statistician Ronald Fisher. In its simplest form, it provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. == History == While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing in the 1770s. Around


id: analysis-of-variance-20260505-1
file: data/en.wikipedia.org/wiki/Analysis_of_variance-1.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
== Classes of models == There are three classes of models used in the analysis of variance, and these are outlined here. === Fixed-effects models === The fixed-effects model (class I) of analysis of variance applies to situations in which the experimenter applies one or more treatments to the subjects of the experiment to see whether the response variable values change. This allows the experimenter to estimate the ranges of response variable values that the treatment would generate in the population as a whole. === Random-effects models === Random-effects model (class II) is used when the treatments are not fixed. This occurs when the various factor levels are sampled from a larger population. Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments (a multi-variable generalization of simple differences) differ from the fixed-effects model. === Mixed-effects models === A mixed-effects model (class III) contains experimental factors of both fixed and random-effects types, with appropriately different interpretations and analysis for the two types. === Example === Teaching experiments could be performed by a college or university department to find a good introductory textbook, with each text considered a treatment. The fixed-effects model would compare a


id: analysis-of-variance-20260505-2
file: data/en.wikipedia.org/wiki/Analysis_of_variance-2.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
The normal-model based ANOVA analysis assumes the independence, normality, and homogeneity of variances of the residuals. The randomization-based analysis assumes only the homogeneity of the variances of the residuals (as a consequence of unit-treatment additivity) and uses the randomization procedure of the experiment. Both these analyses require homoscedasticity, as an assumption for the normal-model analysis and as a consequence of randomization and additivity for the randomization-based analysis. However, studies of processes that change variances rather than means (called dispersion effects) have been successfully conducted using ANOVA. There are no necessary assumptions for ANOVA in its full generality, but the F-test used for ANOVA hypothesis testing has assumptions and practical limitations which are of continuing interest. Problems which do not satisfy the assumptions of ANOVA can often be transformed to satisfy the assumptions. The property of unit-treatment additivity is not invariant under a "change of scale", so statisticians often use transformations to achieve unit-treatment additivity. If the response variable is expected to follow a parametric family of probability distributions, then the statistician may specify (in the protocol for the experiment or observational study) that the responses be transformed to stabilize the variance. Also, a statistician may specify that logarithmic transforms be


id: analysis-of-variance-20260505-3
file: data/en.wikipedia.org/wiki/Analysis_of_variance-3.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
The textbook method is to compare the observed value of F with the critical value of F determined from tables. The critical value of F is a function of the degrees of freedom of the numerator and the denominator and the significance level (α). If F ≥ FCritical, the null hypothesis is rejected. The computer method calculates the probability (p-value) of a value of F greater than or equal to the observed value. The null hypothesis is rejected if this probability is less than or equal to the significance level (α). The ANOVA F-test is known to be nearly optimal in the sense of minimizing false negative errors for a fixed rate of false positive errors (i.e. maximizing power for a fixed significance level). For example, to test the hypothesis that various medical treatments have exactly the same effect, the F-test's p-values closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced. Such permutation tests characterize tests with maximum power against all alternative hypotheses, as observed by Rosenbaum. The ANOVA F-test (of the null-hypothesis that all treatments have exactly the same effect) is recommended as a practical test, because of its robustness against many


id: analysis-of-variance-20260505-4
file: data/en.wikipedia.org/wiki/Analysis_of_variance-4.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
==== The number of experimental units ==== In the design of an experiment, the number of experimental units is planned to satisfy the goals of the experiment. Experimentation is often sequential. Early experiments are often designed to provide mean-unbiased estimates of treatment effects and of experimental error. Later experiments are often designed to test a hypothesis that a treatment effect has an important magnitude; in this case, the number of experimental units is chosen so that the experiment is within budget and has adequate power, among other goals. Reporting sample size analysis is generally required in psychology. "Provide information on sample size and the process that led to sample size decisions." The analysis, which is written in the experimental protocol before the experiment is conducted, is examined in grant applications and administrative review boards. Besides the power analysis, there are less formal methods for selecting the number of experimental units. These include graphical methods based on limiting the probability of false negative errors, graphical methods based on an expected variation increase (above the residuals) and methods based on achieving a desired confidence interval. ==== Power analysis ==== Power analysis is often applied in the context of ANOVA in order to


id: analysis-of-variance-20260505-5
file: data/en.wikipedia.org/wiki/Analysis_of_variance-5.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
== Cautions == Balanced experiments (those with an equal sample size for each treatment) are relatively easy to interpret; unbalanced experiments offer more complexity. For single-factor (one-way) ANOVA, the adjustment for unbalanced data is easy, but the unbalanced analysis lacks both robustness and power. For more complex designs the lack of balance leads to further complications. "The orthogonality property of main effects and interactions present in balanced data does not carry over to the unbalanced case. This means that the usual analysis of variance techniques do not apply. Consequently, the analysis of unbalanced factorials is much more difficult than that for balanced designs." In the general case, "The analysis of variance can also be applied to unbalanced data, but then the sums of squares, mean squares, and F-ratios will depend on the order in which the sources of variation are considered." ANOVA is (in part) a test of statistical significance. The American Psychological Association (and many other organisations) holds the view that simply reporting statistical significance is insufficient and that reporting confidence bounds is preferred. == Generalizations == ANOVA is considered to be a special case of linear regression which in turn is a special case of the general linear


id: analysis-of-variance-20260505-6
file: data/en.wikipedia.org/wiki/Analysis_of_variance-6.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
== References == Anscombe, F. J. (1948). "The Validity of Comparative Experiments". Journal of the Royal Statistical Society. Series A (General). 111 (3): 181–211. doi:10.2307/2984159. JSTOR 2984159. MR 0030181. Bailey, R. A. (2008). Design of Comparative Experiments. Cambridge University Press. ISBN 978-0-521-68357-9. Pre-publication chapters are available on-line. Belle, Gerald van (2008). Statistical rules of thumb (2nd ed.). Hoboken, N.J: Wiley. ISBN 978-0-470-14448-0. Cochran, William G.; Cox, Gertrude M. (1992). Experimental designs (2nd ed.). New York: Wiley. ISBN 978-0-471-54567-5. Cohen, Jacob (1988). Statistical power analysis for the behavior sciences (2nd ed.). Routledge ISBN 978-0-8058-0283-2 Cohen, Jacob (1992). "Statistics a power primer". Psychological Bulletin. 112 (1): 155–159. doi:10.1037/0033-2909.112.1.155. PMID 19565683. S2CID 14411587. Cox, David R. (1958). Planning of experiments. Reprinted as ISBN 978-0-471-57429-3 Cox, David R. (2006). Principles of statistical inference. Cambridge New York: Cambridge University Press. ISBN 978-0-521-68567-2. Freedman, David A.(2005). Statistical Models: Theory and Practice, Cambridge University Press. ISBN 978-0-521-67105-7 Gelman, Andrew (2005). "Analysis of variance? Why it is more important than ever". The Annals of Statistics. 33: 1–53. arXiv:math/0504499. doi:10.1214/009053604000001048. S2CID 13529149. Gelman, Andrew (2008). "Variance, analysis of". The new Palgrave dictionary of economics (2nd ed.). Basingstoke, Hampshire New York: Palgrave Macmillan. ISBN 978-0-333-78676-5. Hinkelmann, Klaus & Kempthorne, Oscar


id: animal-perception-of-magic-20260505-0
file: data/en.wikipedia.org/wiki/Animal_perception_of_magic-0.md
category: reference
title: Animal perception of magic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Animal_perception_of_magic
date_saved: 2026-05-05T09:48:54.537395+00:00
instance: kb-cron
parent: animal-perception-of-magic-20260505-0
summary:
Researchers study the reactions of animals observing humans performing magic tricks in order to better understand animal cognition. Using these studies, evolutionary psychologists aim to gain insights into the evolution of perception and attention by comparing responses of different species, including humans. == Background == Magic is about violating expectations. It capitalises on specific blind spots in attention and perception. While scientific interest in humans' perception of magic dates back to the late 19th century, when in 1896 Alfred Binet presented his work, this faded quickly, and has only recently, in the early 21st century, been revived. Some researchers have coined terms such as neuromagic or magicology for the study of magic. Other scientists are critical of the new field, saying it is not worthy to stand as a field of its own. Scientists aim to get insight into how the human mind operates. Some animal species are capable of misdirection, an important skill magicians possess to trick humans. For example, chimpanzees have been observed to deliberately look away from an object they desire as to avoid it being noticed by a competitor. Jays and other corvids pretend to store food in various places, trying to obscure the cache's true


id: antecedent-variable-20260505-0
file: data/en.wikipedia.org/wiki/Antecedent_variable-0.md
category: reference
title: Antecedent variable
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Antecedent_variable
date_saved: 2026-05-05T09:48:55.799600+00:00
instance: kb-cron
parent: antecedent-variable-20260505-0
summary:
In statistics and social sciences, an antecedent variable is a variable that cannot help to explain the apparent relationship (or part of the relationship) between other variables that are nominally in a cause and effect relationship. In a regression analysis, an antecedent variable would be one that influences both the independent variable and the dependent variable. == See also == Path analysis (statistics) Latent variable Intervening variable Confounding variable == References == Olobatuyi, M. E. (2006). "Definition of Basic Terms and Concepts". A User's Guide to Path Analysis. University Press of America. pp. 21–52. ISBN 0-7618-3230-0.


id: arrive-guidelines-20260505-0
file: data/en.wikipedia.org/wiki/ARRIVE_guidelines-0.md
category: reference
title: ARRIVE guidelines
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/ARRIVE_guidelines
date_saved: 2026-05-05T09:48:57.054025+00:00
instance: kb-cron
parent: arrive-guidelines-20260505-0
summary:
The ARRIVE guidelines (short for Animals in Research: Reporting In Vivo Experiments) are a set of guidelines for improving experimental design and reporting standards for animal research, drawn up by the National Centre for the Replacement, Refinement and Reduction of Animals in Research. First published in 2010 as a checklist of 20 items, a revision, titled ARRIVE 2.0, was published in 2020 as two checklists of 10 "essential" items and 11 "recommended" items. While the guidelines have been endorsed by over a thousand scientific journals, their adoption and enforcement has remained limited. == Origin == A 2009 review of the quality of experimental design, analysis, and reporting methods of animal research conducted by the National Centre for the Replacement, Refinement and Reduction of Animals in Research (NC3Rs) found that most biomedical journals were providing little or no guidance on how animal research should be analyzed and reported, outside of ethical guidelines for experimental design, such as the Three Rs. Additionally, it found issues with the way animal research is reported, with large proportions of articles not stating a hypothesis or objective of the study, lacking specifics about the characteristics of the animals used, not having used techniques such as randomization


id: association-scheme-20260505-0
file: data/en.wikipedia.org/wiki/Association_scheme-0.md
category: reference
title: Association scheme
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Association_scheme
date_saved: 2026-05-05T09:48:58.210111+00:00
instance: kb-cron
parent: association-scheme-20260505-0
summary:
The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. In algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial designs and the theory of error-correcting codes. In algebra, the theory of association schemes generalizes the character theory of linear representations of groups. == Definition == An n-class association scheme consists of a set X together with a partition S of X × X into n + 1 binary relations, R0, R1, ..., Rn which satisfy: R 0 = { ( x , x ) : x ∈ X } {\displaystyle R_{0}=\{(x,x):x\in X\}} ; it is called the identity relation. Defining R ∗ := { ( x , y ) : ( y , x ) ∈ R } {\displaystyle R^{*}:=\{(x,y):(y,x)\in R\}} , if R in S, then R* in S. If ( x , y ) ∈ R k {\displaystyle (x,y)\in R_{k}} , the number of z ∈ X {\displaystyle z\in X} such that ( x , z ) ∈ R i {\displaystyle (x,z)\in R_{i}} and ( z , y ) ∈ R j {\displaystyle


id: association-scheme-20260505-1
file: data/en.wikipedia.org/wiki/Association_scheme-1.md
category: reference
title: Association scheme
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Association_scheme
date_saved: 2026-05-05T09:48:58.210111+00:00
instance: kb-cron
parent: association-scheme-20260505-0
summary:
== History == The term association scheme is due to (Bose & Shimamoto 1952) but the concept is already inherent in (Bose & Nair 1939). These authors were studying what statisticians have called partially balanced incomplete block designs (PBIBDs). The subject became an object of algebraic interest with the publication of (Bose & Mesner 1959) and the introduction of the Bose–Mesner algebra. The most important contribution to the theory was the thesis of Ph. Delsarte (Delsarte 1973) who recognized and fully used the connections with coding theory and design theory. A generalization called coherent configurations has been studied by D. G. Higman. == Basic facts == p 00 0 = 1 {\displaystyle p_{00}^{0}=1} , i.e., if ( x , y ) ∈ R 0 {\displaystyle (x,y)\in R_{0}} then x = y {\displaystyle x=y} and the only z {\displaystyle z} such that ( x , z ) ∈ R 0 {\displaystyle (x,z)\in R_{0}} is z = x {\displaystyle z=x} . ∑ i = 0 k p i i 0 = | X | {\displaystyle \sum _{i=0}^{k}p_{ii}^{0}=|X|} ; this is because the R i {\displaystyle R_{i}} partition X {\displaystyle X} . == The Bose–Mesner algebra == The adjacency matrices A i {\displaystyle


id: association-scheme-20260505-2
file: data/en.wikipedia.org/wiki/Association_scheme-2.md
category: reference
title: Association scheme
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Association_scheme
date_saved: 2026-05-05T09:48:58.210111+00:00
instance: kb-cron
parent: association-scheme-20260505-0
summary:
== References == Bailey, Rosemary A. (2004), Association Schemes: Designed Experiments, Algebra and Combinatorics, Cambridge University Press, ISBN 978-0-521-82446-0, MR 2047311. (Chapters from preliminary draft are available on-line.) Bannai, Eiichi; Ito, Tatsuro (1984), Algebraic combinatorics I: Association schemes, Menlo Park, CA: Benjamin/Cummings, ISBN 0-8053-0490-8, MR 0882540 Bose, R. C.; Mesner, D. M. (1959), "On linear associative algebras corresponding to association schemes of partially balanced designs", Annals of Mathematical Statistics, 30 (1): 21–38, doi:10.1214/aoms/1177706356, JSTOR 2237117, MR 0102157 Bose, R. C.; Nair, K. R. (1939), "Partially balanced incomplete block designs", Sankhyā, 4 (3): 337–372, JSTOR 40383923 Bose, R. C.; Shimamoto, T. (1952), "Classification and analysis of partially balanced incomplete block designs with two associate classes", Journal of the American Statistical Association, 47 (258): 151–184, doi:10.1080/01621459.1952.10501161 Camion, P. (1998), "18. Codes and Association Schemes: Basic Properties of Association Schemes Relevant to Coding", in Pless, V.S.; Huffman, W.C.; Brualdi, R.A. (eds.), Handbook of Coding Theory, vol. 1, Elsevier, pp. 1441–, ISBN 978-0-444-50088-5 Delsarte, P. (1973), "An Algebraic Approach to the Association Schemes of Coding Theory", Philips Research Reports (Supplement No. 10), OCLC 641852316 Delsarte, P.; Levenshtein, V. I. (1998). "Association schemes and coding theory". IEEE Transactions on Information Theory. 44 (6): 2477–2504. doi:10.1109/18.720545.


id: bayesian-experimental-design-20260505-0
file: data/en.wikipedia.org/wiki/Bayesian_experimental_design-0.md
category: reference
title: Bayesian experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bayesian_experimental_design
date_saved: 2026-05-05T09:48:59.414261+00:00
instance: kb-cron
parent: bayesian-experimental-design-20260505-0
summary:
Bayesian experimental design provides a general probability-theoretical framework from which other theories on experimental design can be derived. It is based on Bayesian inference to interpret the observations/data acquired during the experiment. This allows accounting for both any prior knowledge on the parameters to be determined as well as uncertainties in observations. The theory of Bayesian experimental design is to a certain extent based on the theory for making optimal decisions under uncertainty. The aim when designing an experiment is to maximize the expected utility of the experiment outcome. The utility is most commonly defined in terms of a measure of the accuracy of the information provided by the experiment (e.g., the Shannon information or the negative of the variance) but may also involve factors such as the financial cost of performing the experiment. What will be the optimal experiment design depends on the particular utility criterion chosen. == Relations to more specialized optimal design theory == === Linear theory === If the model is linear, the prior probability density function (PDF) is homogeneous and observational errors are normally distributed, the theory simplifies to the classical optimal experimental design theory. === Approximate normality === In numerous publications on Bayesian experimental


id: bayesian-experimental-design-20260505-1
file: data/en.wikipedia.org/wiki/Bayesian_experimental_design-1.md
category: reference
title: Bayesian experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bayesian_experimental_design
date_saved: 2026-05-05T09:48:59.414261+00:00
instance: kb-cron
parent: bayesian-experimental-design-20260505-0
summary:
of which the latter can be evaluated without the need for evaluating individual posterior probability p ( θ ∣ y , ξ ) {\displaystyle p(\theta \mid y,\xi )} for all possible observations y {\displaystyle y} . It is worth noting that the second term on the second equation line will not depend on the design ξ {\displaystyle \xi } , as long as the observational uncertainty doesn't. On the other hand, the integral of p ( θ ) log ⁡ p ( θ ) {\displaystyle p(\theta )\log p(\theta )} in the first form is constant for all ξ {\displaystyle \xi } , so if the goal is to choose the design with the highest utility, the term need not be computed at all. Several authors have considered numerical techniques for evaluating and optimizing this criterion. Note that U ( ξ ) = I ( θ ; y ) , {\displaystyle U(\xi )=I(\theta ;y)\,,} the expected information gain being exactly the mutual information between the parameter θ and the observation y. An example of Bayesian design for linear dynamical model identification are given in . Since I ( θ ; y ) , {\displaystyle I(\theta ;y)\,,} was difficult to calculate, its


id: between-group-design-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Between-group_design_experiment-0.md
category: reference
title: Between-group design experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Between-group_design_experiment
date_saved: 2026-05-05T09:49:00.617094+00:00
instance: kb-cron
parent: between-group-design-experiment-20260505-0
summary:
In the design of experiments, a between-group design is an experiment that has two or more groups of subjects each being tested by a different testing factor simultaneously. This design is usually used in place of, or in some cases in conjunction with, the within-subject design, which applies the same variations of conditions to each subject to observe the reactions. The simplest between-group design occurs with two groups; one is generally regarded as the treatment group, which receives the ‘special’ treatment (that is, it is treated with some variable), and the control group, which receives no variable treatment and is used as a reference (prove that any deviation in results from the treatment group is, indeed, a direct result of the variable). The between-group design is widely used in psychological, economic, and sociological experiments, as well as in several other fields in the natural or social sciences. == Experimental blinds == In order to avoid experimental bias, experimental blinds are usually applied in between-group designs. The most commonly used type is the single blind, which keeps the subjects blind without identifying them as members of the treatment group or the control group. In a single-blind experiment, a placebo is usually


id: blinded-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Blinded_experiment-0.md
category: reference
title: Blinded experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blinded_experiment
date_saved: 2026-05-05T09:49:01.984530+00:00
instance: kb-cron
parent: blinded-experiment-20260505-0
summary:
In a blind or blinded experiment, information that could influence participants or investigators is withheld until the experiment is completed. Blinding is used to reduce or eliminate potential sources of bias, such as participants’ expectations, the observer-expectancy effect, observer bias, confirmation bias, and other cognitive or procedural influences. Blinding can be applied to different participants in an experiment, including study subjects, researchers, technicians, data analysts, and outcome assessors. When multiple groups are blinded simultaneously (for example, both participants and researchers), the design is referred to as a double-blind study. In some cases, blinding is desirable but impractical or unethical. For example, it is not possible to blind a participant receiving a physical therapy intervention, or a surgeon performing an operative procedure. Well-designed clinical protocols therefore aim to maximize the effectiveness of blinding within ethical and practical constraints. During the course of an experiment, a participant becomes unblinded if they deduce or otherwise obtain information that has been masked to them. For example, a patient who experiences a side effect may correctly guess their treatment, becoming unblinded. Unblinding is common in blinded experiments, particularly in pharmacological trials. In particular, trials on pain medication and antidepressants are poorly blinded. Unblinding that occurs


id: blinded-experiment-20260505-1
file: data/en.wikipedia.org/wiki/Blinded_experiment-1.md
category: reference
title: Blinded experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blinded_experiment
date_saved: 2026-05-05T09:49:01.984530+00:00
instance: kb-cron
parent: blinded-experiment-20260505-0
summary:
== Unblinding == "Unblinding" occurs in a blinded experiment when information is revealed to someone to whom it has been masked. In clinical studies, unblinding may occur unintentionally when a patient deduces their treatment group. Unblinding that occurs before the conclusion of an experiment is a source of bias. Some degree of premature unblinding is common in blinded experiments. When a blind is imperfect, its success is judged on a spectrum with no blind (or complete failure of blinding) on one end, perfect blinding on the other, and poor or good blinding between. Thus, the common view of studies as blinded or unblinded exemplifies a false dichotomy. The success of blinding is assessed by asking study participants about information that has been masked from them (e.g., whether the participant received the drug or placebo?). In a perfectly blinded experiment, the responses should be consistent with no knowledge of the masked information. However, if unblinding has occurred, the responses will indicate the degree of unblinding. Since unblinding cannot be measured directly, but must be inferred from participants' responses, its measured value will depend on the nature of the questions asked. As a result, it is not possible to objectively measure unblinding.


id: blinded-experiment-20260505-2
file: data/en.wikipedia.org/wiki/Blinded_experiment-2.md
category: reference
title: Blinded experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blinded_experiment
date_saved: 2026-05-05T09:49:01.984530+00:00
instance: kb-cron
parent: blinded-experiment-20260505-0
summary:
==== Acupuncture ==== While the possibility of blinded trials on acupuncture is controversial, a 2003 review of 47 randomized controlled trials found no fewer than four methods of blinding patients to acupuncture treatment: 1) superficial needling of true acupuncture points, 2) use of acupuncture points which are not indicated for the condition being treated, 3) insertion of needles outside of true acupuncture points, and 4) the use of placebo needles which are designed not to penetrate the skin. The authors concluded that there was "no clear association between the type of sham intervention used and the results of the trials." A 2018 study on acupuncture, which used needles that did not penetrate the skin as a sham treatment, found that 68% of patients and 83% of acupuncturists correctly identified their group allocation. The authors concluded that blinding had failed, but that more advanced placebos may someday enable well-blinded studies in acupuncture. === In physics === It is standard practice in physics to perform blinded data analysis. Once the data analysis is complete, one may unblind the data. A prior agreement to publish the data regardless of the results of the study may be made to prevent publication bias. === In


id: block-design-20260505-0
file: data/en.wikipedia.org/wiki/Block_design-0.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such that number of occurrences of each element satisfies certain conditions making the collection of blocks exhibit symmetry (balance). Block designs have applications in many areas, including experimental design, finite geometry, physical chemistry, software testing, cryptography, and algebraic geometry. Without further specifications the term block design usually refers to a balanced incomplete block design (BIBD), specifically (and also synonymously) a 2-design, which has been the most intensely studied type historically due to its application in the design of experiments. Its generalization is known as a t-design. == Overview == A design is said to be balanced (up to t) if all t-subsets of the original set occur in equally many (i.e., λ) blocks. When t is unspecified, it can usually be assumed to be 2, which means that each pair of elements is found in the same number of blocks and the design is pairwise balanced. For t = 1, each element occurs in the same number of blocks (the replication number, denoted r) and the design is said to be regular. A block design in


id: block-design-20260505-1
file: data/en.wikipedia.org/wiki/Block_design-1.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
obtained from counting for a fixed x the triples (x, y, B) where x and y are distinct points and B is a block that contains them both. This equation for every x also proves that r is constant (independent of x) even without assuming it explicitly, thus proving that the condition that any x in X is contained in r blocks is redundant and r can be computed from the other parameters. The resulting b and r must be integers, which imposes conditions on v, k, and λ. These conditions are not sufficient as, for example, a (43,7,1)-design does not exist. The order of a 2-design is defined to be n = r − λ. The complement of a 2-design is obtained by replacing each block with its complement in the point set X. It is also a 2-design and has parameters v′ = v, b′ = b, r′ = b − r, k′ = v − k, λ′ = λ + b − 2r. A 2-design and its complement have the same order. A fundamental theorem, Fisher's inequality, named after the statistician Ronald Fisher, is that b ≥ v in any 2-design. A rather surprising and not very


id: block-design-20260505-2
file: data/en.wikipedia.org/wiki/Block_design-2.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
Since k = r we can write the order of a projective plane as n = k − 1 and, from the displayed equation above, we obtain v = (n + 1)n + 1 = n2 + n + 1 points in a projective plane of order n. As a projective plane is a symmetric design, we have b = v, meaning that b = n2 + n + 1 also. The number b is the number of lines of the projective plane. There can be no repeated lines since λ = 1, so a projective plane is a simple 2-design in which the number of lines and the number of points are always the same. For a projective plane, k is the number of points on each line and it is equal to n + 1. Similarly, r = n + 1 is the number of lines with which a given point is incident. For n = 2 we get a projective plane of order 2, also called the Fano plane, with v = 4 + 2 + 1 = 7 points and 7 lines. In the Fano plane, each line has n + 1 = 3 points and


id: block-design-20260505-3
file: data/en.wikipedia.org/wiki/Block_design-3.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
== General balanced designs (t-designs) == Given any positive integer t, a t-design B is a class of k-element subsets of X, called blocks, such that every point x in X appears in exactly r blocks, and every t-element subset T appears in exactly λ blocks. The numbers v (the number of elements of X), b (the number of blocks), k, r, λ, and t are the parameters of the design. The design may be called a t-(v,k,λ)-design. Again, these four numbers determine b and r and the four numbers themselves cannot be chosen arbitrarily. The equations are λ i = λ ( v − i t − i ) / ( k − i t − i ) for i = 0 , 1 , … , t , {\displaystyle \lambda _{i}=\lambda \left.{\binom {v-i}{t-i}}\right/{\binom {k-i}{t-i}}{\text{ for }}i=0,1,\ldots ,t,} where λi is the number of blocks that contain any i-element set of points and λt = λ. Note that b = λ 0 = λ ( v t ) / ( k t ) {\displaystyle b=\lambda _{0}=\lambda {v \choose t}/{k \choose t}} and r = λ 1 = λ ( v − 1 t − 1 ) / ( k


id: block-design-20260505-4
file: data/en.wikipedia.org/wiki/Block_design-4.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
R 0 = { ( x , x ) : x ∈ X } {\displaystyle R_{0}=\{(x,x):x\in X\}} and is called the Identity relation. Defining R ∗ := { ( x , y ) ∣ ( y , x ) ∈ R } {\displaystyle R^{*}:=\{(x,y)\mid (y,x)\in R\}} , if R in S, then R* in S If ( x , y ) ∈ R k {\displaystyle (x,y)\in R_{k}} , the number of z ∈ X {\displaystyle z\in X} such that ( x , z ) ∈ R i {\displaystyle (x,z)\in R_{i}} and ( z , y ) ∈ R j {\displaystyle (z,y)\in R_{j}} is a constant p i j k {\displaystyle p_{ij}^{k}} depending on i, j, k but not on the particular choice of x and y. An association scheme is commutative if p i j k = p j i k {\displaystyle p_{ij}^{k}=p_{ji}^{k}} for all i, j and k. Most authors assume this property. A partially balanced incomplete block design with n associate classes (PBIBD(n)) is a block design based on a v-set X with b blocks each of size k and with each element appearing in r blocks, such that there is an association scheme with n classes defined


id: block-design-20260505-5
file: data/en.wikipedia.org/wiki/Block_design-5.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
== References == Aschbacher, Michael (1971). "On collineation groups of symmetric block designs". Journal of Combinatorial Theory. Series A. 11 (3): 272–281. doi:10.1016/0097-3165(71)90054-9. Assmus, E.F.; Key, J.D. (1992), Designs and Their Codes, Cambridge: Cambridge University Press, ISBN 0-521-41361-3 Beth, Thomas; Jungnickel, Dieter; Lenz, Hanfried (1986), Design Theory, Cambridge University Press. 2nd ed. (1999) ISBN 978-0-521-44432-3. Bose, R. C. (1949), "A Note on Fisher's Inequality for Balanced Incomplete Block Designs", Annals of Mathematical Statistics, 20 (4): 619–620, doi:10.1214/aoms/1177729958 Bose, R. C.; Shimamoto, T. (1952), "Classification and analysis of partially balanced incomplete block designs with two associate classes", Journal of the American Statistical Association, 47 (258): 151–184, doi:10.1080/01621459.1952.10501161 Cameron, P. J.; van Lint, J. H. (1991), Designs, Graphs, Codes and their Links, Cambridge University Press, ISBN 0-521-42385-6 Colbourn, Charles J.; Dinitz, Jeffrey H. (2007), Handbook of Combinatorial Designs (2nd ed.), Boca Raton: Chapman & Hall/ CRC, ISBN 978-1-58488-506-1 Fisher, R.A. (1940), "An examination of the different possible solutions of a problem in incomplete blocks", Annals of Eugenics, 10: 52–75, doi:10.1111/j.1469-1809.1940.tb02237.x, hdl:2440/15239 Hall, Marshall Jr. (1986), Combinatorial Theory (2nd ed.), New York: Wiley-Interscience, ISBN 0-471-09138-3 Hughes, D.R.; Piper, E.C. (1985), Design theory, Cambridge: Cambridge University Press, ISBN 0-521-25754-9 Kaski, Petteri; Östergård, Patric (2008).


id: blocking-statistics-20260505-0
file: data/en.wikipedia.org/wiki/Blocking_(statistics)-0.md
category: reference
title: Blocking (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blocking_(statistics)
date_saved: 2026-05-05T09:49:20.919707+00:00
instance: kb-cron
parent: blocking-statistics-20260505-0
summary:
In the statistical theory of the design of experiments, blocking is the arranging of experimental units that are similar to one another in groups (blocks) based on one or more variables. These variables are chosen carefully to minimize the effect of their variability on the observed outcomes. There are different ways that blocking can be implemented, resulting in different confounding effects. However, the different methods share the same purpose: to control variability introduced by specific factors that could influence the outcome of an experiment. The roots of blocking originated from the statistician, Ronald Fisher, following his development of ANOVA. == History == The use of blocking in experimental design has an evolving history that spans multiple disciplines. The foundational concepts of blocking date back to the early 20th century with statisticians like Ronald A. Fisher. His work in developing analysis of variance (ANOVA) set the groundwork for grouping experimental units to control for extraneous variables. Blocking evolved over the years, leading to the formalization of randomized block designs and Latin square designs. Today, blocking still plays a pivotal role in experimental design, and in recent years, advancements in statistical software and computational capabilities have allowed researchers to explore more intricate


id: blocking-statistics-20260505-1
file: data/en.wikipedia.org/wiki/Blocking_(statistics)-1.md
category: reference
title: Blocking (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blocking_(statistics)
date_saved: 2026-05-05T09:49:20.919707+00:00
instance: kb-cron
parent: blocking-statistics-20260505-0
summary:
In our previous diet pills example, a blocking factor could be the sex of a patient. We could put individuals into one of two blocks (male or female). And within each of the two blocks, we can randomly assign the patients to either the diet pill (treatment) or placebo pill (control). By blocking on sex, this source of variability is controlled, therefore, leading to greater interpretation of how the diet pills affect weight loss. === Definition of blocking factors === A nuisance factor is used as a blocking factor if every level of the primary factor occurs the same number of times with each level of the nuisance factor. The analysis of the experiment will focus on the effect of varying levels of the primary factor within each block of the experiment. === Block a few of the most important nuisance factors === The general rule is: "Block what you can; randomize what you cannot." Blocking is used to remove the effects of a few of the most important nuisance variables. Randomization is then used to reduce the contaminating effects of the remaining nuisance variables. For important nuisance variables, blocking will yield higher significance in the variables of interest than


id: blocking-statistics-20260505-2
file: data/en.wikipedia.org/wiki/Blocking_(statistics)-2.md
category: reference
title: Blocking (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blocking_(statistics)
date_saved: 2026-05-05T09:49:20.919707+00:00
instance: kb-cron
parent: blocking-statistics-20260505-0
summary:
Yij is any observation for which X1 = i and X2 = j X1 is the primary factor X2 is the blocking factor μ is the general location parameter (i.e., the mean) Ti is the effect for being in treatment i (of factor X1) Bj is the effect for being in block j (of factor X2) === Estimates === Estimate for μ : Y ¯ {\displaystyle {\overline {Y}}} = the average of all the data Estimate for Ti : Y ¯ i ⋅ − Y ¯ {\displaystyle {\overline {Y}}_{i\cdot }-{\overline {Y}}} with Y ¯ i ⋅ {\displaystyle {\overline {Y}}_{i\cdot }} = average of all Y for which X1 = i. Estimate for Bj : Y ¯ ⋅ j − Y ¯ {\displaystyle {\overline {Y}}_{\cdot j}-{\overline {Y}}} with Y ¯ ⋅ j {\displaystyle {\overline {Y}}_{\cdot j}} = average of all Y for which X2 = j. === Generalizations === Generalized randomized block designs (GRBD) allow tests of block–treatment interaction, and has exactly one blocking factor like the RCBD. Latin squares (and other row–column designs) have two blocking factors that are believed to have no interaction. Latin hypercube sampling Graeco-Latin squares Hyper-Graeco-Latin square designs == See also == Algebraic statistics Block design


id: bose-mesner-algebra-20260505-0
file: data/en.wikipedia.org/wiki/Bose–Mesner_algebra-0.md
category: reference
title: Bose–Mesner algebra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bose–Mesner_algebra
date_saved: 2026-05-05T09:49:22.162239+00:00
instance: kb-cron
parent: bose-mesner-algebra-20260505-0
summary:
In mathematics, a Bose–Mesner algebra is a special set of matrices which arise from a combinatorial structure known as an association scheme, together with the usual set of rules for combining (forming the products of) those matrices, such that they form an associative algebra, or, more precisely, a unitary commutative algebra. Among these rules are: the result of a product is also within the set of matrices, there is an identity matrix in the set, and taking products is commutative. Bose–Mesner algebras have applications in physics to spin models, and in statistics to the design of experiments. They are named for R. C. Bose and Dale Marsh Mesner. == Definition == Let X be a set of v elements. Consider a partition of the 2-element subsets of X into n non-empty subsets, R1, ..., Rn, such that: given an x ∈ X {\displaystyle x\in X} , the number of y ∈ X {\displaystyle y\in X} such that { x , y } ∈ R i {\displaystyle \{x,y\}\in R_{i}} depends only on i (and not on x). This number will be denoted by vi, and given x , y ∈ X {\displaystyle x,y\in X} with { x , y } ∈


id: bose-mesner-algebra-20260505-1
file: data/en.wikipedia.org/wiki/Bose–Mesner_algebra-1.md
category: reference
title: Bose–Mesner algebra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bose–Mesner_algebra
date_saved: 2026-05-05T09:49:22.162239+00:00
instance: kb-cron
parent: bose-mesner-algebra-20260505-0
summary:
∑ i = 0 n J i = I . ( 5 ) {\displaystyle \sum _{i=0}^{n}J_{i}=I.\qquad (5)} The Bose–Mesner algebra has two distinguished bases: the basis consisting of the adjacency matrices D i {\displaystyle D_{i}} , and the basis consisting of the irreducible idempotent matrices J k {\displaystyle J_{k}} . By definition, there exist well-defined complex numbers such that D i = ∑ k = 0 n p i ( k ) J k , ( 6 ) {\displaystyle D_{i}=\sum _{k=0}^{n}p_{i}(k)J_{k},\qquad (6)} and | X | J k = ∑ i = 0 n q k ( i ) D i . ( 7 ) {\displaystyle |X|J_{k}=\sum _{i=0}^{n}q_{k}\left(i\right)D_{i}.\qquad (7)} The p-numbers p i ( k ) {\displaystyle p_{i}(k)} , and the q-numbers q k ( i ) {\displaystyle q_{k}(i)} , play a prominent role in the theory. They satisfy well-defined orthogonality relations. The p-numbers are the eigenvalues of the adjacency matrix D i {\displaystyle D_{i}} . == Theorem == The eigenvalues of p i ( k ) {\displaystyle p_{i}(k)} and q k ( i ) {\displaystyle q_{k}(i)} , satisfy the orthogonality conditions: ∑ k = 0 n μ i p i ( k ) p ℓ ( k ) =


id: box-behnken-design-20260505-0
file: data/en.wikipedia.org/wiki/Box–Behnken_design-0.md
category: reference
title: Box–Behnken design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Box–Behnken_design
date_saved: 2026-05-05T09:49:23.484470+00:00
instance: kb-cron
parent: box-behnken-design-20260505-0
summary:
In statistics, Box–Behnken designs are experimental designs for response surface methodology, devised by George E. P. Box and Donald Behnken in 1960, to achieve the following goals: Each factor, or independent variable, is placed at one of three equally spaced values, usually coded as −1, 0, +1. (At least three levels are needed for the following goal.) The design should be sufficient to fit a quadratic model, that is, one containing squared terms, products of two factors, linear terms and an intercept. The ratio of the number of experimental points to the number of coefficients in the quadratic model should be reasonable (in fact, their designs kept in the range of 1.5 to 2.6). The estimation variance should more or less depend only on the distance from the centre (this is achieved exactly for the designs with 4 and 7 factors), and should not vary too much inside the smallest (hyper)cube containing the experimental points. (See "rotatability" in "Comparisons of response surface designs".) Box-Behnken design is still considered to be more proficient and more powerful than other designs such as the three-level full factorial design, central composite design (CCD) and Doehlert design, despite its poor coverage of the corner of


id: bruck-ryser-chowla-theorem-20260505-0
file: data/en.wikipedia.org/wiki/Bruck–Ryser–Chowla_theorem-0.md
category: reference
title: Bruck–Ryser–Chowla theorem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bruck–Ryser–Chowla_theorem
date_saved: 2026-05-05T09:49:24.722968+00:00
instance: kb-cron
parent: bruck-ryser-chowla-theorem-20260505-0
summary:
The Bruck–Ryser–Chowla theorem is a result on the combinatorics of symmetric block designs that implies nonexistence of certain kinds of design. It states that if a (v, b, r, k, λ)-design exists with v = b (implying k = r and λ(v − 1) = k(k − 1)), then: if v is even, then k − λ is a square; if v is odd, then the following Diophantine equation has a nontrivial solution: x2 − (k − λ)y2 − (−1)(v−1)/2 λ z2 = 0. The theorem was proved in the case of projective planes by Bruck & Ryser (1949). It was extended to symmetric designs by Chowla & Ryser (1950). == Projective planes == In the special case of a symmetric design with λ = 1, that is, a projective plane, the theorem (which in this case is referred to as the Bruck–Ryser theorem) can be stated as follows: If a finite projective plane of order q exists and q is congruent to 1 or 2 (mod 4), then q must be the sum of two squares. Note that for a projective plane, the design parameters are v = b = q2 + q + 1, r = k =


id: case-control-study-20260505-0
file: data/en.wikipedia.org/wiki/Case–control_study-0.md
category: reference
title: Case–control study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Case–control_study
date_saved: 2026-05-05T09:49:25.991019+00:00
instance: kb-cron
parent: case-control-study-20260505-0
summary:
A case–control study (also known as case–referent study) is a type of observational study in which two existing groups differing in outcome are identified and compared on the basis of some supposed causal attribute. Case–control studies are often used to identify factors that may contribute to a medical condition by comparing subjects who have the condition with patients who do not have the condition but are otherwise similar. They require fewer resources but provide less evidence for causal inference than a randomized controlled trial. A case–control study is often used to produce an odds ratio. Some statistical methods make it possible to use a case–control study to also estimate relative risk, risk differences, and other quantities. == Definition == Porta's Dictionary of Epidemiology defines the case–control study as: "an observational epidemiological study of persons with the disease (or another outcome variable) of interest and a suitable control group of persons without the disease (comparison group, reference group). The potential relationship of a suspected risk factor or an attribute to the disease is examined by comparing the diseased and nondiseased subjects with regard to how frequently the factor or attribute is present (or, if quantitative, the levels of the attribute) in


id: case-control-study-20260505-1
file: data/en.wikipedia.org/wiki/Case–control_study-1.md
category: reference
title: Case–control study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Case–control_study
date_saved: 2026-05-05T09:49:25.991019+00:00
instance: kb-cron
parent: case-control-study-20260505-0
summary:
== Examples == One of the most significant triumphs of the case–control study was the demonstration of the link between tobacco smoking and lung cancer, by Richard Doll and Bradford Hill. They showed a statistically significant association in a large case–control study. Opponents argued for many years that this type of study cannot prove causation, but the eventual results of cohort studies confirmed the causal link which the case–control studies suggested, and it is now accepted that tobacco smoking is the cause of about 87% of all lung cancer mortality in the US. == Analysis == Case–control studies were initially analyzed by testing whether or not there were significant differences between the proportion of exposed subjects among cases and controls. Subsequently, Cornfield pointed out that, when the disease outcome of interest is rare, the odds ratio of exposure can be used to estimate the relative risk (see rare disease assumption). The validity of the odds ratio depends highly on the nature of the disease studied, on the sampling methodology and on the type of follow-up. Although in classical case–control studies, it remains true that the odds ratio can only approximate the relative risk in the case of rare diseases, there


id: central-composite-design-20260505-0
file: data/en.wikipedia.org/wiki/Central_composite_design-0.md
category: reference
title: Central composite design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Central_composite_design
date_saved: 2026-05-05T09:49:27.222255+00:00
instance: kb-cron
parent: central-composite-design-20260505-0
summary:
In statistics, a central composite design is an experimental design, useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level factorial experiment. After the designed experiment is performed, linear regression is used, sometimes iteratively, to obtain results. Coded variables are often used when constructing this design. == Implementation == The design consists of three distinct sets of experimental runs: A factorial (perhaps fractional) design in the factors studied, each having two levels; A set of center points, experimental runs whose values of each factor are the medians of the values used in the factorial portion. This point is often replicated in order to improve the precision of the experiment; A set of axial points, experimental runs identical to the centre points except for one factor, which will take on values both below and above the median of the two factorial levels, and typically both outside their range. All factors are varied in this way. == Design matrix == The design matrix for a central composite design experiment involving k factors is derived from a matrix, d, containing the following three different parts corresponding to the three types


id: challenge-dechallenge-rechallenge-20260505-0
file: data/en.wikipedia.org/wiki/Challenge–dechallenge–rechallenge-0.md
category: reference
title: Challenge–dechallenge–rechallenge
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Challenge–dechallenge–rechallenge
date_saved: 2026-05-05T09:49:28.505082+00:00
instance: kb-cron
parent: challenge-dechallenge-rechallenge-20260505-0
summary:
Challenge–dechallenge–rechallenge (CDR) is a medical testing protocol in which a medicine or drug is administered, withdrawn, then re-administered, while being monitored for adverse effects at each stage. The protocol is used when statistical testing is inappropriate due to an idiosyncratic reaction by a specific individual, or a lack of sufficient test subjects and unit of analysis is the individual. During the dechallenge (withdrawal) phase, the medication is allowed to wash out of the system in order to determine what effect the medication is having on an individual. == Use in drug testing == CDR is one means of establishing the validity and benefits of medication in treating specific conditions as well as any adverse drug reactions. The Food and Drug Administration of the United States lists positive dechallenge reactions (an adverse event which disappears on withdrawal of the medication) as well as negative (an adverse event which continues after withdrawal), as well as positive rechallenge (symptoms re-occurring on re-administration) and negative rechallenge (failure of a symptom to re-occur after re-administration). It is one of the standard means of assessing adverse drug reactions in France. == Fluoxetine and suicide == Peter Breggin asserted that there was an association between fluoxetine (Prozac)


id: choice-set-20260505-0
file: data/en.wikipedia.org/wiki/Choice_set-0.md
category: reference
title: Choice set
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Choice_set
date_saved: 2026-05-05T09:49:29.753162+00:00
instance: kb-cron
parent: choice-set-20260505-0
summary:
A choice set is a finite collection of available options selected from a larger theoretical decision space. For example, a consumer has thousands of conceivable alternatives when purchasing a car, far more than they could reasonably be expected to evaluate. As such they will often narrow their search to only vehicles of a certain make, or within a specific price range. By reducing the choice set to a manageable number of alternatives, people are able to make complex decisions between theoretically infinite alternatives in a practical time frame. Choice sets are often used in psychological and market research to make data collection and evaluation more manageable, or to make direct comparisons between a specific set of choices. == Choice task == The respondent is asked a choice task. Usually this is which of the alternatives they prefer. In this example, the Choice task is 'forced'. An 'unforced' choice would allow the respondents to also select 'Neither'. The choice task is used as the dependent variable in the resulting choice model. == Example of a choice set == A choice set has the following elements: Alternatives: A number of hypothetical alternatives, Car A and Car B in this example. There may


id: civilization-s-waiting-room-20260505-0
file: data/en.wikipedia.org/wiki/Civilization's_Waiting_Room-0.md
category: reference
title: Civilization's Waiting Room
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Civilization's_Waiting_Room
date_saved: 2026-05-05T09:49:30.962781+00:00
instance: kb-cron
parent: civilization-s-waiting-room-20260505-0
summary:
Sivilisasjonens venterom (Norwegian for "Civilization's Waiting Room") was a research larp (live-action roleplaying game) held in Bergen in November 2021. It was designed to explore the potential of larps as a research methodology and as research dissemination, and was specifically intended to investigate ethical questions that arise when encountering new surveillance technologies. == Background == The project was funded by the Research Council of Norway as part of a scheme to increase the Norwegian impact of EU-funded research. The stated goal was to "create arenas where the general public can practice making ethical decisions about the use of new technologies, specifically machine vision technologies such as facial recognition, deepfakes and VR" The creative lead for the project was veteran larp developer Anita Myhre Andersen, working with Harald Misje, Jon Andreas Edland, Toril Mjelva Saatvedt, Sebastian Sjøvold and Eskil Mjelva Saatvedt. The researchers in the development team were Marianne Gunderson, Kristian A. Bjørkelo, and Jill Walker Rettberg, who had initiated the project. The larp drew upon the Nordic larp genre as well as on research on educational larping (Edu-larp) and larps as research tools. In a scholarly paper about Sivilisasjonens venterom, Malthe Stavning Erslev describes it as a research larp, which


id: clinical-study-design-20260505-0
file: data/en.wikipedia.org/wiki/Clinical_study_design-0.md
category: reference
title: Clinical study design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_study_design
date_saved: 2026-05-05T09:49:32.252147+00:00
instance: kb-cron
parent: clinical-study-design-20260505-0
summary:
Clinical study design is the formulation of clinical trials and other experiments, as well as observational studies, in medical research involving human beings and involving clinical aspects, including epidemiology . It is the design of experiments as applied to these fields. The goal of a clinical study is to assess the safety, efficacy, and / or the mechanism of action of an investigational medicinal product (IMP) or procedure, or new drug or device that is in development, but potentially not yet approved by a health authority (e.g. Food and Drug Administration). It can also be to investigate a drug, device or procedure that has already been approved but is still in need of further investigation, typically with respect to long-term effects or cost-effectiveness. Some of the considerations here are shared under the more general topic of design of experiments but there can be others, in particular related to patient confidentiality and medical ethics. == Outline of types of designs for clinical studies == === Treatment studies === Randomized controlled trial Blind trial Non-blind trial Adaptive clinical trial Platform Trials Nonrandomized trial (quasi-experiment) Interrupted time series design (measures on a sample or a series of samples from the same population are


id: clinical-trial-20260505-0
file: data/en.wikipedia.org/wiki/Clinical_trial-0.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dietary choices, dietary supplements, and medical devices) and known interventions that warrant further study and comparison. Clinical trials generate data on dosage, safety and efficacy. They are conducted only after they have received health authority/ethics committee approval in the country where approval of the therapy is sought. These authorities are responsible for vetting the risk/benefit ratio of the trial—their approval does not mean the therapy is 'safe' or effective, only that the trial may be conducted. Depending on product type and development stage, investigators initially enroll volunteers or patients into small pilot studies, and subsequently conduct progressively larger scale comparative studies. Clinical trials can vary in size and cost, and they can involve a single research center or multiple centers, in one country or in multiple countries. Clinical study design aims to ensure the scientific validity and reproducibility of the results. Costs for clinical trials can range into the billions of dollars per approved drug, and the complete trial process to approval may require 7–15 years. The sponsor may be


id: clinical-trial-20260505-1
file: data/en.wikipedia.org/wiki/Clinical_trial-1.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
=== Trials of procedures === Similarly to drugs, medical or surgical procedures may be subjected to clinical trials, such as comparing different surgical approaches in treatment of fibroids for subfertility. However, when clinical trials are unethical or logistically impossible in the surgical setting, case-controlled studies will be replaced. === Patient and public involvement === Besides being participants in a clinical trial, members of the public can be actively collaborate with researchers in designing and conducting clinical research. This is known as patient and public involvement (PPI). Public involvement involves a working partnership between patients, caregivers, people with lived experience, and researchers to shape and influence what is researched and how. PPI can improve the quality of research and make it more relevant and accessible. People with current or past experience of illness can provide a different perspective than professionals and compliment their knowledge. Through their personal knowledge they can identify research topics that are relevant and important to those living with an illness or using a service. They can also help to make the research more grounded in the needs of the specific communities they are part of. Public contributors can also ensure that the research is presented in plain


id: clinical-trial-20260505-2
file: data/en.wikipedia.org/wiki/Clinical_trial-2.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
Ideas of Sir Ronald A. Fisher still play a role in clinical trials. While working for the Rothamsted experimental station in the field of agriculture, Fisher developed his Principles of experimental design in the 1920s as an accurate methodology for the proper design of experiments. Among his major ideas include the importance of randomization—the random assignment of individual elements (eg crops or patients) to different groups for the experiment; replication—to reduce uncertainty, measurements should be repeated and experiments replicated to identify sources of variation; blocking—to arrange experimental units into groups of units that are similar to each other, and thus reducing irrelevant sources of variation; use of factorial experiments—efficient at evaluating the effects and possible interactions of several independent factors. Of these, blocking and factorial design are seldom applied in clinical trials, because the experimental units are human subjects and there is typically only one independent intervention: the treatment. The British Medical Research Council officially recognized the importance of clinical trials from the 1930s. The council established the Therapeutic Trials Committee to advise and assist in the arrangement of properly controlled clinical trials on new products that seem likely on experimental grounds to have value in the treatment of disease.


id: clinical-trial-20260505-3
file: data/en.wikipedia.org/wiki/Clinical_trial-3.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
Clinical trials involving new drugs are commonly classified into five phases. Each phase of the drug approval process is treated as a separate clinical trial. The drug development process will normally proceed through phases I–IV over many years, frequently involving a decade or longer. 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 performed after the newly approved drug, diagnostic or device is marketed, providing assessment about risks, benefits, or best uses. == Trial design == A fundamental distinction in evidence-based practice is between observational studies and randomized controlled trials. Types of observational studies in epidemiology, such as the cohort study and the case-control study, provide less compelling evidence than the randomized controlled trial. In observational studies, the investigators retrospectively assess associations between the treatments given to participants and their health status, with potential for considerable errors in design and interpretation. A randomized controlled trial can provide compelling evidence that the study treatment causes an effect on human health. Some phase II and most phase III drug trials are designed as randomized, double-blind, and placebo-controlled. Randomized: Each study


id: clinical-trial-20260505-4
file: data/en.wikipedia.org/wiki/Clinical_trial-4.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
==== Statistical power ==== In any clinical trial, the number of subjects, also called the sample size, has a large impact on the ability to reliably detect and measure the effects of the intervention. This ability is described as its "power", which must be calculated before initiating a study to figure out if the study is worth its costs. In general, a larger sample size increases the statistical power, also the cost. The statistical power estimates the ability of a trial to detect a difference of a particular size (or larger) between the treatment and control groups. For example, a trial of a lipid-lowering drug versus placebo with 100 patients in each group might have a power of 0.90 to detect a difference between placebo and trial groups receiving dosage of 10 mg/dL or more, but only 0.70 to detect a difference of 6 mg/dL. === Placebo groups === Merely giving a treatment can have nonspecific effects. These are controlled for by the inclusion of patients who receive only a placebo. Subjects are assigned randomly without informing them to which group they belonged. Many trials are doubled-blinded so that researchers do not know to which group a subject is assigned.


id: clinical-trial-20260505-5
file: data/en.wikipedia.org/wiki/Clinical_trial-5.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
Clinical trials designed by a local investigator, and (in the US) federally funded clinical trials, are almost always administered by the researcher who designed the study and applied for the grant. Small-scale device studies may be administered by the sponsoring company. Clinical trials of new drugs are usually administered by a contract research organization (CRO) hired by the sponsoring company. The sponsor provides the drug and medical oversight. A CRO is contracted to perform all the administrative work on a clinical trial. For phases II–IV the CRO recruits participating researchers, trains them, provides them with supplies, coordinates study administration and data collection, sets up meetings, monitors the sites for compliance with the clinical protocol, and ensures the sponsor receives data from every site. Specialist site management organizations can also be hired to coordinate with the CRO to ensure rapid IRB/IEC approval and faster site initiation and patient recruitment. Phase I clinical trials of new medicines are often conducted in a specialist clinical trial clinic, with dedicated pharmacologists, where the subjects can be observed by full-time staff. These clinics are often run by a CRO which specialises in these studies. At a participating site, one or more research assistants (often nurses)


id: clinical-trial-20260505-6
file: data/en.wikipedia.org/wiki/Clinical_trial-6.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
A clinical trial produces data that could reveal quantitative differences between two or more interventions; statistical analyses are used to determine whether such differences are true, result from chance, or are the same as no treatment (placebo). Data from a clinical trial accumulate gradually over the trial duration, extending from months to years. Accordingly, results for participants recruited early in the study become available for analysis while subjects are still being assigned to treatment groups in the trial. Early analysis may allow the emerging evidence to assist decisions about whether to stop the study, or to reassign participants to the more successful segment of the trial. Investigators may also want to stop a trial when data analysis shows no treatment effect. == Ethical aspects == Clinical trials are closely supervised by appropriate regulatory authorities. All studies involving a medical or therapeutic intervention on patients must be approved by a supervising ethics committee before permission is granted to run the trial. The local ethics committee has discretion on how it will supervise noninterventional studies (observational studies or those using already collected data). In the US, this body is called the Institutional Review Board (IRB); in the EU, they are called Ethics


id: clinical-trial-20260505-7
file: data/en.wikipedia.org/wiki/Clinical_trial-7.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
=== During public health crisis === Conducting clinical trials of vaccines during epidemics and pandemics is subject to ethical concerns. For diseases with high mortality rates like Ebola, assigning individuals to a placebo or control group can be viewed as a death sentence. In response to ethical concerns regarding clinical research during epidemics, the National Academy of Medicine authored a report identifying seven ethical and scientific considerations. These considerations are: === Pregnant women and children === Pregnant women and children are typically excluded from clinical trials as vulnerable populations, though the data to support excluding them is not robust. By excluding them from clinical trials, information about the safety and effectiveness of therapies for these populations is often lacking. During the early history of the HIV/AIDS epidemic, a scientist noted that by excluding these groups from potentially life-saving treatment, they were being "protected to death". Projects such as Research Ethics for Vaccines, Epidemics, and New Technologies (PREVENT) have advocated for the ethical inclusion of pregnant women in vaccine trials. Inclusion of children in clinical trials has additional moral considerations, as children lack decision-making autonomy. Trials in the past had been criticized for using hospitalized children or orphans; these ethical concerns


id: clinical-trial-20260505-8
file: data/en.wikipedia.org/wiki/Clinical_trial-8.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
=== Institutional review boards (IRBs) === Approval by an Institutional Review Board (IRB), or Independent Ethics Committee (IEC), is necessary before all but the most informal research can begin. In commercial clinical trials, the study protocol is not approved by an IRB before the sponsor recruits sites to conduct the trial. However, the study protocol and procedures have been tailored to fit generic IRB submission requirements. In this case, and where there is no independent sponsor, each local site investigator submits the study protocol, the consent(s), the data collection forms, and supporting documentation to the local IRB. Universities and most hospitals have in-house IRBs. Other researchers (such as in walk-in clinics) use independent IRBs. The IRB scrutinizes the study both for medical safety and for protection of the patients involved in the study, before it allows the researcher to begin the study. It may require changes in study procedures or in the explanations given to the patient. A required yearly "continuing review" report from the investigator updates the IRB on the progress of the study and any new safety information related to the study. === Regulatory agencies === In the US, the Food and Drug Administration (FDA) can audit the


id: clinical-trial-20260505-9
file: data/en.wikipedia.org/wiki/Clinical_trial-9.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
production of the drug(s) or device(s) being evaluated staff salaries for the designers and administrators of the trial payments to the contract research organization, the site management organization (if used) and any outside consultants payments to local researchers and their staff for their time and effort in recruiting test subjects and collecting data for the sponsor the cost of study materials and the charges incurred to ship them communication with the local researchers, including on-site monitoring by the CRO before and (in some cases) multiple times during the study one or more investigator training meetings expense incurred by the local researchers, such as pharmacy fees, IRB fees and postage any payments to subjects enrolled in the trial the expense of treating a test subject who develops a medical condition caused by the study drug These expenses are incurred over several years. In the US, sponsors may receive a 50 percent tax credit for clinical trials conducted on drugs being developed for the treatment of orphan diseases. National health agencies, such as the US National Institutes of Health, offer grants to investigators who design clinical trials that attempt to answer research questions of interest to the agency. In these cases, the


id: cluster-randomised-controlled-trial-20260505-0
file: data/en.wikipedia.org/wiki/Cluster-randomised_controlled_trial-0.md
category: reference
title: Cluster-randomised controlled trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cluster-randomised_controlled_trial
date_saved: 2026-05-05T09:49:34.771792+00:00
instance: kb-cron
parent: cluster-randomised-controlled-trial-20260505-0
summary:
A cluster-randomised controlled trial (cRCT, CRCT) is a type of randomised controlled trial in which groups of subjects (as opposed to individual subjects) are randomised. Cluster randomised controlled trials are also known as cluster-randomised trials, group-randomised trials, and place-randomized trials. Cluster-randomised controlled trials are used when there is a strong reason for randomising treatment and control groups over randomising participants. == Prevalence == A 2004 bibliometric study documented an increasing number of publications in the medical literature on cluster-randomised controlled trials since the 1980s. == Advantages == Advantages of cluster-randomised controlled trials over individually randomised controlled trials include: The ability to study interventions that cannot be directed toward selected individuals (e.g., a radio show about lifestyle changes) and the ability to control for "contamination" across individuals (e.g., one individual's changing behaviors may influence another individual to do so). Reduced cost in running a survey. For example, when wanting to survey households, it could often be cheaper to choose street blocks and survey all the houses there in order to reduce the cost of traveling for the people conducting the survey. Sometimes due to data availability, it is only possible to do cluster sampling. For example, if wanting to survey households,


id: code-break-procedure-20260505-0
file: data/en.wikipedia.org/wiki/Code-break_procedure-0.md
category: reference
title: Code-break procedure
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Code-break_procedure
date_saved: 2026-05-05T09:49:36.054406+00:00
instance: kb-cron
parent: code-break-procedure-20260505-0
summary:
A code-break procedure is a set of rules which determine when planned unblinding should occur in a blinded experiment. FDA guidelines recommend that sponsors of blinded trials include a code-break procedure in their standard operating procedure. A code-break procedure should only allow a participant to be unblinded before the conclusion of a trial in the event of an emergency. Code-break usually refers to the unmasking of treatment allocation, but can refer to any form of unblinding. Traditionally, each patient's treatment allocation data was stored in a sealed envelopes, which was to be opened to break code. However, this system is prone to abuse. Reports of researchers opening envelopes prematurely or holding the envelopes up to lights to determine their contents has led some researchers to say that the use of sealed envelopes is no longer acceptable. As of 2016, sealed envelopes were still in use in some clinical trials. Modern clinical trials usually store this information in computer files. == See also == Sealedenvelope.com – a provider of code-break services == References ==


id: combinatorial-design-20260505-0
file: data/en.wikipedia.org/wiki/Combinatorial_design-0.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:
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in sudoku grids. Combinatorial design theory can be applied to the area of design of experiments. Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including finite geometry, tournament scheduling, lotteries, mathematical chemistry, mathematical biology, algorithm design and analysis, networking, group testing and cryptography. == Example == Given a certain number n of people, is it possible to assign them to sets so that each person is in at least one set, each pair of people is in exactly one set together, every two sets have exactly one person in common, and


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
instance: kb-cron
parent: gittins-index-20260505-0
summary:
== 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


