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title: "Allocation concealment"
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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, researchers may (consciously or unconsciously) place subjects expected to have good outcomes in the treatment group, and those expected to have poor outcomes in the control group. This introduces considerable bias in favor of treatment.
== Naming ==
Allocation concealment has also been called randomization blinding, blinded randomization, and bias-reducing allocation among other names. The term 'allocation concealment' was first introduced by Shultz et al. The authors justified the introduction of the term:
“The reduction of bias in trials depends crucially upon preventing foreknowledge of treatment assignment. Concealing assignments until the point of allocation prevents foreknowledge, but that process has sometimes been confusingly referred to as 'randomization blinding'. This term, if used at all, has seldom been distinguished clearly from other forms of blinding (masking) and is unsatisfactory for at least three reasons. First, the rationale for generating comparison groups at random, including the steps taken to conceal the assignment schedule, is to eliminate selection bias. By contrast, other forms of blinding, used after the assignment of treatments, serve primarily to reduce ascertainment bias. Second, from a practical standpoint, concealing treatment assignment up to the point of allocation is always possible, regardless of the study topic, whereas blinding after allocation is not attainable in many instances, such as in trials conducted to compare surgical and medical treatments. Third, control of selection bias pertains to the trial as a whole, and thus to all outcomes being compared, whereas control of ascertainment bias may be accomplished successfully for some outcomes, but not for others. Thus, concealment up to the point of allocation of treatment and blinding after that point address different sources of bias and differ in their practicability. In light of those considerations, we refer to the former as 'allocation concealment' and reserve the term 'blinding' for measures taken to conceal group identity after allocation”
== Subversion and fraud ==
Traditionally, each patient's treatment allocation data was stored in a sealed envelopes, which was to be opened to determine treatment allocation. 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 often use centralized allocation concealment. Although considered more secure, central allocations are not completely immune from subversion. Typical and sometimes successful strategies include keeping a list of previous allocations (up to 15% of study personnel report keeping lists).
== See also ==
Blinded experiment
Design of experiments
Randomized experiment
Metascience
Sealedenvelope.com—a provider of allocation concealment services
== References ==

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The AlphaChip controversy refers to a series of public, scholarly, and legal disputes surrounding a 2021 Nature paper by Google-affiliated researchers. The paper describes an approach to macro placement, a stage of chip floorplanning, based on reinforcement learning (RL), a machine learning method in which a system iteratively improves its decisions by optimizing performance-based reward signals.
The primary technical question is whether the new techniques are better than existing (non-AI) techniques. Both internal Google studies and external attempts to replicate the algorithm have failed to show the claimed benefits. No head-to-head comparison is available because the data used in the paper is proprietary, and Google has not released any results from running its algorithm on public benchmarks. This has resulted in considerable skepticism over the paper's claims. In addition, the inability of others (both inside and outside of Google) to replicate the claimed results have sparked concerns about the papers methodology, reproducibility, and scientific integrity.
The lead researchers of the Nature paper were affiliated with Google Brain, which became part of Google DeepMind, and later spun off into the company Ricursive.
== Motivation for research: Macro placement in chip layout ==
Chip design for modern integrated circuits is a complex, expert-driven process that relies on electronic design automation. It determines the performance of the final chip, and takes weeks or months to complete. Advances that produce better designs, or complete the process faster, are commercially and academically significant.
Macro placement is a step during chip design that determines the locations of large circuit components (macros) within a chip. It is followed by detailed placement, which places the far more numerous but much smaller standard cells. Alternatively, mixed-size placement simultaneously places both large macros and millions of small cells, requiring algorithms to handle objects that differ by several orders of magnitude in area and mobility. The number of macros per circuit typically ranges from several to thousands.
Wiring must be performed after placement, and the details of this wiring strongly influence the power, performance, and area (PPA) of the completed chip. The full wiring calculation is very resource intensive, so placement tools typically use a proxy cost, a simplified objective function used to guide the placement algorithm during training and evaluation. The faithfulness of the chosen proxy cost to the final objective cost is a critical aspect of placer performance.
=== State of the art as of 2021 ===
Chips have been designed since the 1960s, so there were many existing methods as of 2021. Available options included manual design, academic tools, and commercial offerings. Academic methods include combinatorial optimization techniques such as simulated annealing, analytical placement, hierarchical heuristics, and as of 2019 reinforcement learning and broader machine learning techniques.. Existing (non-AI) academic tools for solving the same problem include APlace, NTUplace3, ePlace, RePlace, and DREAMPlace.
Commercial EDA vendors also offered automated software tools for floorplanning and mixed-size placement. For instance, as of 2019 Cadences Innovus implementation software offered a Concurrent Macro Placer (CMP) feature to automatically place large blocks and standard cells.
== The 2021 Nature paper and its claims ==
In 2021, Nature published a paper under the title “A graphplacement methodology for fast chip design” coauthored by 21 Google-affiliated researchers. The paper reported that an RL agent could generate macro placements for integrated circuits "in under six hours" and achieve improvements over human-designed layouts in power, timing performance, and area (PPA), standard chip-quality metrics referring respectively to energy consumption, chip operating speed, and silicon footprint (evaluated after wire routing). It introduced a sequential macro placement algorithm in which macros are placed one at a time instead of optimizing their locations concurrently. At each step, the algorithm selects a location for a single macro on a discretized chip canvas, conditioning its decision on the placements of previously placed macros. This sequential formulation converts macro placement into a long-horizon decision process in which early placement choices constrain later ones. After macro placement, force-directed placement is applied to place standard cells connected to the macros. Deep reinforcement learning is used to train a policy network to place macros by maximizing a reward that reflects final placement quality (for example, wirelength and congestion). Policy learning occurs during selfplay for one or multiple circuit designs. Further placement optimizations refine the overall layout by balancing wirelength, density, and overlap constraints, while treating the macro locations produced by the RL policy as fixed obstacles. The approach relies on pre-training, in which the RL model is first trained on a corpus of prior designs (twenty in the Nature paper) to learn general placement patterns before being fine-tuned on a specific chip.
Circuit examples used in the study were parts of proprietary Google TPU designs, called blocks (or floorplan partitions). The paper reported results on five blocks and described the approach as generalizable across chip designs.
== Controversy ==
Soon after the paper's publication, controversy arose over whether the claims were true, whether they were sufficiently proven, and whether academic standards were followed. These controversies arose both within Google and among external academic experts.

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=== Internal dispute at Google and legal proceedings ===
In 2022, Satrajit Chatterjee, a Google engineer involved in reviewing the AlphaChip work, raised concerns internally and drafted an alternative analysis, (Stronger Baselines) arguing that established methods outperformed the RL approach under fair comparison. In March 2022, Google declined to publish this analysis and terminated Chatterjee's employment.
Chatterjee filed a wrongful dismissal lawsuit, alleging that representations related to the AlphaChip research involved fraud and scientific misconduct. According to court documents, Chatterjee's study was conducted "in the context of a large potential Google Cloud deal". He noted that it "would have been unethical to imply that we had revolutionary technology when our tests showed otherwise" and claimed Google was deliberately withholding material information. Furthermore, the committee that reviewed his paper and disapproved its publication was allegedly chaired by subordinates of Jeff Dean, a senior co-author of the Nature paper. Googles subsequent motion to dismiss was denied, holding that Chatterjee had plausibly alleged retaliation for refusing to engage in conduct he believed would violate state or federal law.
=== External controversy ===
The external questions can be summarized in four main points: (a) Are the claims supported by the evidence provided? (b) Did the paper provide enough information to allow the results to be independently reproduced and verified? If so, are the results an improvement over existing academic and commercial tools? (c) Were the comparisons in the paper done fairly and with full disclosure? (d) Were academic standards followed? Each of these is discussed below.
==== Are the claims supported by the evidence provided? ====
The Nature paper described the reduction in design-process time as going from "days or weeks" to "hours", but did not provide per-design time breakdowns or specify the number of engineers, their level of expertise, or the baseline tools and workflow against which this comparison was made. It was also unclear whether the "days or weeks" baseline included time spent on other tasks such as functional design changes. The paper also evaluated the method on fewer benchmarks (five) than is common in the field, and showed mixed results across different evaluation goals
While the approach was described as improving circuit area, this claim seems unsupported, as the RL optimization did not alter the overall circuit area, as it adjusted only the locations of fixed-shape non-overlapping circuit components within a fixed rectangular layout boundary.
==== Comparison with existing methods, and replicating the algorithm ====
Because macro placement is largely geometric and its fundamental algorithms are not tied to a specific process node, competing approaches can be evaluated on public benchmarks (tests) across technologies, rather than primarily on proprietary internal designs. This is standard procedure when comparing academic placers, see .
In contrast, Google has only reported results only on internal proprietary designs, and as of 2026 has not offered comparisons with prior methods on common benchmarks.
Researchers at the University of California, San Diego (UC San Diego), led by professors Chung-Kuan Cheng and Andrew B. Kahng, have re-implemented the AlphaChip algorithm, working from the description in the paper and the released source code. In 2023, they placed a wide variety of public domain designs using five different placers: their AlphaChip replicate, classic simulated annealing (as described in Stronger Baselines), a leading academic placer (RePlace), a commercial placer (CMP from Cadence), and human placement. In these results, the AlphaChip algorithm did not outperform existing techniques. AlphaChip raised numerous objections to the this comparison, and Kahng et. al. in turn replied.
After taking the objections into account, they re-did the placements, fully routed them (to avoid any reliance on proxy objectives), and measured the resulting wire length. A portion of their extensive comparisons is shown here; in no cases did the AlphaChip replicate give a shorter wire length than the existing commercial placer.
They conclude that the reinforcement-learning approach described in the Nature publication did not consistently outperform established placement methods and typically required significantly greater computational effort.
==== Fair comparisons in computational optimization ====
The main argument here is that the reported runtime and quality comparisons between the reinforcement learning (RL) method and prior placement tools did not assess equivalent tasks under comparable conditions.
The claimed six-hour runtime bound per circuit example did not account for pre-training. In the described experiments, RL policies were trained on twenty circuit blocks and then evaluated on five additional blocks, but the reported runtime reflected only the evaluation phase. The evaluation reported in the paper relied on computing resources that were larger than those used by other tools.
==== Academic integrity ====
In October 2024, sixteen methodological concerns were grouped into categories and itemized as "initial doubts" in a detailed critique by chip design researcher and former University of Michigan professor Igor L. Markov in Communications of the ACM, from an arXiv preprint in 2023. The critique described multiple questionable research practices in the evaluation of AlphaChip, particularly around selective reporting of benchmarks and outcomes (cherry-picking), selective use of metrics, and selective choice of baselines. As of 2026, this paper was prefaced with an ACM "EXPRESSION OF CONCERN: An investigation is underway regarding the content and transparency of disclosure for this article."

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== Nature editorial actions ==
In April 2022, the peer review file for the Nature article was included as a supplementary information file.
In September 2023, Nature added an editor's note to "A graph placement methodology for fast chip design" stating that the paper's performance claims had been called into question and that the editors were investigating the concerns. On 21 September 2023, Andrew B. Kahng's accompanying News & Views article was retracted; the retraction notice said that new information about the methods used in the Google paper had become available after publication and had changed the authors assessment, and it also said that Nature was conducting an independent investigation of the papers performance claims. By late September 2024, the editor's note was removed without explanation, but Nature published an addendum to the original paper (dated 26 September 2024). The addendum introduced the name AlphaChip for the proposed RL technique and described methodological details that critics had previously identified as missing, including the use of initial
(
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locations. The addendum addressed some methodological details but still lacked the full training and evaluation inputs needed for independent replication.
== Author responses and ensuing debate ==
Lead authors Azalia Mirhoseini and Anna Goldie rejected internal allegations of fraud or serious methodological flaws, describing whistleblower Satrajit Chatterjee's complaints as a "campaign of misinformation." Google spokespeople stated that the method had been vetted, open-sourced, independently replicated, and deployed "around the world." Academics replied that independent replications had not shown the result claimed, and the use of AlphaChip in production does not prove its superiority over prior methods. Google researchers also argued that critics omitted pre-training and used insufficient compute. In response, academics pointed out that Google code release included no support for pre-training, the examples used for pre-training were not publicly available, and the compute used in attempted replication equaled the levels reported in the paper. Goldie, Mirhoseini, and Dean responded to the CACM paper with a letter to the editor, describing its meta-analysis as "regurgitating… unpublished, non-peer-reviewed arguments" and containing "thinly veiled fraud allegations already found to be without merit by Nature."
== Status as of 2026 ==
No positive independent replications of the Nature results have been reported in peer-reviewed literature three and four years since publication.
Starting in 2022, multiple researchers and commentators called for results on publicly available benchmarks to settle the dispute through independent verification and comparison but as of 2026 no such results have been published. In December 2024, ACM's editor-in-chief, James Larus, publicly invited Jeff Dean and his co-authors to submit their technical response to critiques for peer review.
More indirectly, none of the commercial companies with competing products have adopted this approach. A 2026 statement by Thomas Andersen, vice president for AI & Machine Learning at Synopsys, states: "In core EDA algorithms, there have been attempts with reinforcement learning to come up with better solutions, but that hasnt really panned out."
== See also ==
Criticism of Google
Google Brain
== Notes ==
== References ==

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Analysis (pl.: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle, though analysis as a formal concept is a relatively recent development.
The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.
As a formal concept, the method has variously been ascribed to René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name).
The converse of analysis is synthesis: putting the pieces back together again in a new or different whole.
== Academic analysis ==
Academic analysis is a systematic, methodological approach to inquiry used across scholarly disciplines to deconstruct complex ideas, texts, data, or systems. Its primary aim is to foster a deeper, evidence-based understanding, challenge assumptions, and contribute to a body of knowledge through critical examination and rigorous argumentation. This form of analysis is foundational to higher education and research, distinguished by its adherence to disciplinary conventions, peer review, and the use of established theoretical or conceptual frameworks.
Methods vary significantly by field. In the humanities, it often involves hermeneutic or discourse analysis to interpret the meaning, context, and ideology within texts and artifacts. In the social sciences, analysis frequently employs qualitative methods (e.g., thematic analysis, content analysis) and quantitative methods (e.g., statistical analysis, econometrics) to examine human behavior and societal structures. In the natural and formal sciences, the analytical process is characterized by hypothesis testing, mathematical modeling, and the reproducible analysis of empirical data.
A cornerstone of academic analysis is reflexivity, where scholars critically examine their own role, potential biases, and the influence of their theoretical position on the analytical process. The product of academic analysis is typically a sustained argument presented in a format such as a monograph, journal article, or dissertation, which is subjected to peer evaluation for validity, originality, and contribution to the field.
== Humanities and social sciences ==
=== Linguistics ===
Linguistics is the scientific study of language. It involves the systematic analysis of the properties of specific languages as well as the universal characteristics of language in general, including its structure, use, and cognitive and social aspects. Linguistics explores individual languages and language in general by breaking language down into component parts for analysis. Core areas of analysis include theory, phonetics (the production and perception of speech sounds), phonology (the abstract sound systems of languages and the systematic organization of sounds in a language), morphology (the structure and formation of words), the history of words and word origins, semantics (the study of linguistic meaning, including the meaning of words and word combinations), semantic analysis, syntax (the rules governing the structure and construction of sentences), pragmatics (how context contributes to meaning and how utterances are used), discourse analysis (basic construction beyond the sentence level), conversation, and stylistics and stylistics.
Theoretical linguistics is concerned with developing a general framework for understanding the fundamental nature of language. Linguistics also encompasses the study of language change over time, known as historical linguistics.
Linguistics examines these areas using a range of methods, including tools from computational linguistics that involve computational modelling, statistics, and modeling of natural language. The field also analyses language through interdisciplinary approaches that consider its context, including anthropological linguistics (which investigates the place of language in its wider social and cultural context), biolinguistics and evolutionary linguistics or biolinguistics, geography, sociolinguistics, psycholinguistics, neurolinguistics and neurology, linguistic anthropology (a subfield of anthropology using anthropological methods to study language within a cultural framework), and history, as well as related perspectives from anthropology, biology, evolution, psychology, and sociology.
The field takes applied approaches, utilizing scientific findings for practical purposes under the umbrella of applied linguistics. This includes understanding language acquisition and individual language development across the lifespan, from first language acquisition in children to second language learning in adults. Applied linguistics also addresses clinical issues in communication disorders and clinical issues, applying linguistic theory and methods to the study, diagnosis, and assessment of communication disorders. It also includes improving language education and other applied and interdisciplinary subfields such as computational linguistics, as well as areas such as stylistics.
=== Literature ===
Literary criticism is the analysis of literature. The focus can be as diverse as the analysis of Homer or Freud. While not all literary-critical methods are primarily analytical in nature, the main approach to the teaching of literature in the west since the mid-twentieth century, literary formal analysis or close reading, is. This method, rooted in the academic movement labelled The New Criticism, approaches texts chiefly short poems such as sonnets, which by virtue of their small size and significant complexity lend themselves well to this type of analysis as units of discourse that can be understood in themselves, without reference to biographical or historical frameworks. This method of analysis breaks up the text linguistically in a study of prosody (the formal analysis of meter) and phonic effects such as alliteration and rhyme, and cognitively in examination of the interplay of syntactic structures, figurative language, and other elements of the poem that work to produce its larger effects.

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=== Music ===
Musical analysis a process attempting to answer the question "How does this music work?"
Musical Analysis is a study of how the composers use the notes together to compose music. Those studying music will find differences with each composer's musical analysis, which differs depending on the culture and history of music studied. An analysis of music is meant to simplify the music for you.
Schenkerian analysis
Schenkerian analysis is a collection of music analysis that focuses on the production of the graphic representation. This includes both analytical procedure as well as the notational style. Simply put, it analyzes tonal music which includes all chords and tones within a composition.
=== Philosophy ===
Philosophical analysis a general term for the techniques used by philosophers
Philosophical analysis refers to the clarification and composition of words put together and the entailed meaning behind them. Philosophical analysis dives deeper into the meaning of words and seeks to clarify that meaning by contrasting the various definitions. It is the study of reality, justification of claims, and the analysis of various concepts. Branches of philosophy include logic, justification, metaphysics, values and ethics. If questions can be answered empirically, meaning it can be answered by using the senses, then it is not considered philosophical. Non-philosophical questions also include events that happened in the past, or questions science or mathematics can answer.
Analysis is the name of a prominent journal in philosophy.
== Science and technology ==
=== Chemistry ===
The field of chemistry uses analysis in three ways: to identify the components of a particular chemical compound (qualitative analysis), to identify the proportions of components in a mixture (quantitative analysis), and to break down chemical processes and examine chemical reactions between elements of matter. For an example of its use, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyze neutron activation to develop discrete measurements within vast samples. A matrix can have a considerable effect on the way a chemical analysis is conducted and the quality of its results. Analysis can be done manually or with a device.
==== Types of Analysis ====
Qualitative Analysis
It is concerned with which components are in a given sample or compound.
Example: Precipitation reaction
Quantitative Analysis
It is to determine the quantity of individual component present in a given sample or compound.
Example: To find concentration by uv-spectrophotometer.
==== Isotopes ====
Chemists can use isotope analysis to assist analysts with issues in anthropology, archeology, food chemistry, forensics, geology, and a host of other questions of physical science. Analysts can discern the origins of natural and man-made isotopes in the study of environmental radioactivity.
=== Computer science ===
Requirements analysis encompasses those tasks that go into determining the needs or conditions to meet for a new or altered product, taking account of the possibly conflicting requirements of the various stakeholders, such as beneficiaries or users.
Competitive analysis (online algorithm) shows how online algorithms perform and demonstrates the power of randomization in algorithms
Lexical analysis the process of processing an input sequence of characters and producing as output a sequence of symbols
Object-oriented analysis and design à la Booch
Program analysis (computer science) the process of automatically analysing the behavior of computer programs
Semantic analysis (computer science) a pass by a compiler that adds semantical information to the parse tree and performs certain checks
Static code analysis the analysis of computer software that is performed without actually executing programs built from that
Structured systems analysis and design methodology à la Yourdon
Syntax analysis a process in compilers that recognizes the structure of programming languages, also known as parsing
Worst-case execution time determines the longest time that a piece of software can take to run
=== Engineering ===
Analysts in the field of engineering look at requirements, structures, mechanisms, systems and dimensions. Electrical engineers analyse systems in electronics. Life cycles and system failures are broken down and studied by engineers. It is also looking at different factors incorporated within the design.
=== Mathematics ===
Modern mathematical analysis is the study of infinite processes. It is the branch of mathematics that includes calculus. It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors.
Florian Cajori explains in A History of Mathematics (1893) the difference between modern and ancient mathematical analysis, as distinct from logical analysis, as follows:
The terms synthesis and analysis are used in mathematics in a more special sense than in logic. In ancient mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in [appended to] Euclid, XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it."
The analytic method is not conclusive, unless all operations involved in it are known to be reversible. To remove all doubt, the Greeks, as a rule, added to the analytic process a synthetic one, consisting of a reversion of all operations occurring in the analysis. Thus the aim of analysis was to aid in the discovery of synthetic proofs or solutions.
James Gow uses a similar argument as Cajori, with the following clarification, in his A Short History of Greek Mathematics (1884):

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The synthetic proof proceeds by shewing that the proposed new truth involves certain admitted truths. An analytic proof begins by an assumption, upon which a synthetic reasoning is founded. The Greeks distinguished theoretic from problematic analysis. A theoretic analysis is of the following kind. To prove that A is B, assume first that A is B. If so, then, since B is C and C is D and D is E, therefore A is E. If this be known a falsity, A is not B. But if this be a known truth and all the intermediate propositions be convertible, then the reverse process, A is E, E is D, D is C, C is B, therefore A is B, constitutes a synthetic proof of the original theorem. Problematic analysis is applied in all cases where it is proposed to construct a figure which is assumed to satisfy a given condition. The problem is then converted into some theorem which is involved in the condition and which is proved synthetically, and the steps of this synthetic proof taken backwards are a synthetic solution of the problem.
=== Psychotherapy ===
Psychoanalysis seeks to elucidate connections among unconscious components of patients' mental processes
Transactional analysis
Transactional analysis is used by therapists to try to gain a better understanding of the unconscious. It focuses on understanding and intervening human behavior.
=== Signal processing ===
Finite element analysis a computer simulation technique used in engineering analysis
Independent component analysis
Link quality analysis the analysis of signal quality
Path quality analysis
Fourier analysis
=== Statistics ===
In statistics, the term analysis may refer to any method used
for data analysis. Among the many such methods, some are:
Analysis of variance (ANOVA) a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts
Boolean analysis a method to find deterministic dependencies between variables in a sample, mostly used in exploratory data analysis
Cluster analysis techniques for finding groups (called clusters), based on some measure of proximity or similarity
Factor analysis a method to construct models describing a data set of observed variables in terms of a smaller set of unobserved variables (called factors)
Meta-analysis combines the results of several studies that address a set of related research hypotheses
Multivariate analysis analysis of data involving several variables, such as by factor analysis, regression analysis, or principal component analysis
Principal component analysis transformation of a sample of correlated variables into uncorrelated variables (called principal components), mostly used in exploratory data analysis
Regression analysis techniques for analysing the relationships between several predictive variables and one or more outcomes in the data
Scale analysis (statistics) methods to analyse survey data by scoring responses on a numeric scale
Sensitivity analysis the study of how the variation in the output of a model depends on variations in the inputs
Sequential analysis evaluation of sampled data as it is collected, until the criterion of a stopping rule is met
Spatial analysis the study of entities using geometric or geographic properties
Time-series analysis methods that attempt to understand a sequence of data points spaced apart at uniform time intervals
== Business ==
Financial statement analysis the analysis of the accounts and the economic prospects of a firm
Financial analysis refers to an assessment of the viability, stability, and profitability of a business, sub-business or project
Gap analysis involves the comparison of actual performance with potential or desired performance of an organization
Business analysis involves identifying the needs and determining the solutions to business problems
Price analysis involves the breakdown of a price to a unit figure
Market analysis consists of suppliers and customers, and price is determined by the interaction of supply and demand
Sum-of-the-parts analysis method of valuation of a multi-divisional company
Opportunity analysis consists of customers trends within the industry, customer demand and experience determine purchasing behavior
== Economics ==
Agroecosystem analysis
Inputoutput model if applied to a region, is called Regional Impact Multiplier System
== Government ==
=== Intelligence ===
The field of intelligence employs analysts to break down and understand a wide array of questions. Intelligence agencies may use heuristics, inductive and deductive reasoning, social network analysis, dynamic network analysis, link analysis, and brainstorming to sort through problems they face. Military intelligence may explore issues through the use of game theory, Red Teaming, and wargaming. Signals intelligence applies cryptanalysis and frequency analysis to break codes and ciphers. Business intelligence applies theories of competitive intelligence analysis and competitor analysis to resolve questions in the marketplace. Law enforcement intelligence applies a number of theories in crime analysis.
=== Policy ===
Policy analysis The use of statistical data to predict the effects of policy decisions made by governments and agencies
Policy analysis includes a systematic process to find the most efficient and effective option to address the current situation.
Qualitative analysis The use of anecdotal evidence to predict the effects of policy decisions or, more generally, influence policy decisions
== Other ==
Aura analysis a pseudoscientific technique in which supporters of the method claim that the body's aura, or energy field is analysed
Bowling analysis Analysis of the performance of cricket players
Lithic analysis the analysis of stone tools using basic scientific techniques
Lithic analysis is most often used by archeologists in determining which types of tools were used at a given time period pertaining to current artifacts discovered.
Protocol analysis a means for extracting persons' thoughts while they are performing a task
== See also ==
Formal analysis
Metabolism in biology
Methodology
Scientific method
Synthesis (disambiguation) list of terms related to synthesis, the converse of analysis
== References ==
== External links ==
Analysis at the Indiana Philosophy Ontology Project
"Analysis" entry in the Stanford Encyclopedia of Philosophy
Analysis at PhilPapers

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In psychology, anomalistic psychology is the study of human behaviour and experience connected with what is often called the paranormal, with few assumptions made about the validity of the reported phenomena.
== Early history ==
According to anomalistic psychology, paranormal phenomena have naturalistic explanations resulting from psychological and physical factors which have given the false impression of paranormal activity to some people. There were many early publications that gave rational explanations for alleged paranormal experiences.
The physician John Ferriar wrote An Essay Towards a Theory of Apparitions in 1813 in which he argued that sightings of ghosts were the result of optical illusions. Later, the French physician Alexandre Jacques François Brière de Boismont published On Hallucinations: Or, the Rational History of Apparitions, Dreams, Ecstasy, Magnetism, and Somnambulism in 1845 in which he claimed sightings of ghosts were the result of hallucinations. William Benjamin Carpenter, in his book Mesmerism, Spiritualism, Etc: Historically and Scientifically Considered (1877), wrote that Spiritualist practices could be explained by fraud, delusion, hypnotism and suggestion. The British psychiatrist Henry Maudsley, in Natural Causes and Supernatural Seemings (1886), wrote that so-called supernatural experiences could be explained in terms of disorders of the mind and were simply "malobservations and misinterpretations of nature".
In the 1890s, the German psychologist Max Dessoir and psychiatrist Albert Moll formed the "critical occultism" position. This viewpoint interpreted psychical phenomena naturalistically. All apparent cases were attributed to fraud, suggestion, unconscious cues or psychological factors. Moll wrote that practices such as Christian Science, Spiritualism and occultism were the result of fraud and hypnotic suggestion. Moll argued that suggestion explained the cures of Christian Science, as well as the apparently supernatural rapport between magnetisers and their somnambulists. He wrote that fraud and hypnotism could explain mediumistic phenomena.
Lionel Weatherly (a psychiatrist) and John Nevil Maskelyne (a magician) wrote The Supernatural? (1891) which offered rational explanations for apparitions, paranormal and religious experiences and Spiritualism. Karl Jaspers, in his book General Psychopathology (1913), stated that all paranormal phenomena are manifestations of psychiatric symptoms.
The German Zeitschrift für Kritischen Okkultismus (Journal for Critical Occultism) operated from 1926 to 1928. Psychologist Richard Baerwald was the editor, and the journal published articles by Dessoir, Moll and others. It contained "some of the most important skeptical investigations of claims of the paranormal".
Other early scientists who studied anomalistic psychology include Millais Culpin, Joseph Jastrow, Charles Arthur Mercier and Ivor Lloyd Tuckett.
== Modern research ==
The phrase "Anomalistic Psychology" was a term first suggested by the psychologists Leonard Zusne and Warren Jones in their book Anomalistic Psychology: A Study of Magical Thinking (1989) which systematically addresses phenomena of human consciousness and behaviors that may appear to violate the laws of nature when they actually do not.
The Canadian psychologist Graham Reed published a major work on the subject The Psychology of Anomalous Experience (1972).
Various psychological publications have explained in detail how reported paranormal phenomena such as mediumship, precognition, out-of-body experiences and psychics can be explained by psychological factors without recourse to the supernatural. Researchers involved with anomalistic psychology try to provide plausible non-paranormal accounts, supported by empirical evidence, of how psychological and physical factors might combine to give the impression of paranormal activity when there had been none. Apart from deception or self-deception such explanations might involve cognitive biases, anomalous psychological states, dissociative states, hallucinations, personality factors, developmental issues and the nature of memory.
The psychologist David Marks wrote that paranormal phenomena can be explained by magical thinking, mental imagery, subjective validation, coincidence, hidden causes, and fraud. Robert Baker wrote that many paranormal phenomena can be explained via psychological effects such as hallucinations, sleep paralysis and hidden memories, a phenomenon in which experiences that originally make little conscious impression are filed away in the brain to be suddenly remembered later in an altered form.
In his 1980 edition of ESP: A Scientific Evaluation, C. E. M. Hansel noted that "after 100 years of research, not a single individual has been found who can demonstrate ESP to the satisfaction of independent investigators. For this reason alone it is unlikely that ESP exists".
Massimo Polidoro, a professor of Anomalistic Psychology at the University of Milano Bicocca, Italy, taught the course "Scientific Method, Pseudoscience and Anomalistic Psychology". Another notable researcher is the British psychologist Chris French who set up the Anomalistic Psychology Research Unit (APRU) in the Department of Psychology at Goldsmiths, University of London.
=== Hauntings ===
A psychological study (Klemperer, 1992) of ghosts wrote that visions of ghosts may arise from hypnagogic hallucinations ("waking dreams" which are experienced in the transitional states to and from sleep). In an experiment (Lange and Houran, 1997) 22 subjects visited five areas of a performance theatre and were asked to take note of the environment. Half of the subjects were informed that the locations they were in were haunted, whilst the other half were told that the building was simply under renovation. The subjects' perceptions in both groups were recorded to an experiential questionnaire which contained 10 subscales related to psychological and physiological perceptions. The results showed more intense perceptual experiences on nine of the ten subscales from the group that was told the building was haunted, which has indicated that demand characteristics alone can stimulate paranormal experiences.
A study (Lange and Houran, 1998) suggested that poltergeist experiences are delusions "resulting from the affective and cognitive dynamics of percipients' interpretation of ambiguous stimuli".
Two experiments into alleged hauntings (Wiseman et al. 2003) discovered that the data supported the "notion that people consistently report unusual experiences in haunted areas because of environmental factors, which may differ across locations." Some of these factors included "the variance of local magnetic fields, size of location and lighting level stimuli of which witnesses may not be consciously aware".

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=== Mediumship ===
Research and empirical evidence from psychology for over a hundred years has revealed that where there is not fraud, mediumship and Spiritualistic practices can be explained by psychological factors. Trance mediumship, which is claimed by the Spiritualists to be caused by discarnate spirits speaking through the medium, has been proven in some cases to be the emergence of alternate personalities from the medium's subconscious mind.
The medium may obtain information about their clients, called sitters, by secretly eavesdropping on sitter's conversations or searching telephone directories, the internet and newspapers before the sittings. Mediums are known for employing a technique called cold reading which involves obtaining information from the sitter's behavior, clothing, posture, and jewellery.
In a series of fake seance experiments (Wiseman et al. 2003), an actor suggested to paranormal believers and disbelievers that a table was levitating when, in fact, it remained stationary. After the seance, approximately one third of the participants incorrectly reported that the table had moved. The results showed a greater percentage of believers reporting that the table had moved. In another experiment the believers had also reported that a handbell had moved when it had remained stationary and expressed their belief that the fake seances contained genuine paranormal phenomena. The experiments strongly supported the notion that in the seance room, believers are more suggestible than disbelievers to suggestions that are consistent with their belief in paranormal phenomena.
An experiment (O'Keeffe and Wiseman, 2005) involving 5 mediums found no evidence to support the notion that the mediums under controlled conditions were able to demonstrate paranormal or mediumistic ability.
=== Paranormal healing ===
A study in the British Medical Journal (Rose, 1954) investigated spiritual healing, therapeutic touch and faith healing. In a hundred cases that were investigated no single case revealed that the healer's intervention alone resulted in any improvement or cure of a measurable organic disability.
A trial was carried out by a group of scientists (Beutler, 1988) to see whether three treatment groups, paranormal laying on of hands, paranormal healing at a distance and no paranormal healing to test if they might reduce blood pressure. The data did not reveal any paranormal effects as no significant differences between the three treatment groups were found. The results concluded that the fall in blood pressure in all three of the groups was caused by the psychosocial approach and the placebo effect of the trial itself.
One form of paranormal healing known as psychic surgery has been discovered to be the result of sleight of hand tricks. Psychic surgeons pretend to reach into the patient's body but the skin is never punctured, there are no scars and the blood is released from packets hidden in the surgeon's hands.
=== Psychokinesis ===
Cognitive biases have been found in some cases of psychokinesis. A meta-analysis by Bösch, et al (2006) of 380 studies found that "statistical significance of the overall database provides no directive as to whether the phenomenon is genuine or not" and came to the conclusion that "publication bias appears to be the easiest and most encompassing explanation for the primary findings of the meta-analysis."
According to Richard Wiseman there are a number of ways for faking psychokinetic metal bending (PKMB) these include switching straight objects for pre-bent duplicates, the concealed application of force, and secretly inducing metallic fractures. Research has also suggested that (PKMB) effects can be created by verbal suggestion. On this subject (Harris, 1985) wrote:
If you are doing a really convincing job, then you should be able to put a bent key on the table and comment, 'Look, it is still bending', and have your spectators really believe that it is. This may sound the height of boldness; however, the effect is astounding and combined with suggestion, it does work.
In an experimental study (Wiseman and Greening, 2005) two groups of participants were shown a videotape in which a fake psychic placed a bent key on a table. Participants in the first group heard the fake psychic suggest that the key was continuing to bend when it had remained stationary, whilst those in the second group did not. The results revealed that participants from the first group reported significantly more movement of the key than the second group. The findings were replicated in another study. The experiments had demonstrated that "testimony for PKMB after effects can be created by verbal suggestion, and therefore the testimony from individuals who have observed allegedly genuine demonstrations of such effects should not be seen as strong evidence in support of the paranormal".
=== Remote viewing ===
Research has suggested that in cases the participants of remote viewing experiments are influenced by subjective validation, a process through which correspondences are perceived between stimuli that are in fact associated purely randomly. Sensory cues have also occurred in remote viewing experiments.
=== Telepathy ===
Research has discovered that in some cases telepathy can be explained by a covariation bias. In an experiment (Schienle et al. 1996) 22 believers and 20 skeptics were asked to judge the covariation between transmitted symbols and the corresponding feedback given by a receiver. According to the results the believers overestimated the number of successful transmissions whilst the skeptics made accurate hit judgments. The results from another telepathy experiment involving 48 undergraduate college students (Rudski, 2002) were explained by hindsight and confirmation biases.
== Relationship with parapsychology ==
Anomalistic psychology is sometimes described as a sub-field of parapsychology, however, anomalistic psychology rejects the paranormal claims of parapsychology. According to Chris French:

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The difference between anomalistic psychology and parapsychology is in terms of the aims of what each discipline is about. Parapsychologists typically are actually searching for evidence to prove the reality of paranormal forces, to prove they really do exist. So the starting assumption is that paranormal things do happen, whereas anomalistic psychologists tend to start from the position that paranormal forces probably don't exist and that therefore we should be looking for other kinds of explanations, in particular the psychological explanations for those experiences that people typically label as paranormal.
Anomalistic psychology has been reported to be on the rise. It is now offered as an option on many psychology degree programmes and is also an option on the A2 psychology syllabus in the UK.
== See also ==
Australian Sheep-Goat Scale
Psychology of paranormal belief
== References ==
== Further reading ==
Gustav Jahoda. (1974). The Psychology of Superstition. Jason Aronson, Inc. Publisher. ISBN 978-0876681855
David Marks. (2000). The Psychology of the Psychic. Prometheus Books. ISBN 978-1573927987
Andrew Neher. (2011). Paranormal and Transcendental Experience: A Psychological Examination. Dover Publications. ISBN 978-0486261676
John Schumaker. (1990). Wings of Illusion: The Origin, Nature and Future of Paranormal Belief. Prometheus Books. ISBN 978-0879756246
Etzel Cardeña, Steven Jay Lynn, Stanley Krippner. (2000). Varieties of Anomalous Experience. American Psychological Association. ISBN 978-1557986252
== External links ==
What is Anomalistic Psychology?
Prof Chris French explains anomalistic psychology on Pulse Project Expert Explanations.

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In marketing, a blind taste test is often used as a tool for companies to compare their brand to another brand. For example, the Pepsi Challenge is a famous taste test that has been run by Pepsi since 1975. Additionally, taste tests are sometimes used as a tool by companies to develop their brand or new products.
Blind taste tests are ideal for goods such as food or wine (see blind wine tasting) that are consumed directly. Researchers use blind taste tests to obtain information about customers' perceptions and preferences on the goods. Blind taste test can be used to:
Track views on a product over time
assess changes or improvements made to a product
gauge reactions to a new product
== Overview ==
Blind taste tests require a "blind testing" meaning the people taking the blind taste test are unaware of the identity of the brand being tested, or if done at home this can be as simple as a blindfold over the person taking the test. This means that any bias, preconceived ideas about a particular brand or food, is eliminated. The people taking the test will also be unaware of any changes done to the product.
In the famous Pepsi Challenge, people took a sip from two different unlabelled glasses, not knowing which was Coke and which was Pepsi.
== Types of blind taste tests ==
There are two types of blind taste tests:
In a single blind taste test, experimenters know information about the participants, but the participants know nothing about the experimenters or the product they are testing. The aforementioned Pepsi Challenge is an example of a single blind test.
In a double blind taste test, the experimenters know nothing about the participants, and the participants know nothing about the experimenters or the product they are testing.
== In popular culture ==
Taste tests are commonly employed by the public television show America's Test Kitchen and its spin-off series Cook's Country, typically administered by Jack Bishop.
== References ==

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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 before the conclusion of a study is a source of experimental error, as the bias that was eliminated by blinding is re-introduced. The CONSORT reporting guidelines recommend that all studies assess and report unblinding. In practice, very few studies do so.
Blinding is an important tool of the scientific method, and is used in many fields of research. In some fields, such as medicine, it is considered essential. In clinical research, a trial that is not blinded is called an open trial.
== History ==
The first known blind experiment was conducted by the French Royal Commission on Animal Magnetism in 1784 to investigate the claims of mesmerism as proposed by Charles d'Eslon, a former associate of Franz Mesmer. In the investigations, the researchers (physically) blindfolded mesmerists and asked them to identify objects that the experimenters had previously filled with "vital fluid". The subjects were unable to do so.
In 1817, the first recorded blind experiment conducted outside a scientific setting compared the musical quality of a Stradivarius violin with that of a guitar-like violin. A violinist played each instrument while a committee of scientists and musicians listened from another room to avoid prejudice.
An early example of a double-blind protocol was the Nuremberg salt test of 1835 performed by Friedrich Wilhelm von Hoven, Nuremberg's highest-ranking public health official, as well as a close friend of Friedrich Schiller. This trial contested the effectiveness of homeopathic dilution.
In 1865, Claude Bernard published his Introduction to the Study of Experimental Medicine, which advocated blinding researchers. Bernard's recommendation that an experiment's observer should not know the hypothesis being tested contrasted starkly with the prevalent Enlightenment-era attitude that scientific observation can only be objectively valid when undertaken by a well-educated, informed scientist. The first study recorded to have a blinded researcher was conducted in 1907 by W. H. R. Rivers and H. N. Webber to investigate the effects of caffeine. The need to blind researchers became widely recognized in the mid-20th century.
== Background ==
=== Bias ===
Several biases arise when a study is insufficiently blinded. Patient-reported outcomes may differ when patients are not blinded to their treatment. Likewise, failure to blind researchers results in observer bias. Unblinded data analysts may favor an analysis that supports their existing beliefs (confirmation bias). These biases are typically the result of subconscious influences, and are present even when study participants believe they do not influence them.
=== Terminology ===
In medical research, the terms single-blind, double-blind and triple-blind are commonly used to describe blinding. These terms describe experiments in which (respectively) one, two, or three parties are blinded to some information. Most often, single-blind studies blind patients to their treatment allocation, double-blind studies blind both patients and researchers to treatment allocations, and triple-blinded studies blind patients, researcher, and some other third party (such as a monitoring committee) to treatment allocations. However, the meaning of these terms can vary across studies.
CONSORT guidelines state that these terms should no longer be used because they are ambiguous. For instance, "double-blind" may mean that the data analysts and patients were blinded; the patients and outcome assessors were blinded; or the patients and those administering the intervention were blinded. The terms also fail to convey the information that was masked and the extent of unblinding. It is not sufficient to specify the number of parties that have been blinded. To describe an experiment's blinding, it is necessary to report who has been blinded to what information, and how well each blind succeeded.

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== 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. Nonetheless, it is still possible to make informed judgments about the quality of a blinding. Poorly blinded studies rank above unblinded studies and below well-blinded studies in the hierarchy of evidence.
=== Post-study unblinding ===
Post-study unblinding is the release of masked data upon completion of a study. In clinical studies, post-study unblinding informs subjects of their treatment allocation. Removing a blind upon completion of a study is never mandatory, but is typically performed as a courtesy to study participants. Unblinding that occurs after the conclusion of a study is not a source of bias, because data collection and analysis are both complete at this time.
=== Premature unblinding ===
Premature unblinding is any unblinding that occurs before the conclusion of a study. In contrast with post-study unblinding, premature unblinding is a source of bias. A code-break procedure dictates when a subject should be unblinded prematurely. A code-break procedure should allow unblinding only in cases of emergency. Unblinding that occurs in compliance with the code-break procedure is strictly documented and reported.
Premature unblinding may also occur when a participant infers, from the experimental conditions, information that has been masked from him. A common cause for unblinding is the presence of side effects (or effects) in the treatment group. In pharmacological trials, premature unblinding can be reduced with the use of an active placebo, which conceals treatment allocation by ensuring the presence of side effects in both groups. However, side effects are not the only cause of unblinding; any perceptible difference between the treatment and control groups can contribute to premature unblinding.
A problem arises in assessing blinding because asking subjects to guess masked information may prompt them to infer it. Researchers speculate that this may contribute to premature unblinding. Furthermore, it has been reported that some subjects of clinical trials attempt to determine if they have received an active treatment by gathering information on social media and message boards. While researchers counsel patients not to use social media to discuss clinical trials, their accounts are not monitored. This behavior is believed to be a source of unblinding. CONSORT standards and good clinical practice guidelines recommend the reporting of all premature unblinding. In practice, unintentional unblinding is rarely reported.
=== Significance ===
Bias due to poor blinding tends to favor the experimental group, resulting in inflated effect size and risk of false positives. Success or failure of blinding is rarely reported or measured; it is implicitly assumed that experiments reported as "blind" are truly blind. Critics have pointed out that without assessment and reporting, there is no way to know if blinding succeeded. This shortcoming is especially concerning given that even a small error in blinding can produce a statistically significant result in the absence of any real difference between test groups when a study is sufficiently powered (i.e. statistical significance is not robust to bias). As such, many statistically significant results in randomized controlled trials may be caused by error in blinding. Some researchers have called for the mandatory assessment of blinding efficacy in clinical trials.
== Applications ==
=== In medicine ===
Blinding is considered essential in medicine, but is often difficult to achieve. For example, it is difficult to compare surgical and non-surgical interventions in blind trials. In some cases, sham surgery may be necessary to blind the study. A good clinical protocol ensures that blinding is as adequate as possible within ethical and practical constraints.
Studies of blinded pharmacological trials across diverse domains report high rates of unblinding. Unblinding has been shown to affect both patients and clinicians. This evidence challenges the common assumption that blinding is highly effective in pharmacological trials. Unblinding has also been documented in clinical trials outside of pharmacology.
==== Pain ====
A 2018 meta-analysis found that assessment of blinding was reported in only 23 out of 408 randomized controlled trials for chronic pain (5.6%). The study concluded, based on an analysis of pooled data, that the overall quality of blinding was poor and that blinding was "not successful." Additionally, both pharmaceutical sponsorship and the presence of side effects were associated with lower rates of reporting assessment of blinding.
==== Depression ====
Studies have found evidence of extensive unblinding in antidepressant trials: at least three-quarters of patients were able to guess their treatment assignment correctly. Unblinding also occurs in clinicians. Better blinding of patients and clinicians reduces effect size. Researchers concluded that unblinding inflates the effect size in antidepressant trials. Some researchers believe that antidepressants are not effective for the treatment of depression and only outperform placebos due to systematic error. These researchers argue that antidepressants are just active placebos.

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==== 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 social sciences ===
Social science research is particularly prone to observer bias, so it is essential in these fields to properly blind the researchers. In some cases, while blind experiments would be helpful, they are impractical or unethical. Blinded data analysis can reduce bias, but is rarely used in social science research.
=== In forensics ===
In a police photo lineup, an officer shows a group of photos to a witness and asks the witness to identify the individual who committed the crime. Since the officer is typically aware of who the suspect is, they may (subconsciously or consciously) influence the witness to choose the individual that they believe committed the crime. There is a growing movement in law enforcement toward a blind procedure in which the officer who shows the photos to the witness does not know the suspect's identity.
=== In music ===
Auditions for symphony orchestras take place behind a curtain so that the judges cannot see the performer. Blinding the judges to the gender of the performers has been shown to increase the hiring of women. Blind tests can also be used to compare the quality of musical instruments.
== See also ==
Allocation concealment
Amplified placebo effect
Black boxing
Blind taste test
Inverse placebo effect
Jadad scale
Lessebo effect
Observational study
Metascience
Royal Commission on Animal Magnetism
Scientific control
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A case study is an in-depth, detailed examination of a particular case (or cases) within a real-world context. For example, case studies in medicine may focus on an individual patient or ailment; case studies in business might cover a particular firm's strategy or a broader market; similarly, case studies in politics can range from a narrow happening over time like the operations of a specific political campaign, to an enormous undertaking like world war, or more often the policy analysis of real-world problems affecting multiple stakeholders.
Generally, a case study can highlight nearly any individual, group, organization, event, belief system, or action. A case study does not necessarily have to be one observation (N=1), but may include many observations (one or multiple individuals and entities across multiple time periods, all within the same case study). Research projects involving numerous cases are frequently called cross-case research, whereas a study of a single case is called within-case research.
Case study research has been extensively practiced in both the social and natural sciences.
== Definition ==
There are multiple definitions of case studies, which may emphasize the number of observations (a small N), the method (qualitative), the thickness of the research (a comprehensive examination of a phenomenon and its context), and the naturalism (a "real-life context" is being examined) involved in the research. There is general agreement among scholars that a case study does not necessarily have to entail one observation (N=1), but can include many observations within a single case or across numerous cases. For example, a case study of the French Revolution would at the bare minimum be an observation of two observations: France before and after a revolution. John Gerring writes that the N=1 research design is so rare in practice that it amounts to a "myth".
The term cross-case research is frequently used for studies of multiple cases, whereas within-case research is frequently used for a single case study.
John Gerring defines the case study approach as an "intensive study of a single unit or a small number of units (the cases), for the purpose of understanding a larger class of similar units (a population of cases)". According to Gerring, case studies lend themselves to an idiographic style of analysis, whereas quantitative work lends itself to a nomothetic style of analysis. He adds that "the defining feature of qualitative work is its use of noncomparable observations—observations that pertain to different aspects of a causal or descriptive question", whereas quantitative observations are comparable.
According to John Gerring, the key characteristic that distinguishes case studies from all other methods is the "reliance on evidence drawn from a single case and its attempts, at the same time, to illuminate features of a broader set of cases". Scholars use case studies to shed light on a "class" of phenomena.
== Research design ==
As with other social science methods, no single research design dominates case study research. Case studies can use at least four types of designs. First, there may be a "no theory first" type of case study design, which is closely connected to Kathleen M. Eisenhardt's methodological work. A second type of research design highlights the distinction between single- and multiple-case studies, following Robert K. Yin's guidelines and extensive examples. A third design deals with a "social construction of reality", represented by the work of Robert E. Stake. Finally, the design rationale for a case study may be to identify "anomalies". A representative scholar of this design is Michael Burawoy. Each of these four designs may lead to different applications, and understanding their sometimes unique ontological and epistemological assumptions becomes important. However, although the designs can have substantial methodological differences, the designs also can be used in explicitly acknowledged combinations with each other.
While case studies can be intended to provide bounded explanations of single cases or phenomena, they are often intended to raise theoretical insights about the features of a broader population.
=== Case selection and structure ===
Case selection in case study research is generally intended to find cases that are representative samples and which have variations on the dimensions of theoretical interest. Using that is solely representative, such as an average or typical case is often not the richest in information. In clarifying lines of history and causation it is more useful to select subjects that offer an interesting, unusual, or particularly revealing set of circumstances. A case selection that is based on representativeness will seldom be able to produce these kinds of insights.
While a random selection of cases is a valid case selection strategy in large-N research, there is a consensus among scholars that it risks generating serious biases in small-N research. Random selection of cases may produce unrepresentative cases, as well as uninformative cases. Cases should generally be chosen that have a high expected information gain. For example, outlier cases (those which are extreme, deviant or atypical) can reveal more information than the potentially representative case. A case may also be chosen because of the inherent interest of the case or the circumstances surrounding it. Alternatively, it may be chosen because of researchers' in-depth local knowledge; where researchers have this local knowledge they are in a position to "soak and poke" as Richard Fenno put it, and thereby to offer reasoned lines of explanation based on this rich knowledge of setting and circumstances.
Beyond decisions about case selection and the subject and object of the study, decisions need to be made about the purpose, approach, and process of the case study. Gary Thomas thus proposes a typology for the case study wherein purposes are first identified (evaluative or exploratory), then approaches are delineated (theory-testing, theory-building, or illustrative), then processes are decided upon, with a principal choice being between whether the study is to be single or multiple, and choices also about whether the study is to be retrospective, snapshot or diachronic, and whether it is nested, parallel or sequential.
In a 2015 article, John Gerring and Jason Seawright list seven case selection strategies:

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Typical cases are cases that exemplify a stable cross-case relationship. These cases are representative of the larger population of cases, and the purpose of the study is to look within the case rather than compare it with other cases.
Diverse cases are cases that have variations on the relevant X and Y variables. Due to the range of variation on the relevant variables, these cases are representative of the full population of cases.
Extreme cases are cases that have an extreme value on the X or Y variable relative to other cases.
Deviant cases are cases that defy existing theories and common sense. They not only have extreme values on X or Y (like extreme cases) but defy existing knowledge about causal relations.
Influential cases are cases that are central to a model or theory (for example, Nazi Germany in theories of fascism and the far-right).
Most similar cases are cases that are similar on all the independent variables, except the one of interest to the researcher.
Most different cases are cases that are different on all the independent variables, except the one of interest to the researcher.
For theoretical discovery, Jason Seawright recommends using deviant cases or extreme cases that have an extreme value on the X variable.
Arend Lijphart, and Harry Eckstein identified five types of case study research designs (depending on the research objectives), Alexander George and Andrew Bennett added a sixth category:
Atheoretical (or configurative idiographic) case studies aim to describe a case very well, but not to contribute to a theory.
Interpretative (or disciplined configurative) case studies aim to use established theories to explain a specific case.
Hypothesis-generating (or heuristic) case studies aim to inductively identify new variables, hypotheses, causal mechanisms, and causal paths.
Theory testing case studies aim to assess the validity and scope conditions of existing theories.
Plausibility probes, aim to assess the plausibility of new hypotheses and theories.
Building block studies of types or subtypes, aim to identify common patterns across cases.
Aaron Rapport reformulated "least-likely" and "most-likely" case selection strategies into the "countervailing conditions" case selection strategy. The countervailing conditions case selection strategy has three components:
The chosen cases fall within the scope conditions of both the primary theory being tested and the competing alternative hypotheses.
For the theories being tested, the analyst must derive clearly stated expected outcomes.
In determining how difficult a test is, the analyst should identify the strength of countervailing conditions in the chosen cases.
In terms of case selection, Gary King, Robert Keohane, and Sidney Verba warn against "selecting on the dependent variable". They argue for example that researchers cannot make valid causal inferences about war outbreaks by only looking at instances where war did happen (the researcher should also look at cases where war did not happen). Scholars of qualitative methods have disputed this claim, however. They argue that selecting the dependent variable can be useful depending on the purposes of the research. Barbara Geddes shares their concerns with selecting the dependent variable (she argues that it cannot be used for theory testing purposes), but she argues that selecting on the dependent variable can be useful for theory creation and theory modification.
King, Keohane, and Verba argue that there is no methodological problem in selecting the explanatory variable, however. They do warn about multicollinearity (choosing two or more explanatory variables that perfectly correlate with each other).
== Uses ==
Case studies have commonly been seen as a fruitful way to come up with hypotheses and generate theories. Case studies are useful for understanding outliers or deviant cases. Classic examples of case studies that generated theories includes Darwin's theory of evolution (derived from his travels to the Galapagos Islands), and Douglass North's theories of economic development (derived from case studies of early developing states, such as England).
Case studies are also useful for formulating concepts, which are an important aspect of theory construction. The concepts used in qualitative research will tend to have higher conceptual validity than concepts used in quantitative research (due to conceptual stretching: the unintentional comparison of dissimilar cases). Case studies add descriptive richness, and can have greater internal validity than quantitative studies. Case studies are suited to explain outcomes in individual cases, which is something that quantitative methods are less equipped to do. Case studies have been characterized as useful to assess the plausibility of arguments that explain empirical regularities. By emphasizing context across cases, case studies can be useful in identifying scope conditions and evaluating to what extent concepts and theories apply across cases.
Through fine-grained knowledge and description, case studies can fully specify the causal mechanisms in a way that may be harder in a large-N study. In terms of identifying "causal mechanisms", some scholars distinguish between "weak" and "strong chains". Strong chains actively connect elements of the causal chain to produce an outcome whereas weak chains are just intervening variables.
Case studies of cases that defy existing theoretical expectations may contribute knowledge by delineating why the cases violate theoretical predictions and specifying the scope conditions of the theory. Case studies are useful in situations of causal complexity where there may be equifinality, complex interaction effects and path dependency. They may also be more appropriate for empirical verifications of strategic interactions in rationalist scholarship than quantitative methods. Case studies can identify necessary and insufficient conditions, as well as complex combinations of necessary and sufficient conditions. They argue that case studies may also be useful in identifying the scope conditions of a theory: whether variables are sufficient or necessary to bring about an outcome.
Qualitative research may be necessary to determine whether a treatment is as-if random or not. As a consequence, good quantitative observational research often entails a qualitative component.

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== Limitations ==
Designing Social Inquiry (also called "KKV"), an influential 1994 book written by Gary King, Robert Keohane, and Sidney Verba, primarily applies lessons from regression-oriented analysis to qualitative research, arguing that the same logics of causal inference can be used in both types of research. The authors' recommendation is to increase the number of observations (a recommendation that Barbara Geddes also makes in Paradigms and Sand Castles), because few observations make it harder to estimate multiple causal effects, as well as increase the risk that there is measurement error, and that an event in a single case was caused by random error or unobservable factors. KKV sees process-tracing and qualitative research as being "unable to yield strong causal inference" because qualitative scholars would struggle with determining which of many intervening variables truly links the independent variable with a dependent variable. The primary problem is that qualitative research lacks a sufficient number of observations to properly estimate the effects of an independent variable. They write that the number of observations could be increased through various means, but that would simultaneously lead to another problem: that the number of variables would increase and thus reduce degrees of freedom. Christopher H. Achen and Duncan Snidal similarly argue that case studies are not useful for theory construction and theory testing.
The purported "degrees of freedom" problem that KKV identify is widely considered flawed; while quantitative scholars try to aggregate variables to reduce the number of variables and thus increase the degrees of freedom, qualitative scholars intentionally want their variables to have many different attributes and complexity. For example, James Mahoney writes, "the Bayesian nature of process of tracing explains why it is inappropriate to view qualitative research as suffering from a small-N problem and certain standard causal identification problems." By using Bayesian probability, it may be possible to make strong causal inferences from a small sliver of data.
KKV also identify inductive reasoning in qualitative research as a problem, arguing that scholars should not revise hypotheses during or after data has been collected because it allows for ad hoc theoretical adjustments to fit the collected data. However, scholars have pushed back on this claim, noting that inductive reasoning is a legitimate practice (both in qualitative and quantitative research).
A commonly described limit of case studies is that they do not lend themselves to generalizability. Due to the small number of cases, it may be harder to ensure that the chosen cases are representative of the larger population.
As small-N research should not rely on random sampling, scholars must be careful in avoiding selection bias when picking suitable cases. A common criticism of qualitative scholarship is that cases are chosen because they are consistent with the scholar's preconceived notions, resulting in biased research. Alexander George and Andrew Bennett also note that a common problem in case study research is that of reconciling conflicting interpretations of the same data. Another limit of case study research is that it can be hard to estimate the magnitude of causal effects.
== Teaching case studies ==
Teachers may prepare a case study that will then be used in classrooms in the form of a "teaching" case study (also see case method and casebook method). For instance, as early as 1870 at Harvard Law School, Christopher Langdell departed from the traditional lecture-and-notes approach to teaching contract law and began using cases pled before courts as the basis for class discussions. By 1920, this practice had become the dominant pedagogical approach used by law schools in the United States.
Outside of law, teaching case studies have become popular in many different fields and professions, ranging from business education to science education. The Harvard Business School has been among the most prominent developers and users of teaching case studies. Teachers develop case studies with particular learning objectives in mind. Additional relevant documentation, such as financial statements, time-lines, short biographies, and multimedia supplements (such as video-recordings of interviews) often accompany the case studies. Similarly, teaching case studies have become increasingly popular in science education, covering different biological and physical sciences. The National Center for Case Studies in Teaching Science has made a growing body of teaching case studies available for classroom use, for university as well as secondary school coursework.
== See also ==
Analytic narrative
Casebook method
Case method
Case competition
Case report
Process tracing
== References ==
== Further reading ==
Baskarada, Sasa (October 19, 2014). "Qualitative Case Study Guidelines". The Qualitative Report. 19 (40): 125. SSRN 2559424.
Bartlett, L. and Vavrus, F. (2017). Rethinking Case Study Research. Routledge.
Baxter, Pamela; Jack, Susan (2008). "Qualitative Case Study Methodology: Study Design and Implementation for Novice Researchers". The Qualitative Report. 13 (4): 54459.
Eisenhardt, Kathleen M. (1989). "Building Theories from Case Study Research". The Academy of Management Review. 14 (4): 53250. doi:10.2307/258557. JSTOR 258557.
George, Alexander L. and Bennett, Andrew. (2005) Case studies and theory development in the social sciences. MIT Press. ISBN 0-262-57222-2
Gerring, John. (2008) Case Study Research. New York: Cambridge University Press. ISBN 978-0-521-67656-4
Kyburz-Graber, Regula (2004). "Does case-study methodology lack rigour? The need for quality criteria for sound case-study research, as illustrated by a recent case in secondary and higher education". Environmental Education Research. 10 (1): 5365. doi:10.1080/1350462032000173706. S2CID 218499108.
Mills, Albert J.; Durepos, Gabrielle; Wiebe, Elden, eds. (2010). Encyclopedia of Case Study Research. SAGE Publications. ISBN 978-1-4129-5670-3.
Ragin, Charles C. and Becker, Howard S. Eds. (1992) What is a Case? Exploring the Foundations of Social Inquiry. Cambridge University Press. ISBN 0-521-42188-8
Scholz, Roland W. and Tietje, Olaf. (2002) Embedded Case Study Methods. Integrating Quantitative and Qualitative Knowledge. Sage. ISBN 0-7619-1946-5
Straits, Bruce C. and Singleton, Royce A. (2004) Approaches to Social Research, 4th ed. Oxford University Press. ISBN 0-19-514794-4.
Thomas, Gary (2011). How to Do Your Case Study: A Guide for Students and Researchers. SAGE Publications.
Yin, Robert K (October 2017). Case study research: design and methods (6th ed.). Thousand Oaks, California, US: SAGE Publications. ISBN 978-1-5063-3616-9.
== External links ==

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Causality is an influence by which one event, process, state, or subject (i.e., a cause) contributes to the production of another event, process, state, or object (i.e., an effect) where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause. The cause of something may also be described as the reason behind the event or process.
In general, a process can have multiple causes, which are also said to be causal factors for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Thus, the distinction between cause and effect either follows from or else provides the distinction between past and future. While the former viewpoint is more prevalent in physics, some writers have held that causality is metaphysically prior to notions of time and space. Causality is an abstraction that indicates how the world progresses. As such, it is a basic concept, and one might expect it to be more apt as an explanation of other concepts of progression than as something to be explained by yet more fundamental ideas. The concept is like those of agency and efficacy. For this reason, a leap of intuition may be needed to grasp it. Accordingly, causality is implicit in the structure of ordinary language, as well as explicit in the language of scientific causal notation.
In English studies of Aristotelian philosophy, the word "cause" is used as a specialized technical term, the translation of Aristotle's term αἰτία, by which Aristotle meant "explanation" or "answer to a 'why' question". Aristotle categorized the four types of answers as material, formal, efficient, and final "causes". In this case, the "cause" is the explanans for the explanandum, and failure to recognize that different kinds of "cause" are being considered can lead to futile debate. Of Aristotle's four explanatory modes, the one nearest to the concerns of the present article is the "efficient" one.
David Hume, as part of his opposition to rationalism, argued that pure reason alone cannot prove the reality of efficient causality; instead, he appealed to custom and mental habit, observing that all human knowledge derives solely from experience.
The topic of causality remains a staple in contemporary philosophy.
== Concept ==
=== Metaphysics ===
The nature of cause and effect is a concern of the subject known as metaphysics. Influential 18th century German philosopher Immanuel Kant thought that time and space were notions prior to human understanding of the progress or evolution of the world, and he also recognized the priority of causality. But he did not have the understanding that came with knowledge of Minkowski geometry and the special theory of relativity, that the notion of causality can be used as a prior foundation from which to construct notions of time and space.
==== Ontology ====
A general metaphysical question about cause and effect is: "what kind of entity can be a cause, and what kind of entity can be an effect?"
One viewpoint on this question is that cause and effect are of one and the same kind of entity, causality being an asymmetric relation between them. That is to say, it would make good sense grammatically to say either "A is the cause and B the effect" or "B is the cause and A the effect", though only one of those two can be actually true. In this view, one opinion, proposed as a metaphysical principle in process philosophy, is that every cause and every effect is respectively some process, event, becoming, or happening. An example is 'his tripping over the step was the cause, and his breaking his ankle the effect'. Another view is that causes and effects are 'states of affairs', with the exact natures of those entities being more loosely defined than in process philosophy.
Another viewpoint on this question is the more classical one, that a cause and its effect can be of different kinds of entity. For example, in Aristotle's efficient causal explanation, an action can be a cause while an enduring object is its effect. For example, the generative actions of his parents can be regarded as the efficient cause, with Socrates being the effect, Socrates being regarded as an enduring object, in philosophical tradition called a 'substance', as distinct from an action.
==== Epistemology ====
Since causality is a subtle metaphysical notion, considerable intellectual effort, along with exhibition of evidence, is needed to establish knowledge of it in particular empirical circumstances. According to David Hume, the human mind is unable to perceive causal relations directly. On this ground, the scholar distinguished between the regularity view of causality and the counterfactual notion. According to the counterfactual view, X causes Y if and only if, without X, Y would not exist. Hume interpreted the latter as an ontological view, i.e., as a description of the nature of causality; but, given the limitations of the human mind, advised using the former (stating, roughly, that X causes Y if and only if the two events are spatiotemporally conjoined, and X precedes Y) as an epistemic definition of causality. We need an epistemic concept of causality in order to distinguish between causal and noncausal relations. The contemporary philosophical literature on causality can be divided into five major approaches to causality. These include the (mentioned above) regularity, probabilistic, counterfactual, mechanistic, and manipulationist views. The five approaches can be shown to be reductive, i.e., they define causality in terms of relations of other types. According to this reading, they define causality in terms of, respectively, empirical regularities (constant conjunctions of events), changes in conditional probabilities, counterfactual conditions, mechanisms underlying causal relations, and invariance under intervention.

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==== Geometrical significance ====
Causality has the properties of antecedence and contiguity. These are topological, and are ingredients for space-time geometry. As developed by Alfred Robb, these properties allow the derivation of the notions of time and space. Max Jammer writes "the Einstein postulate ... opens the way to a straightforward construction of the causal topology ... of Minkowski space." Causal efficacy propagates no faster than light.
Thus, the notion of causality is metaphysically prior to the notions of time and space. In practical terms, this is because use of the relation of causality is necessary for the interpretation of empirical experiments. Interpretation of experiments is needed to establish the physical and geometrical notions of time and space.
==== Volition ====
The deterministic world-view holds that the history of the universe can be exhaustively represented as a progression of events following one after the other as cause and effect. Incompatibilism holds that determinism is incompatible with free will, so if determinism is true, "free will" does not exist. Compatibilism, on the other hand, holds that determinism is compatible with, or even necessary for, free will.
=== Necessary and sufficient causes ===
Causes may sometimes be distinguished into two types: necessary and sufficient. A third type of causation, which requires neither necessity nor sufficiency, but which contributes to the effect, is called a "contributory cause".
Necessary causes
If x is a necessary cause of y, then the presence of y necessarily implies the prior occurrence of x. The presence of x, however, does not imply that y will occur.
Sufficient causes
If x is a sufficient cause of y, then the presence of x necessarily implies the subsequent occurrence of y. However, another cause z may alternatively cause y. Thus the presence of y does not imply the prior occurrence of x.
Contributory causes
For some specific effect, in a singular case, a factor that is a contributory cause is one among several co-occurrent causes. It is implicit that all of them are contributory. For the specific effect, in general, there is no implication that a contributory cause is necessary, though it may be so. In general, a factor that is a contributory cause is not sufficient, because it is by definition accompanied by other causes, which would not count as causes if it were sufficient. For the specific effect, a factor that is on some occasions a contributory cause might on some other occasions be sufficient, but on those other occasions it would not be merely contributory.
J. L. Mackie argues that usual talk of "cause" in fact refers to an INUS condition (insufficient but non-redundant parts of a condition which is itself unnecessary but sufficient for the occurrence of the effect). An example is a short circuit as a cause for a house burning down. Consider the collection of events: the short circuit, the proximity of flammable material, and the absence of firefighters. Together these are unnecessary but sufficient to the house's burning down (since many other collections of events certainly could have led to the house burning down, for example shooting the house with a flamethrower in the presence of oxygen and so forth). Within this collection, the short circuit is an insufficient (since the short circuit by itself would not have caused the fire) but non-redundant (because the fire would not have happened without it, everything else being equal) part of a condition which is itself unnecessary but sufficient for the occurrence of the effect. So, the short circuit is an INUS condition for the occurrence of the house burning down.
However, Mackie's INUS account succumbs to the problem of joint effects of a common cause: it incorrectly identifies one effect of a common cause as an instantiated INUS condition for another effect of the same common cause, even though the two effects are not causally related. Modern regularity theories aim to overcome this problem using so-called non-redundant regularities.
=== Contrasted with conditionals ===
Conditional statements are not statements of causality. An important distinction is that statements of causality require the antecedent to precede or coincide with the consequent in time, whereas conditional statements do not require this temporal order. Confusion commonly arises since many different statements in English may be presented using "If ..., then ..." form (and, arguably, because this form is far more commonly used to make a statement of causality). The two types of statements are distinct, however.
For example, all of the following statements are true when interpreting "If ..., then ..." as the material conditional:
If Barack Obama is president of the United States in 2011, then Germany is in Europe.
If George Washington is president of the United States in 2011, then ⟨arbitrary statement⟩.
The first is true since both the antecedent and the consequent are true. The second is true in sentential logic and indeterminate in natural language, regardless of the consequent statement that follows, because the antecedent is false.
The ordinary indicative conditional has somewhat more structure than the material conditional. For instance, although the first is the closest, neither of the preceding two statements seems true as an ordinary indicative reading. But the sentence:
If Shakespeare of Stratford-on-Avon did not write Macbeth, then someone else did.
intuitively seems to be true, even though there is no straightforward causal relation in this hypothetical situation between Shakespeare's not writing Macbeth and someone else's actually writing it.
Another sort of conditional, the counterfactual conditional, has a stronger connection with causality, yet even counterfactual statements are not all examples of causality. Consider the following two statements:

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Material cause, the material whence a thing has come or that which persists while it changes, as for example, one's mother or the bronze of a statue (see also substance theory).
Formal cause, whereby a thing's dynamic form or static shape determines the thing's properties and function, as a human differs from a statue of a human or as a statue differs from a lump of bronze.
Efficient cause, which imparts the first relevant movement, as a human lifts a rock or raises a statue. This is the main topic of the present article.
Final cause, the criterion of completion, or the end; it may refer to an action or to an inanimate process. Examples: Socrates takes a walk after dinner for the sake of his health; earth falls to the lowest level because that is its nature.
Of Aristotle's four kinds or explanatory modes, only one, the 'efficient cause' is a cause as defined in the leading paragraph of this present article. The other three explanatory modes might be rendered material composition, structure and dynamics, and, again, criterion of completion. The word that Aristotle used was αἰτία. For the present purpose, that Greek word would be better translated as "explanation" than as "cause" as those words are most often used in current English. Another translation of Aristotle is that he meant "the four Becauses" as four kinds of answer to "why" questions.
Aristotle assumed efficient causality as referring to a basic fact of experience, not explicable by, or reducible to, anything more fundamental or basic.
In some works of Aristotle, the four causes are listed as (1) the essential cause, (2) the logical ground, (3) the moving cause, and (4) the final cause. In this listing, a statement of essential cause is a demonstration that an indicated object conforms to a definition of the word that refers to it. A statement of logical ground is an argument as to why an object statement is true. These are further examples of the idea that a "cause" in general in the context of Aristotle's usage is an "explanation".
The word "efficient" used here can also be translated from Aristotle as "moving" or "initiating".
Efficient causation was connected with Aristotelian physics, which recognized the four elements (earth, air, fire, water), and added the fifth element (aether). Water and earth by their intrinsic property gravitas or heaviness intrinsically fall toward, whereas air and fire by their intrinsic property levitas or lightness intrinsically rise away from, Earth's center—the motionless center of the universe—in a straight line while accelerating during the substance's approach to its natural place.
As air remained on Earth, however, and did not escape Earth while eventually achieving infinite speed—an absurdity—Aristotle inferred that the universe is finite in size and contains an invisible substance that holds planet Earth and its atmosphere, the sublunary sphere, centered in the universe. And since celestial bodies exhibit perpetual, unaccelerated motion orbiting planet Earth in unchanging relations, Aristotle inferred that the fifth element, aither, that fills space and composes celestial bodies intrinsically moves in perpetual circles, the only constant motion between two points. (An object traveling a straight line from point A to B and back must stop at either point before returning to the other.)
Left to itself, a thing exhibits natural motion, but can—according to Aristotelian metaphysics—exhibit enforced motion imparted by an efficient cause. The form of plants endows plants with the processes nutrition and reproduction, the form of animals adds locomotion, and the form of humankind adds reason atop these. A rock normally exhibits natural motion—explained by the rock's material cause of being composed of the element earth—but a living thing can lift the rock, an enforced motion diverting the rock from its natural place and natural motion. As a further kind of explanation, Aristotle identified the final cause, specifying a purpose or criterion of completion in light of which something should be understood.
Aristotle himself explained,
Cause means
(a) in one sense, that as the result of whose presence something comes into being—e.g., the bronze of a statue and the silver of a cup, and the classes which contain these [i.e., the material cause];
(b) in another sense, the form or pattern; that is, the essential formula and the classes which contain it—e.g. the ratio 2:1 and number in general is the cause of the octave—and the parts of the formula [i.e., the formal cause].
(c) The source of the first beginning of change or rest; e.g. the man who plans is a cause, and the father is the cause of the child, and in general that which produces is the cause of that which is produced, and that which changes of that which is changed [i.e., the efficient cause].
(d) The same as "end"; i.e. the final cause; e.g., as the "end" of walking is health. For why does a man walk? "To be healthy", we say, and by saying this we consider that we have supplied the cause [the final cause].
(e) All those means towards the end which arise at the instigation of something else, as, e.g., fat-reducing, purging, drugs, and instruments are causes of health; for they all have the end as their object, although they differ from each other as being some instruments, others actions [i.e., necessary conditions].
Aristotle further discerned two modes of causation: proper (prior) causation and accidental (chance) causation. All causes, proper and accidental, can be spoken as potential or as actual, particular or generic. The same language refers to the effects of causes, so that generic effects are assigned to generic causes, particular effects to particular causes, and actual effects to operating causes.
Averting infinite regress, Aristotle inferred the first mover—an unmoved mover. The first mover's motion, too, must have been caused, but, being an unmoved mover, must have moved only toward a particular goal or desire.
==== Pyrrhonism ====
While the plausibility of causality was accepted in Pyrrhonism, it was equally accepted that it was plausible that nothing was the cause of anything.

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==== Middle Ages ====
In line with Aristotelian cosmology, Thomas Aquinas posed a hierarchy prioritizing Aristotle's four causes: "final > efficient > material > formal". Aquinas sought to identify the first efficient cause—now simply first cause—as everyone would agree, said Aquinas, to call it God. Later in the Middle Ages, many scholars conceded that the first cause was God, but explained that many earthly events occur within God's design or plan, and thereby scholars sought freedom to investigate the numerous secondary causes.
==== After the Middle Ages ====
For Aristotelian philosophy before Aquinas, the word cause had a broad meaning. It meant 'answer to a why question' or 'explanation', and Aristotelian scholars recognized four kinds of such answers. With the end of the Middle Ages, in many philosophical usages, the meaning of the word 'cause' narrowed. It often lost that broad meaning, and was restricted to just one of the four kinds. For authors such as Niccolò Machiavelli, in the field of political thinking, and Francis Bacon, concerning science more generally, Aristotle's moving cause was the focus of their interest. A widely used modern definition of causality in this newly narrowed sense was assumed by David Hume. He undertook an epistemological and metaphysical investigation of the notion of moving cause. He denied that we can ever perceive cause and effect, except by developing a habit or custom of mind where we come to associate two types of object or event, always contiguous and occurring one after the other. In Part III, section XV of his book A Treatise of Human Nature, Hume expanded this to a list of eight ways of judging whether two things might be cause and effect. The first three:
"The cause and effect must be contiguous in space and time."
"The cause must be prior to the effect."
"There must be a constant union betwixt the cause and effect. 'Tis chiefly this quality, that constitutes the relation."
And then additionally there are three connected criteria which come from our experience and which are "the source of most of our philosophical reasonings":
And then two more:
In 1949, physicist Max Born distinguished determination from causality. For him, determination meant that actual events are so linked by laws of nature that certainly reliable predictions and retrodictions can be made from sufficient present data about them. He describes two kinds of causation: nomic or generic causation and singular causation. Nomic causality means that cause and effect are linked by more or less certain or probabilistic general laws covering many possible or potential instances; this can be recognized as a probabilized version of Hume's criterion 3. An occasion of singular causation is a particular occurrence of a definite complex of events that are physically linked by antecedence and contiguity, which may be recognized as criteria 1 and 2.
== See also ==
== References ==
== Further reading ==
Spirtes, Peter, Clark Glymour and Richard Scheines Causation, Prediction, and Search, MIT Press, ISBN 0-262-19440-6
University of California journal articles, including Judea Pearl's articles between 1984 and 1998 Search Results - Technical Reports Archived 5 July 2022 at the Wayback Machine.
Miguel Espinoza, Théorie du déterminisme causal, L'Harmattan, Paris, 2006. ISBN 2-296-01198-5.

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If A were a triangle, then A would have three sides.
If switch S were thrown, then bulb B would light.
In the first case, it would be incorrect to say that A's being a triangle caused it to have three sides, since the relationship between triangularity and three-sidedness is that of definition. The property of having three sides actually determines A's state as a triangle. Nonetheless, even when interpreted counterfactually, the first statement is true. An early version of Aristotle's "four cause" theory is described as recognizing "essential cause". In this version of the theory, that the closed polygon has three sides is said to be the "essential cause" of its being a triangle. This use of the word 'cause' is of course now far obsolete. Nevertheless, it is within the scope of ordinary language to say that it is essential to a triangle that it has three sides.
A full grasp of the concept of conditionals is important to understanding the literature on causality. In everyday language, loose conditional statements are often enough made, and need to be interpreted carefully.
=== Questionable cause ===
Fallacies of questionable cause, also known as causal fallacies, non-causa pro causa (Latin for "non-cause for cause"), or false cause, are informal fallacies where a cause is incorrectly identified.
== Theories ==
=== Counterfactual theories ===
Counterfactual theories define causation in terms of a counterfactual relation, and can often be seen as "floating" their account of causality on top of an account of the logic of counterfactual conditionals. Counterfactual theories reduce facts about causation to facts about what would have been true under counterfactual circumstances. The idea is that causal relations can be framed in the form of "Had C not occurred, E would not have occurred." This approach can be traced back to David Hume's definition of the causal relation as that "where, if the first object had not been, the second never had existed." More full-fledged analysis of causation in terms of counterfactual conditionals only came in the 20th century after development of the possible world semantics for the evaluation of counterfactual conditionals. In his 1973 paper "Causation," David Lewis proposed the following definition of the notion of causal dependence:
An event E causally depends on C if, and only if, (i) if C had occurred, then E would have occurred, and (ii) if C had not occurred, then E would not have occurred.
Causation is then analyzed in terms of counterfactual dependence. That is, C causes E if and only if there exists a sequence of events C, D1, D2, ... Dk, E such that each event in the sequence counterfactually depends on the previous. This chain of causal dependence may be called a mechanism.
Note that the analysis does not purport to explain how we make causal judgements or how we reason about causation, but rather to give a metaphysical account of what it is for there to be a causal relation between some pair of events. If correct, the analysis has the power to explain certain features of causation. Knowing that causation is a matter of counterfactual dependence, we may reflect on the nature of counterfactual dependence to account for the nature of causation. For example, in his paper "Counterfactual Dependence and Time's Arrow," Lewis sought to account for the time-directedness of counterfactual dependence in terms of the semantics of the counterfactual conditional. If correct, this theory can serve to explain a fundamental part of our experience, which is that we can causally affect the future but not the past.
One challenge for the counterfactual account is overdetermination, whereby an effect has multiple causes. For instance, suppose Alice and Bob both throw bricks at a window and it breaks. If Alice hadn't thrown the brick, then it still would have broken, suggesting that Alice wasn't a cause; however, intuitively, Alice did cause the window to break. The Halpern-Pearl definitions of causality take account of examples like these. The first and third Halpern-Pearl conditions are easiest to understand: AC1 requires that Alice threw the brick and the window broke in the actual work. AC3 requires that Alice throwing the brick is a minimal cause (cf. blowing a kiss and throwing a brick). Taking the "updated" version of AC2(a), the basic idea is that we have to find a set of variables and settings thereof such that preventing Alice from throwing a brick also stops the window from breaking. One way to do this is to stop Bob from throwing the brick. Finally, for AC2(b), we have to hold things as per AC2(a) and show that Alice throwing the brick breaks the window. (The full definition is a little more involved, involving checking all subsets of variables.)
=== Probabilistic causation ===

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Interpreting causation as a deterministic relation means that if A causes B, then A must always be followed by B. In this sense, war does not cause deaths, nor does smoking cause cancer or emphysema. As a result, many turn to a notion of probabilistic causation. Informally, A ("The person is a smoker") probabilistically causes B ("The person has now or will have cancer at some time in the future"), if the information that A occurred increases the likelihood of B's occurrence. Formally, P{B|A}≥ P{B} where P{B|A} is the conditional probability that B will occur given the information that A occurred, and P{B} is the probability that B will occur having no knowledge whether A did or did not occur. This intuitive condition is not adequate as a definition for probabilistic causation because of its being too general and thus not meeting our intuitive notion of cause and effect. For example, if A denotes the event "The person is a smoker," B denotes the event "The person now has or will have cancer at some time in the future" and C denotes the event "The person now has or will have emphysema some time in the future," then the following three relationships hold: P{B|A} ≥ P{B}, P{C|A} ≥ P{C} and P{B|C} ≥ P{B}. The last relationship states that knowing that the person has emphysema increases the likelihood that he will have cancer. The reason for this is that having the information that the person has emphysema increases the likelihood that the person is a smoker, thus indirectly increasing the likelihood that the person will have cancer. However, we would not want to conclude that having emphysema causes cancer. Thus, we need additional conditions such as temporal relationship of A to B and a rational explanation as to the mechanism of action. It is hard to quantify this last requirement and thus different authors prefer somewhat different definitions.
=== Causal calculus ===
When experimental interventions are infeasible or illegal, the derivation of a cause-and-effect relationship from observational studies must rest on some qualitative theoretical assumptions, for example, that symptoms do not cause diseases, usually expressed in the form of missing arrows in causal graphs such as Bayesian networks or path diagrams. The theory underlying these derivations relies on the distinction between conditional probabilities, as in
P
(
c
a
n
c
e
r
|
s
m
o
k
i
n
g
)
{\displaystyle P(cancer|smoking)}
, and interventional probabilities, as in
P
(
c
a
n
c
e
r
|
d
o
(
s
m
o
k
i
n
g
)
)
{\displaystyle P(cancer|do(smoking))}
. The former reads: "the probability of finding cancer in a person known to smoke, having started, unforced by the experimenter, to do so at an unspecified time in the past", while the latter reads: "the probability of finding cancer in a person forced by the experimenter to smoke at a specified time in the past". The former is a statistical notion that can be estimated by observation with negligible intervention by the experimenter, while the latter is a causal notion which is estimated in an experiment with an important controlled randomized intervention. It is specifically characteristic of quantal phenomena that observations defined by incompatible variables always involve important intervention by the experimenter, as described quantitatively by the observer effect. In classical thermodynamics, processes are initiated by interventions called thermodynamic operations. In other branches of science, for example astronomy, the experimenter can often observe with negligible intervention.
The theory of "causal calculus" (also known as do-calculus, Judea Pearl's Causal Calculus, Calculus of
Actions) permits one to infer interventional probabilities from conditional probabilities in causal Bayesian networks with unmeasured variables. One very practical result of this theory is the characterization of confounding variables, namely, a sufficient set of variables that, if adjusted for, would yield the correct causal effect between variables of interest. It can be shown that a sufficient set for estimating the causal effect of
X
{\displaystyle X}
on
Y
{\displaystyle Y}
is any set of non-descendants of
X
{\displaystyle X}
that
d
{\displaystyle d}
-separate
X
{\displaystyle X}
from
Y
{\displaystyle Y}
after removing all arrows emanating from
X
{\displaystyle X}
. This criterion, called "backdoor", provides a mathematical definition of "confounding" and helps researchers identify accessible sets of variables worthy of measurement.
=== Structure learning ===
While derivations in causal calculus rely on the structure of the causal graph, parts of the causal structure can, under certain assumptions, be learned from statistical data. The basic idea goes back to Sewall Wright's 1921 work on path analysis. A "recovery" algorithm was developed by Rebane and Pearl (1987) which rests on Wright's distinction between the three possible types of causal substructures allowed in a directed acyclic graph (DAG):
X
Y
Z
{\displaystyle X\rightarrow Y\rightarrow Z}
X
Y
Z
{\displaystyle X\leftarrow Y\rightarrow Z}
X
Y
Z
{\displaystyle X\rightarrow Y\leftarrow Z}

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Type 1 and type 2 represent the same statistical dependencies (i.e.,
X
{\displaystyle X}
and
Z
{\displaystyle Z}
are independent given
Y
{\displaystyle Y}
) and are, therefore, indistinguishable within purely cross-sectional data. Type 3, however, can be uniquely identified, since
X
{\displaystyle X}
and
Z
{\displaystyle Z}
are marginally independent and all other pairs are dependent. Thus, while the skeletons (the graphs stripped of arrows) of these three triplets are identical, the directionality of the arrows is partially identifiable. The same distinction applies when
X
{\displaystyle X}
and
Z
{\displaystyle Z}
have common ancestors, except that one must first condition on those ancestors. Algorithms have been developed to systematically determine the skeleton of the underlying graph and, then, orient all arrows whose directionality is dictated by the conditional independencies observed.
Alternative methods of structure learning search through the many possible causal structures among the variables, and remove ones which are strongly incompatible with the observed correlations. In general this leaves a set of possible causal relations, which should then be tested by analyzing time series data or, preferably, designing appropriately controlled experiments. In contrast with Bayesian Networks, path analysis (and its generalization, structural equation modeling), serve better to estimate a known causal effect or to test a causal model than to generate causal hypotheses.
For nonexperimental data, causal direction can often be inferred if information about time is available. This is because (according to many, though not all, theories) causes must precede their effects temporally. This can be determined by statistical time series models, for instance, or with a statistical test based on the idea of Granger causality, or by direct experimental manipulation. The use of temporal data can permit statistical tests of a pre-existing theory of causal direction. For instance, our degree of confidence in the direction and nature of causality is much greater when supported by cross-correlations, ARIMA models, or cross-spectral analysis using vector time series data than by cross-sectional data.
=== Derivation theories ===
Nobel laureate Herbert A. Simon and philosopher Nicholas Rescher claim that the asymmetry of the causal relation is unrelated to the asymmetry of any mode of implication that contraposes. Rather, a causal relation is not a relation between values of variables, but a function of one variable (the cause) on to another (the effect). So, given a system of equations, and a set of variables appearing in these equations, we can introduce an asymmetric relation among individual equations and variables that corresponds perfectly to our commonsense notion of a causal ordering. The system of equations must have certain properties, most importantly, if some values are chosen arbitrarily, the remaining values will be determined uniquely through a path of serial discovery that is perfectly causal. They postulate the inherent serialization of such a system of equations may correctly capture causation in all empirical fields, including physics and economics.
=== Manipulation theories ===
Some theorists have equated causality with manipulability. Under these theories, x causes y only in the case that one can change x in order to change y. This coincides with commonsense notions of causations, since often we ask causal questions in order to change some feature of the world. For instance, we are interested in knowing the causes of crime so that we might find ways of reducing it.
These theories have been criticized on two primary grounds. First, theorists complain that these accounts are circular. Attempting to reduce causal claims to manipulation requires that manipulation is more basic than causal interaction. But describing manipulations in non-causal terms has provided a substantial difficulty.
The second criticism centers around concerns of anthropocentrism. It seems to many people that causality is some existing relationship in the world that we can harness for our desires. If causality is identified with our manipulation, then this intuition is lost. In this sense, it makes humans overly central to interactions in the world.
Some attempts to defend manipulability theories are recent accounts that do not claim to reduce causality to manipulation. These accounts use manipulation as a sign or feature in causation without claiming that manipulation is more fundamental than causation.
=== Process theories ===
Some theorists are interested in distinguishing between causal processes and non-causal processes (Russell 1948; Salmon 1984). These theorists often want to distinguish between a process and a pseudo-process. As an example, a ball moving through the air (a process) is contrasted with the motion of a shadow (a pseudo-process). The former is causal in nature while the latter is not.
Salmon (1984) claims that causal processes can be identified by their ability to transmit an alteration over space and time. An alteration of the ball (a mark by a pen, perhaps) is carried with it as the ball goes through the air. On the other hand, an alteration of the shadow (insofar as it is possible) will not be transmitted by the shadow as it moves along.
These theorists claim that the important concept for understanding causality is not causal relationships or causal interactions, but rather identifying causal processes. The former notions can then be defined in terms of causal processes.
A subgroup of the process theories is the mechanistic view on causality. It states that causal relations supervene on mechanisms. While the notion of mechanism is understood differently, the definition put forward by the group of philosophers referred to as the 'New Mechanists' dominate the literature.
== Fields ==

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=== Science ===
For the scientific investigation of efficient causality, the cause and effect are each best conceived of as temporally transient processes.
Within the conceptual frame of the scientific method, an investigator sets up several distinct and contrasting temporally transient material processes that have the structure of experiments, and records candidate material responses, normally intending to determine causality in the physical world. For instance, one may want to know whether a high intake of carrots causes humans to develop the bubonic plague. The quantity of carrot intake is a process that is varied from occasion to occasion. The occurrence or non-occurrence of subsequent bubonic plague is recorded. To establish causality, the experiment must fulfill certain criteria, only one example of which is mentioned here. For example, instances of the hypothesized cause must be set up to occur at a time when the hypothesized effect is relatively unlikely in the absence of the hypothesized cause; such unlikelihood is to be established by empirical evidence. A mere observation of a correlation is not nearly adequate to establish causality. In nearly all cases, establishment of causality relies on repetition of experiments and probabilistic reasoning. Hardly ever is causality established more firmly than as more or less probable. It is most convenient for establishment of causality if the contrasting material states of affairs are precisely matched, except for only one variable factor, perhaps measured by a real number.
==== Physics ====
One has to be careful in the use of the word cause in physics. Properly speaking, the hypothesized cause and the hypothesized effect are each temporally transient processes. For example, force is a useful concept for the explanation of acceleration, but force is not by itself a cause. More is needed. For example, a temporally transient process might be characterized by a definite change of force at a definite time. Such a process can be regarded as a cause. Causality is not inherently implied in equations of motion, but postulated as an additional constraint that needs to be satisfied (i.e. a cause always precedes its effect). This constraint has mathematical implications such as the Kramers-Kronig relations.
Causality is one of the most fundamental and essential notions of physics. Causal efficacy cannot 'propagate' faster than light. Otherwise, reference coordinate systems could be constructed (using the Lorentz transform of special relativity) in which an observer would see an effect precede its cause (i.e. the postulate of causality would be violated).
Causal notions appear in the context of the flow of mass-energy. Any actual process has causal efficacy that can propagate no faster than light. In contrast, an abstraction has no causal efficacy. Its mathematical expression does not propagate in the ordinary sense of the word, though it may refer to virtual or nominal 'velocities' with magnitudes greater than that of light. For example, wave packets are mathematical objects that have group velocity and phase velocity. The energy of a wave packet travels at the group velocity (under normal circumstances); since energy has causal efficacy, the group velocity cannot be faster than the speed of light. The phase of a wave packet travels at the phase velocity; since phase is not causal, the phase velocity of a wave packet can be faster than light.
Causal notions are important in general relativity to the extent that the existence of an arrow of time demands that the universe's semi-Riemannian manifold be orientable, so that "future" and "past" are globally definable quantities.
==== Engineering ====
A causal system is a system with output and internal states that depends only on the current and previous input values. A system that has some dependence on input values from the future (in addition to possible past or current input values) is termed an acausal system, and a system that depends solely on future input values is an anticausal system. Acausal filters, for example, can only exist as postprocessing filters, because these filters can extract future values from a memory buffer or a file.
We have to be very careful with causality in physics and engineering. Cellier, Elmqvist, and Otter describe causality forming the basis of physics as a misconception, because physics is essentially acausal. In their article they cite a simple example: "The relationship between voltage across and current through an electrical resistor can be described by Ohm's law: V = IR, yet, whether it is the current flowing through the resistor that causes a voltage drop, or whether it is the difference between the electrical potentials on the two wires that causes current to flow is, from a physical perspective, a meaningless question". In fact, if we explain cause-effect using the law, we need two explanations to describe an electrical resistor: as a voltage-drop-causer or as a current-flow-causer. There is no physical experiment in the world that can distinguish between action and reaction.
==== Biology, medicine and epidemiology ====
Austin Bradford Hill built upon the work of Hume and Popper and suggested in his paper "The Environment and Disease: Association or Causation?" that aspects of an association such as strength, consistency, specificity, and temporality be considered in attempting to distinguish causal from noncausal associations in the epidemiological situation. (See Bradford Hill criteria.) He did not note however, that temporality is the only necessary criterion among those aspects. Directed acyclic graphs (DAGs) are increasingly used in epidemiology to help enlighten causal thinking.
Causality plays an essential role in the field of Network Physiologyto study the mechanisms through which physiological and organ systems exchange, process, and integrate information within an adaptive dynamic network to generate states and functions at the organism level.
==== Psychology ====

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Psychologists take an empirical approach to causality, investigating how people and non-human animals detect or infer causation from sensory information, prior experience and innate knowledge.
Attribution:
Attribution theory is the theory concerning how people explain individual occurrences of causation. Attribution can be external (assigning causality to an outside agent or force—claiming that some outside thing motivated the event) or internal (assigning causality to factors within the person—taking personal responsibility or accountability for one's actions and claiming that the person was directly responsible for the event). Taking causation one step further, the type of attribution a person provides influences their future behavior.
The intention behind the cause or the effect can be covered by the subject of action. See also accident; blame; intent; and responsibility.
Causal powers
Whereas David Hume argued that causes are inferred from non-causal observations, Immanuel Kant claimed that people have innate assumptions about causes. Within psychology, Patricia Cheng attempted to reconcile the Humean and Kantian views. According to her power PC theory, people filter observations of events through an intuition that causes have the power to generate (or prevent) their effects, thereby inferring specific cause-effect relations.
Causation and salience
Our view of causation depends on what we consider to be the relevant events. Another way to view the statement, "Lightning causes thunder" is to see both lightning and thunder as two perceptions of the same event, viz., an electric discharge that we perceive first visually and then aurally.
Naming and causality
David Sobel and Alison Gopnik from the Psychology Department of UC Berkeley designed a device known as the blicket detector which would turn on when an object was placed on it. Their research suggests that "even young children will easily and swiftly learn about a new causal power of an object and spontaneously use that information in classifying and naming the object."
Perception of launching events
Some researchers such as Anjan Chatterjee at the University of Pennsylvania and Jonathan Fugelsang at the University of Waterloo are using neuroscience techniques to investigate the neural and psychological underpinnings of causal launching events in which one object causes another object to move. Both temporal and spatial factors can be manipulated.
See Causal Reasoning (Psychology) for more information.
==== Statistics and economics ====
Statistics and economics usually employ pre-existing data or experimental data to infer causality by regression methods. The body of statistical techniques involves substantial use of regression analysis. Typically a linear relationship such as
y
i
=
a
0
+
a
1
x
1
,
i
+
a
2
x
2
,
i
+
+
a
k
x
k
,
i
+
e
i
{\displaystyle y_{i}=a_{0}+a_{1}x_{1,i}+a_{2}x_{2,i}+\dots +a_{k}x_{k,i}+e_{i}}

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is postulated, in which
y
i
{\displaystyle y_{i}}
is the ith observation of the dependent variable (hypothesized to be the caused variable),
x
j
,
i
{\displaystyle x_{j,i}}
for j=1,...,k is the ith observation on the jth independent variable (hypothesized to be a causative variable), and
e
i
{\displaystyle e_{i}}
is the error term for the ith observation (containing the combined effects of all other causative variables, which must be uncorrelated with the included independent variables). If there is reason to believe that none of the
x
j
{\displaystyle x_{j}}
s is caused by y, then estimates of the coefficients
a
j
{\displaystyle a_{j}}
are obtained. If the null hypothesis that
a
j
=
0
{\displaystyle a_{j}=0}
is rejected, then the alternative hypothesis that
a
j
0
{\displaystyle a_{j}\neq 0}
and equivalently that
x
j
{\displaystyle x_{j}}
causes y cannot be rejected. On the other hand, if the null hypothesis that
a
j
=
0
{\displaystyle a_{j}=0}
cannot be rejected, then equivalently the hypothesis of no causal effect of
x
j
{\displaystyle x_{j}}
on y cannot be rejected. Here the notion of causality is one of contributory causality as discussed above: If the true value
a
j
0
{\displaystyle a_{j}\neq 0}
, then a change in
x
j
{\displaystyle x_{j}}
will result in a change in y unless some other causative variable(s), either included in the regression or implicit in the error term, change in such a way as to exactly offset its effect; thus a change in
x
j
{\displaystyle x_{j}}
is not sufficient to change y. Likewise, a change in
x
j
{\displaystyle x_{j}}
is not necessary to change y, because a change in y could be caused by something implicit in the error term (or by some other causative explanatory variable included in the model).
The above way of testing for causality requires belief that there is no reverse causation, in which y would cause
x
j
{\displaystyle x_{j}}
. This belief can be established in one of several ways. First, the variable
x
j
{\displaystyle x_{j}}
may be a non-economic variable: for example, if rainfall amount
x
j
{\displaystyle x_{j}}
is hypothesized to affect the futures price y of some agricultural commodity, it is impossible that in fact the futures price affects rainfall amount (provided that cloud seeding is never attempted). Second, the instrumental variables technique may be employed to remove any reverse causation by introducing a role for other variables (instruments) that are known to be unaffected by the dependent variable. Third, the principle that effects cannot precede causes can be invoked, by including on the right side of the regression only variables that precede in time the dependent variable; this principle is invoked, for example, in testing for Granger causality and in its multivariate analog, vector autoregression, both of which control for lagged values of the dependent variable while testing for causal effects of lagged independent variables.
Regression analysis controls for other relevant variables by including them as regressors (explanatory variables). This helps to avoid false inferences of causality due to the presence of a third, underlying, variable that influences both the potentially causative variable and the potentially caused variable: its effect on the potentially caused variable is captured by directly including it in the regression, so that effect will not be picked up as an indirect effect through the potentially causative variable of interest. Given the above procedures, coincidental (as opposed to causal) correlation can be probabilistically rejected if data samples are large and if regression results pass cross-validation tests showing that the correlations hold even for data that were not used in the regression. Asserting with certitude that a common-cause is absent and the regression represents the true causal structure is in principle impossible.
The problem of omitted variable bias, however, has to be balanced against the risk of inserting Causal colliders, in which the addition of a new variable
x
j
+
1
{\displaystyle x_{j+1}}
induces a correlation between
x
j
{\displaystyle x_{j}}
and
y
{\displaystyle y}
via Berkson's paradox.
Apart from constructing statistical models of observational and experimental data, economists use axiomatic (mathematical) models to infer and represent causal mechanisms. Highly abstract theoretical models that isolate and idealize one mechanism dominate microeconomics. In macroeconomics, economists use broad mathematical models that are calibrated on historical data. A subgroup of calibrated models, dynamic stochastic general equilibrium (DSGE) models are employed to represent (in a simplified way) the whole economy and simulate changes in fiscal and monetary policy.
Statistical and economic analyses often rely on regression methods applied to observational or preexisting data to infer causal relationships. Experimental designs, in contrast, establish causality by systematically manipulating independent variables under controlled conditions. Experiments therefore provide stronger internal validity because causal mechanisms are demonstrated directly rather than inferred from patterns in observational data.
=== Management ===
For quality control in manufacturing in the 1960s, Kaoru Ishikawa developed a cause and effect diagram, known as an Ishikawa diagram or fishbone diagram. The diagram categorizes causes, such as into the six main categories shown here. These categories are then sub-divided. Ishikawa's method identifies "causes" in brainstorming sessions conducted among various groups involved in the manufacturing process. These groups can then be labeled as categories in the diagrams. The use of these diagrams has now spread beyond quality control, and they are used in other areas of management and in design and engineering. Ishikawa diagrams have been criticized for failing to make the distinction between necessary conditions and sufficient conditions. It seems that Ishikawa was not even aware of this distinction.
=== Humanities ===

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==== History ====
In the discussion of history, events are sometimes considered as if in some way being agents that can then bring about other historical events. Thus, the combination of poor harvests, the hardships of the peasants, high taxes, lack of representation of the people, and kingly ineptitude are among the causes of the French Revolution. This is a somewhat Platonic and Hegelian view that reifies causes as ontological entities. In Aristotelian terminology, this use approximates to the case of the efficient cause.
Some philosophers of history such as Arthur Danto have claimed that "explanations in history and elsewhere" describe "not simply an event—something that happens—but a change". Like many practicing historians, they treat causes as intersecting actions and sets of actions which bring about "larger changes", in Danto's words: to decide "what are the elements which persist through a change" is "rather simple" when treating an individual's "shift in attitude", but "it is considerably more complex and metaphysically challenging when we are interested in such a change as, say, the break-up of feudalism or the emergence of nationalism".
Much of the historical debate about causes has focused on the relationship between communicative and other actions, between singular and repeated ones, and between actions, structures of action or group and institutional contexts and wider sets of conditions. John Gaddis has distinguished between exceptional and general causes (following Marc Bloch) and between "routine" and "distinctive links" in causal relationships: "in accounting for what happened at Hiroshima on August 6, 1945, we attach greater importance to the fact that President Truman ordered the dropping of an atomic bomb than to the decision of the Army Air Force to carry out his orders." He has also pointed to the difference between immediate, intermediate and distant causes. For his part, Christopher Lloyd puts forward four "general concepts of causation" used in history: the "metaphysical idealist concept, which asserts that the phenomena of the universe are products of or emanations from an omnipotent being or such final cause"; "the empiricist (or Humean) regularity concept, which is based on the idea of causation being a matter of constant conjunctions of events"; "the functional/teleological/consequential concept", which is "goal-directed, so that goals are causes"; and the "realist, structurist and dispositional approach, which sees relational structures and internal dispositions as the causes of phenomena".
==== Law ====
According to law and jurisprudence, legal cause must be demonstrated to hold a defendant liable for a crime or a tort (i.e. a civil wrong such as negligence or trespass). It must be proven that causality, or a "sufficient causal link" relates the defendant's actions to the criminal event or damage in question. Causation is also an essential legal element that must be proven to qualify for remedy measures under international trade law.
== History ==
=== Hindu philosophy ===
Vedic period (c.1750500 BCE) literature contains early discussions of karma. Karma is the belief held by Hinduism and other Indian religions that a person's actions cause certain effects in the current life and/or in future life, positively or negatively. The various philosophical schools (darshanas) provide different accounts of the subject. A doctrine of satkaryavada affirms that the effect inheres in the cause in some way. The effect is thus either a real or apparent modification of the cause. A doctrine of asatkaryavada affirms that the effect does not inhere in the cause, but is a new arising. In Brahma Samhita, Brahma describes Krishna as the prime cause of all causes.
Bhagavad-gītā 18.14 identifies five causes for any action (knowing which it can be perfected): the body, the individual soul, the senses, the efforts and the supersoul.
According to Monier-Williams, in the Nyāya causation theory from Sutra I.2.I,2 in the Vaisheshika philosophy, from causal non-existence is effectual non-existence; but, not effectual non-existence from causal non-existence. A cause precedes an effect. With a threads and cloth metaphors, three causes are:
Co-inherence cause: resulting from substantial contact, 'substantial causes', threads are substantial to cloth, corresponding to Aristotle's material cause.
Non-substantial cause: Methods putting threads into cloth, corresponding to Aristotle's formal cause.
Instrumental cause: Tools to make the cloth, corresponding to Aristotle's efficient cause.
Monier-Williams also proposed that Aristotle's and the Nyaya's causality are considered conditional aggregates necessary to man's productive work.
=== Buddhist philosophy ===

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Karma is the causality principle focusing on 1) causes, 2) actions, 3) effects, where it is the mind's phenomena that guide the actions that the actor performs. Buddhism trains the actor's actions for continued and uncontrived virtuous outcomes aimed at reducing suffering. This follows the Subjectverbobject structure.
The general or universal definition of pratityasamutpada (or "dependent origination" or "dependent arising" or "interdependent co-arising") is that everything arises in dependence upon multiple causes and conditions; nothing exists as a singular, independent entity. A traditional example in Buddhist texts is of three sticks standing upright and leaning against each other and supporting each other. If one stick is taken away, the other two will fall to the ground.
Causality in the Chittamatrin Buddhist school approach, Asanga's (c.400 CE) mind-only Buddhist school, asserts that objects cause consciousness in the mind's image. Because causes precede effects, which must be different entities, then subject and object are different. For this school, there are no objects which are entities external to a perceiving consciousness. The Chittamatrin and the Yogachara Svatantrika schools accept that there are no objects external to the observer's causality. This largely follows the Nikayas approach.
The Vaibhashika (c.500 CE) is an early Buddhist school which favors direct object contact and accepts simultaneous cause and effects. This is based in the consciousness example which says, intentions and feelings are mutually accompanying mental factors that support each other like poles in tripod. In contrast, simultaneous cause and effect rejectors say that if the effect already exists, then it cannot effect the same way again. How past, present and future are accepted is a basis for various Buddhist school's causality viewpoints.
All the classic Buddhist schools teach karma. "The law of karma is a special instance of the law of cause and effect, according to which all our actions of body, speech, and mind are causes and all our experiences are their effects."
=== Western philosophy ===
==== Aristotelian ====
Aristotle identified four kinds of answer or explanatory mode to various "Why?" questions. He thought that, for any given topic, all four kinds of explanatory mode were important, each in its own right. As a result of traditional specialized philosophical peculiarities of language, with translations between ancient Greek, Latin, and English, the word 'cause' is nowadays in specialized philosophical writings used to label Aristotle's four kinds. In ordinary language, the word 'cause' has a variety of meanings, the most common of which refers to efficient causation, which is the topic of the present article.

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The scientific method is an empirical method for acquiring knowledge through careful observation, rigorous skepticism, hypothesis testing, and experimental validation. Developed from ancient and medieval practices, it acknowledges that cognitive assumptions can distort the interpretation of the observation. The scientific method has characterized science since at least the 17th century. Scientific inquiry includes creating a testable hypothesis through inductive reasoning, testing it through experiments and statistical analysis, and adjusting or discarding the hypothesis based on the results.
Although procedures vary across fields, the underlying process is often similar. In more detail: the scientific method involves making conjectures (hypothetical explanations), predicting the logical consequences of hypothesis, then carrying out experiments or empirical observations based on those predictions. A hypothesis is a conjecture based on knowledge obtained while seeking answers to the question. Hypotheses can be very specific or broad but must be falsifiable, implying that it is possible to identify a possible outcome of an experiment or observation that conflicts with predictions deduced from the hypothesis; otherwise, the hypothesis cannot be meaningfully tested.
While the scientific method is often presented as a fixed sequence of steps, it actually represents a set of general principles. Not all steps take place in every scientific inquiry (nor to the same degree), and they are not always in the same order. Numerous discoveries have not followed the textbook model of the scientific method, and, in some cases, chance has played a role.
== History ==
The history of the scientific method is different from the history of science itself. The development of rules for scientific reasoning has not been straightforward; the scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of various approaches to establishing scientific knowledge.
Different early expressions of empiricism and the scientific method can be found throughout history, for instance with the ancient Stoics, Aristotle, Epicurus, Alhazen, Avicenna, Al-Biruni, Roger Bacon, and William of Ockham.
In the Scientific Revolution of the 16th and 17th centuries, some of the most important developments were the furthering of empiricism by Francis Bacon and Robert Hooke, the rationalist approach described by René Descartes, and inductivism, which was further brought to particular prominence by scientists such as Isaac Newton and those who followed him. Newton postulated four principles which form the basis of modern science, and refined the scientific method. Experiments were advocated by Francis Bacon and performed by Giambattista della Porta, Johannes Kepler, and Galileo Galilei. There was particular development aided by theoretical works by the skeptic Francisco Sanches, by idealists as well as empiricists John Locke, George Berkeley, and David Hume. C. S. Peirce formulated the hypothetico-deductive model in the 20th century, and the model has undergone significant revision since.
The term scientific method emerged in the 19th century, as a result of significant institutional development of science, and terminologies establishing clear boundaries between science and non-science, such as scientist and pseudoscience. Throughout the 1830s and 1850s, when Baconianism was popular, naturalists like William Whewell, John Herschel, and John Stuart Mill engaged in debates over "induction" and "facts," and were focused on how to generate knowledge. In the late 19th and early 20th centuries, a debate over realism vs. antirealism was conducted as powerful scientific theories extended beyond the realm of the observable.
=== Modern use and critical thought ===
The term scientific method came into popular use in the twentieth century; Dewey's 1910 book, How We Think, inspired popular guidelines. It appeared in dictionaries and science textbooks, although there was little consensus on its meaning. Although there was growth through the middle of the twentieth century, by the 1960s and 1970s numerous influential philosophers of science such as Thomas Kuhn and Paul Feyerabend had questioned the universality of the "scientific method", and largely replaced the notion of science as a homogeneous and universal method with that of it being a heterogeneous and local practice. In particular, Paul Feyerabend, in the 1975 first edition of his book Against Method, argued against there being any universal rules of science; Karl Popper, and Gauch 2003, disagreed with Feyerabend's claim.
Later stances include physicist Lee Smolin's 2013 essay "There Is No Scientific Method", in which he espouses two ethical principles, and historian of science Daniel Thurs' chapter in the 2015 book Newton's Apple and Other Myths about Science, which concluded that the scientific method is a myth or, at best, an idealization. As myths are beliefs, they are subject to the narrative fallacy, as pointed out by Taleb. Philosophers Robert Nola and Howard Sankey, in their 2007 book Theories of Scientific Method, said that debates over the scientific method continue, and argued that Feyerabend, despite the title of Against Method, accepted certain rules of method and attempted to justify those rules with a meta methodology.
Staddon (2017) argues it is a mistake to try following rules in the absence of an algorithmic scientific method; in that case, "science is best understood through examples". But algorithmic methods, such as disproof of existing theory by experiment have been used since Alhacen (1027) and his Book of Optics, and Galileo (1638) and his Two New Sciences, and The Assayer, which still stand as scientific method.
== Elements of inquiry ==
=== Overview ===

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The scientific method is the process by which science is carried out. As in other areas of inquiry, science (through the scientific method) can build on previous knowledge, and unify understanding of its studied topics over time. Historically, the development of the scientific method was critical to the Scientific Revolution.
The overall process involves making conjectures (hypotheses), predicting their logical consequences, then carrying out experiments based on those predictions to determine whether the original conjecture was correct. However, there are difficulties in a formulaic statement of method. The scientific method represents general principles rather than a fixed sequence, not all steps occur in every inquiry, nor always in the same order. It requires intelligence, imagination, and creativity rather than rigid adherence to procedure.
==== Factors of scientific inquiry ====
There are different ways of outlining the basic method used for scientific inquiry. The scientific community and philosophers of science generally agree on the following classification of method components. These methodological elements and organization of procedures tend to be more characteristic of experimental sciences than social sciences. Nonetheless, the cycle of formulating hypotheses, testing and analyzing the results, and formulating new hypotheses, will resemble the cycle described below.The scientific method is an iterative, cyclical process through which information is continually revised. It is generally recognized to develop advances in knowledge through the following elements, in varying combinations or contributions:
Characterizations (observations, definitions, and measurements of the subject of inquiry)
Hypotheses (theoretical, hypothetical explanations of observations and measurements of the subject)
Predictions (inductive and deductive reasoning from the hypothesis or theory)
Experiments (tests of all of the above)
Each element of the scientific method is subject to peer review for possible mistakes. These activities do not describe all that scientists do but apply mostly to experimental sciences (e.g., physics, chemistry, biology, and psychology). The elements above are often taught in the educational system as "the scientific method".
The scientific method is not a single recipe: it requires intelligence, imagination, and creativity. In this sense, it is not a mindless set of standards and procedures to follow but is rather an ongoing cycle, constantly developing more useful, accurate, and comprehensive models and methods. For example, when Einstein developed the Special and General Theories of Relativity, he did not in any way refute or discount Newton's Principia. On the contrary, if the astronomically massive, the feather-light, and the extremely fast are removed from Einstein's theories all phenomena Newton could not have observed Newton's equations are what remain. Einstein's theories are expansions and refinements of Newton's theories and, thus, increase confidence in Newton's work.
An iterative, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:
Define a question
Gather information and resources (observe)
Form an explanatory hypothesis
Test the hypothesis by performing an experiment and collecting data in a reproducible manner
Analyze the data
Interpret the data and draw conclusions that serve as a starting point for a new hypothesis
Publish results
Retest (frequently done by other scientists)
The iterative cycle inherent in this step-by-step method goes from point 3 to 6 and back to 3 again.
While this schema outlines a typical hypothesis/testing method, many philosophers, historians, and sociologists of science, including Paul Feyerabend, claim that such descriptions of scientific method have little relation to the ways that science is actually practiced.
=== Characterizations ===
The basic elements of the scientific method are illustrated by the following example (which occurred from 1944 to 1953) from the discovery of the structure of DNA (marked with and indented).
In 1950, it was known that genetic inheritance had a mathematical description, starting with the studies of Gregor Mendel, and that DNA contained genetic information (Oswald Avery's transforming principle). But the mechanism of storing genetic information (i.e., genes) in DNA was unclear. Researchers in Bragg's laboratory at Cambridge University made X-ray diffraction pictures of various molecules, starting with crystals of salt, and proceeding to more complicated substances. Using clues painstakingly assembled over decades, beginning with its chemical composition, it was determined that it should be possible to characterize the physical structure of DNA, and the X-ray images would be the vehicle.
The scientific method depends upon increasingly sophisticated characterizations of the subjects of investigation. (The subjects can also be called unsolved problems or the unknowns.) For example, Benjamin Franklin conjectured, correctly, that St. Elmo's fire was electrical in nature, but it has taken a long series of experiments and theoretical changes to establish this. While seeking the pertinent properties of the subjects, careful thought may also entail some definitions and observations; these observations often demand careful measurements and/or counting can take the form of expansive empirical research.
A scientific question can refer to the explanation of a specific observation, as in "Why is the sky blue?" but can also be open-ended, as in "How can I design a drug to cure this particular disease?" This stage frequently involves finding and evaluating evidence from previous experiments, personal scientific observations or assertions, as well as the work of other scientists. If the answer is already known, a different question that builds on the evidence can be posed. When applying the scientific method to research, determining a good question can be very difficult and it will affect the outcome of the investigation.
The systematic, careful collection of measurements or counts of relevant quantities is often the critical difference between pseudo-sciences, such as alchemy, and science, such as chemistry or biology. Scientific measurements are usually tabulated, graphed, or mapped, and statistical manipulations, such as correlation and regression, performed on them. The measurements might be made in a controlled setting, such as a laboratory, or made on more or less inaccessible or unmanipulatable objects such as stars or human populations. The measurements often require specialized scientific instruments such as thermometers, spectroscopes, particle accelerators, or voltmeters, and the progress of a scientific field is usually intimately tied to their invention and improvement.

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Scientific pluralism is a position within the philosophy of science that rejects various proposed unities of scientific method and subject matter. Scientific pluralists hold that science is not unified in one or more of the following ways: the metaphysics of its subject matter, the epistemology of scientific knowledge, or the research methods and models that should be used. Some pluralists believe that pluralism is necessary due to the nature of science. Others say that since scientific disciplines already vary in practice, there is no reason to believe this variation is wrong until a specific unification is empirically proven. Finally, some hold that pluralism should be allowed for normative reasons, even if unity were possible in theory.
=== Unificationism ===
Unificationism, in science, was a central tenet of logical positivism. Different logical positivists construed this doctrine in several different ways, e.g. as a reductionist thesis, that the objects investigated by the special sciences reduce to the objects of a common, putatively more basic domain of science, usually thought to be physics; as the thesis that all theories and results of the various sciences can or ought to be expressed in a common language or "universal slang"; or as the thesis that all the special sciences share a common scientific method.
Development of the idea has been troubled by accelerated advancement in technology that has opened up many new ways to look at the world.
The fact that the standards of scientific success shift with time does not only make the philosophy of science difficult; it also raises problems for the public understanding of science. We do not have a fixed scientific method to rally around and defend.
=== Epistemological anarchism ===
Paul Feyerabend examined the history of science, and was led to deny that science is genuinely a methodological process. In his 1975 book Against Method he argued that no description of scientific method could possibly be broad enough to include all the approaches and methods used by scientists, and that there are no useful and exception-free methodological rules governing the progress of science. In essence, he said that for any specific method or norm of science, one can find a historic episode where violating it has contributed to the progress of science. He jokingly suggested that, if believers in the scientific method wish to express a single universally valid rule, it should be 'anything goes'. As has been argued before him however, this is uneconomic; problem solvers, and researchers are to be prudent with their resources during their inquiry.
A more general inference against formalised method has been found through research involving interviews with scientists regarding their conception of method. This research indicated that scientists frequently encounter difficulty in determining whether the available evidence supports their hypotheses. This reveals that there are no straightforward mappings between overarching methodological concepts and precise strategies to direct the conduct of research.
=== Education ===
In science education, the idea of a general and universal scientific method has been notably influential, and numerous studies (in the US) have shown that this framing of method often forms part of both students' and teachers' conception of science. This convention of traditional education has been argued against by scientists, as there is a consensus that educations' sequential elements and unified view of scientific method do not reflect how scientists actually work. Major organizations of scientists such as the American Association for the Advancement of Science (AAAS) consider the sciences to be a part of the liberal arts traditions of learning and proper understating of science includes understanding of philosophy and history, not just science in isolation.
How the sciences make knowledge has been taught in the context of "the" scientific method (singular) since the early 20th century. Various systems of education, including but not limited to the US, have taught the method of science as a process or procedure, structured as a definitive series of steps: observation, hypothesis, prediction, experiment.
This version of the method of science has been a long-established standard in primary and secondary education, as well as the biomedical sciences. It has long been held to be an inaccurate idealisation of how some scientific inquiries are structured.
Traditional science education faced criticism for presenting an oversimplified, singular methodology that overemphasized experimentation, ignored social context, and suggested automatic knowledge generation through procedural steps.
The scientific method no longer features in the standards for US education of 2013 (NGSS) that replaced those of 1996 (NRC). They, too, influenced international science education, and the standards measured for have shifted since from the singular hypothesis-testing method to a broader conception of scientific methods. These scientific methods, which are rooted in scientific practices and not epistemology, are described as the 3 dimensions of scientific and engineering practices, crosscutting concepts (interdisciplinary ideas), and disciplinary core ideas.
The scientific method, as a result of simplified and universal explanations, is often held to have reached a kind of mythological status; as a tool for communication or, at best, an idealisation. Education's approach was heavily influenced by John Dewey's, How We Think (1910). Van der Ploeg (2016) indicated that Dewey's views on education had long been used to further an idea of citizen education removed from "sound education", claiming that references to Dewey in such arguments were undue interpretations (of Dewey).
=== Sociology of knowledge ===
The sociology of knowledge is a concept in the discussion around scientific method, claiming the underlying method of science to be sociological. King explains that sociology distinguishes here between the system of ideas that govern the sciences through an inner logic, and the social system in which those ideas arise.

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==== Thought collectives ====
A perhaps accessible lead into what is claimed is Fleck's thought, echoed in Kuhn's concept of normal science. According to Fleck, scientists' work is based on a thought-style, that cannot be rationally reconstructed. It gets instilled through the experience of learning, and science is then advanced based on a tradition of shared assumptions held by what he called thought collectives. Fleck also claims this phenomenon to be largely invisible to members of the group.
Comparably, following the field research in an academic scientific laboratory by Latour and Woolgar, Karin Knorr Cetina has conducted a comparative study of two scientific fields (namely high energy physics and molecular biology) to conclude that the epistemic practices and reasonings within both scientific communities are different enough to introduce the concept of "epistemic cultures", in contradiction with the idea that a so-called "scientific method" is unique and a unifying concept.
==== Situated cognition and relativism ====
On the idea of Fleck's thought collectives sociologists built the concept of situated cognition: that the perspective of the researcher fundamentally affects their work; and, too, more radical views.
Norwood Russell Hanson, alongside Thomas Kuhn and Paul Feyerabend, extensively explored the theory-laden nature of observation in science. Hanson introduced the concept in 1958, emphasizing that observation is influenced by the observer's conceptual framework. He used the concept of gestalt to show how preconceptions can affect both observation and description, and illustrated this with examples like the initial rejection of Golgi bodies as an artefact of staining technique, and the differing interpretations of the same sunrise by Tycho Brahe and Johannes Kepler. Intersubjectivity led to different conclusions.
Kuhn and Feyerabend acknowledged Hanson's pioneering work, although Feyerabend's views on methodological pluralism were more radical. Criticisms like those from Kuhn and Feyerabend prompted discussions leading to the development of the strong programme, a sociological approach that seeks to explain scientific knowledge without recourse to the truth or validity of scientific theories. It examines how scientific beliefs are shaped by social factors such as power, ideology, and interests.
The postmodernist critiques of science have themselves been the subject of intense controversy. This ongoing debate, known as the science wars, is the result of conflicting values and assumptions between postmodernist and realist perspectives. Postmodernists argue that scientific knowledge is merely a discourse, devoid of any claim to fundamental truth. In contrast, realists within the scientific community maintain that science uncovers real and fundamental truths about reality. Many books have been written by scientists which take on this problem and challenge the assertions of the postmodernists while defending science as a legitimate way of deriving truth.
== Limits of method ==
=== Role of chance in discovery ===
Somewhere between 33% and 50% of all scientific discoveries are estimated to have been stumbled upon, rather than sought out. This may explain why scientists so often express that they were lucky. Scientists themselves in the 19th and 20th century acknowledged the role of fortunate luck or serendipity in discoveries. Louis Pasteur is credited with the famous saying that "Luck favours the prepared mind", but some psychologists have begun to study what it means to be 'prepared for luck' in the scientific context. Research is showing that scientists are taught various heuristics that tend to harness chance and the unexpected. This is what Nassim Nicholas Taleb calls "Anti-fragility"; while some systems of investigation are fragile in the face of human error, human bias, and randomness, the scientific method is more than resistant or tough it actually benefits from such randomness in many ways (it is anti-fragile). Taleb believes that the more anti-fragile the system, the more it will flourish in the real world.
Psychologist Kevin Dunbar says the process of discovery often starts with researchers finding bugs in their experiments. These unexpected results lead researchers to try to fix what they think is an error in their method. Eventually, the researcher decides the error is too persistent and systematic to be a coincidence. The highly controlled, cautious, and curious aspects of the scientific method are thus what make it well suited for identifying such persistent systematic errors. At this point, the researcher will begin to think of theoretical explanations for the error, often seeking the help of colleagues across different domains of expertise.
=== Relationship with statistics ===
When the scientific method employs statistics as a key part of its arsenal, there are mathematical and practical issues that can have a deleterious effect on the reliability of the output of scientific methods. This is described in a popular 2005 scientific paper "Why Most Published Research Findings Are False" by John Ioannidis, which is considered foundational to the field of metascience. Much research in metascience seeks to identify poor use of statistics and improve its use, an example being the misuse of p-values.
The points raised are both statistical and economical. Statistically, research findings are less likely to be true when studies are small and when there is significant flexibility in study design, definitions, outcomes, and analytical approaches. Economically, the reliability of findings decreases in fields with greater financial interests, biases, and a high level of competition among research teams. As a result, most research findings are considered false across various designs and scientific fields, particularly in modern biomedical research, which often operates in areas with very low pre- and post-study probabilities of yielding true findings. Nevertheless, despite these challenges, most new discoveries will continue to arise from hypothesis-generating research that begins with low or very low pre-study odds. This suggests that expanding the frontiers of knowledge will depend on investigating areas outside the mainstream, where the chances of success may initially appear slim.

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=== Science of complex systems ===
Science applied to complex systems can involve elements such as transdisciplinarity, systems theory, control theory, and scientific modelling.
In general, the scientific method may be difficult to apply stringently to diverse, interconnected systems and large data sets. In particular, practices used within Big data, such as predictive analytics, may be considered to be at odds with the scientific method, as some of the data may have been stripped of the parameters which might be material in alternative hypotheses for an explanation; thus the stripped data would only serve to support the null hypothesis in the predictive analytics application. Fleck (1979), pp. 3850 notes "a scientific discovery remains incomplete without considerations of the social practices that condition it".
== Relationship with mathematics ==
Science is the process of gathering, comparing, and evaluating proposed models against observables. A model can be a simulation, mathematical or chemical formula, or set of proposed steps. Science is like mathematics in that researchers in both disciplines try to distinguish what is known from what is unknown at each stage of discovery. Models, in both science and mathematics, need to be internally consistent and also ought to be falsifiable (capable of disproof). In mathematics, a statement need not yet be proved; at such a stage, that statement would be called a conjecture.
Mathematical work and scientific work can inspire each other. For example, the technical concept of time arose in science, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture has been proved using time as a mathematical concept in which objects can flow (see Ricci flow).
Nevertheless, the connection between mathematics and reality (and so science to the extent it describes reality) remains obscure. Eugene Wigner's paper, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", is a very well-known account of the issue from a Nobel Prize-winning physicist. In fact, some observers (including some well-known mathematicians such as Gregory Chaitin, and others such as Lakoff and Núñez) have suggested that mathematics is the result of practitioner bias and human limitation (including cultural ones), somewhat like the post-modernist view of science.
George Pólya's work on problem solving, the construction of mathematical proofs, and heuristic show that the mathematical method and the scientific method differ in detail, while nevertheless resembling each other in using iterative or recursive steps.
In Pólya's view, understanding involves restating unfamiliar definitions in your own words, resorting to geometrical figures, and questioning what we know and do not know already; analysis, which Pólya takes from Pappus, involves free and heuristic construction of plausible arguments, working backward from the goal, and devising a plan for constructing the proof; synthesis is the strict Euclidean exposition of step-by-step details of the proof; review involves reconsidering and re-examining the result and the path taken to it.
Building on Pólya's work, Imre Lakatos argued that mathematicians actually use contradiction, criticism, and revision as principles for improving their work. In like manner to science, where truth is sought, but certainty is not found, in Proofs and Refutations, what Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that, in non-axiomatic mathematics, we should not think that a theorem is ultimately true, only that no counterexample has yet been found. Once a counterexample, i.e. an entity contradicting/not explained by the theorem is found, we adjust the theorem, possibly extending the domain of its validity. This is a continuous way our knowledge accumulates, through the logic and process of proofs and refutations. (However, if axioms are given for a branch of mathematics, this creates a logical system —Wittgenstein 1921 Tractatus Logico-Philosophicus 5.13; Lakatos claimed that proofs from such a system were tautological, i.e. internally logically true, by rewriting forms, as shown by Poincaré, who demonstrated the technique of transforming tautologically true forms (viz. the Euler characteristic) into or out of forms from homology, or more abstractly, from homological algebra.
Lakatos proposed an account of mathematical knowledge based on Polya's idea of heuristics. In Proofs and Refutations, Lakatos gave several basic rules for finding proofs and counterexamples to conjectures. He thought that mathematical 'thought experiments' are a valid way to discover mathematical conjectures and proofs.
Gauss, when asked how he came about his theorems, once replied "durch planmässiges Tattonieren" (through systematic palpable experimentation).
== See also ==
Evidence-based practice Pragmatic methodology
Methodology Study of research methods
Metascience Scientific study of science
Outline of scientific method
Quantitative research All procedures for the numerical representation of empirical facts
Research transparency
Scientific law Statement based on repeated empirical observations that describes some natural phenomenon
Scientific protocol
Testability Ability to examine a theory by experimentation
== Notes ==
=== Notes: Problem-solving via scientific method ===
=== Notes: Philosophical expressions of method ===
== References ==
=== Footnotes ===
=== Sources ===
== Further reading ==
== External links ==
Andersen, Hanne; Hepburn, Brian. "Scientific Method". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174.
Fieser, James; Dowden, Bradley (eds.). "Confirmation and Induction". Internet Encyclopedia of Philosophy. ISSN 2161-0002. OCLC 37741658.
Scientific method at PhilPapers
Scientific method at the Indiana Philosophy Ontology Project
An Introduction to Science: Scientific Thinking and a scientific method Archived 2018-01-01 at the Wayback Machine by Steven D. Schafersman.
Introduction to the scientific method at the University of Rochester
The scientific method from a philosophical perspective
Theory-ladenness by Paul Newall at The Galilean Library
Lecture on Scientific Method by Greg Anderson (archived 28 April 2006)
Using the scientific method for designing science fair projects
Scientific Methods an online book by Richard D. Jarrard
Richard Feynman on the Key to Science (one minute, three seconds), from the Cornell Lectures.
Lectures on the Scientific Method by Nick Josh Karean, Kevin Padian, Michael Shermer and Richard Dawkins (archived 11 May 2013).
"How Do We Know What Is True?" (animated video; 2:52)

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I am not accustomed to saying anything with certainty after only one or two observations.
==== Definition ====
The scientific definition of a term sometimes differs substantially from its natural language usage. For example, mass and weight overlap in meaning in common discourse, but have distinct meanings in mechanics. Scientific quantities are often characterized by their units of measure which can later be described in terms of conventional physical units when communicating the work.
New theories are sometimes developed after realizing certain terms have not previously been sufficiently clearly defined. For example, Albert Einstein's first paper on relativity begins by defining simultaneity and the means for determining length. These ideas were skipped over by Isaac Newton with, "I do not define time, space, place and motion, as being well known to all." Einstein's paper then demonstrates that they (viz., absolute time and length independent of motion) were approximations. Francis Crick cautions us that when characterizing a subject, however, it can be premature to define something when it remains ill-understood. In Crick's study of consciousness, he actually found it easier to study awareness in the visual system, rather than to study free will, for example. His cautionary example was the gene; the gene was much more poorly understood before Watson and Crick's pioneering discovery of the structure of DNA; it would have been counterproductive to spend much time on the definition of the gene, before them.
=== Hypothesis development ===
Linus Pauling proposed that DNA might be a triple helix. This hypothesis was also considered by Francis Crick and James D. Watson but discarded. When Watson and Crick learned of Pauling's hypothesis, they understood from existing data that Pauling was wrong. and that Pauling would soon admit his difficulties with that structure.
A hypothesis is a suggested explanation of a phenomenon, or alternately a reasoned proposal suggesting a possible correlation between or among a set of phenomena. Normally, hypotheses have the form of a mathematical model. Sometimes, but not always, they can also be formulated as existential statements, stating that some particular instance of the phenomenon being studied has some characteristic and causal explanations, which have the general form of universal statements, stating that every instance of the phenomenon has a particular characteristic.
Scientists are free to use whatever resources they have their own creativity, ideas from other fields, inductive reasoning, Bayesian inference, and so on to imagine possible explanations for a phenomenon under study. Albert Einstein once observed that "there is no logical bridge between phenomena and their theoretical principles." Charles Sanders Peirce, borrowing a page from Aristotle (Prior Analytics, 2.25) described the incipient stages of inquiry, instigated by the "irritation of doubt" to venture a plausible guess, as abductive reasoning. The history of science is filled with stories of scientists claiming a "flash of inspiration", or a hunch, which then motivated them to look for evidence to support or refute their idea. Michael Polanyi made such creativity the centerpiece of his discussion of methodology.
William Glen observes that
the success of a hypothesis, or its service to science, lies not simply in its perceived "truth", or power to displace, subsume or reduce a predecessor idea, but perhaps more in its ability to stimulate the research that will illuminate ... bald suppositions and areas of vagueness.
In general, scientists tend to look for theories that are "elegant" or "beautiful". Scientists often use these terms to refer to a theory that is following the known facts but is nevertheless relatively simple and easy to handle. Occam's Razor serves as a rule of thumb for choosing the most desirable amongst a group of equally explanatory hypotheses.
To minimize the confirmation bias that results from entertaining a single hypothesis, strong inference emphasizes the need for entertaining multiple alternative hypotheses, and avoiding artifacts.
=== Predictions from the hypothesis ===
James D. Watson, Francis Crick, and others hypothesized that DNA had a helical structure. This implied that DNA's X-ray diffraction pattern would be 'x shaped'. This prediction followed from the work of Cochran, Crick and Vand (and independently by Stokes). The Cochran-Crick-Vand-Stokes theorem provided a mathematical explanation for the empirical observation that diffraction from helical structures produces x-shaped patterns.
In their first paper, Watson and Crick also noted that the double helix structure they proposed provided a simple mechanism for DNA replication, writing, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material".Any useful hypothesis will enable predictions, by reasoning including deductive reasoning. It might predict the outcome of an experiment in a laboratory setting or the observation of a phenomenon in nature. The prediction can also be statistical and deal only with probabilities.
It is essential that the outcome of testing such a prediction be currently unknown. Only in this case does a successful outcome increase the probability that the hypothesis is true. If the outcome is already known, it is called a consequence and should have already been considered while formulating the hypothesis.
If the predictions are not accessible by observation or experience, the hypothesis is not yet testable and so will remain to that extent unscientific in a strict sense. A new technology or theory might make the necessary experiments feasible. For example, while a hypothesis on the existence of other intelligent species may be convincing with scientifically based speculation, no known experiment can test this hypothesis. Therefore, science itself can have little to say about the possibility. In the future, a new technique may allow for an experimental test and the speculation would then become part of accepted science.
For example, Einstein's theory of general relativity makes several specific predictions about the observable structure of spacetime, such as that light bends in a gravitational field, and that the amount of bending depends in a precise way on the strength of that gravitational field. Arthur Eddington's observations made during a 1919 solar eclipse supported General Relativity rather than Newtonian gravitation.
=== Experiments ===

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Watson and Crick showed an initial (and incorrect) proposal for the structure of DNA to a team from King's College London Rosalind Franklin, Maurice Wilkins, and Raymond Gosling. Franklin immediately spotted the flaws which concerned the water content. Later Watson saw Franklin's photo 51, a detailed X-ray diffraction image, which showed an X-shape and was able to confirm the structure was helical.
Once predictions are made, they can be sought by experiments. If the test results contradict the predictions, the hypotheses which entailed them are called into question and become less tenable. Sometimes the experiments are conducted incorrectly or are not very well designed when compared to a crucial experiment. If the experimental results confirm the predictions, then the hypotheses are considered more likely to be correct, but might still be wrong and continue to be subject to further testing. The experimental control is a technique for dealing with observational error. This technique uses the contrast between multiple samples, or observations, or populations, under differing conditions, to see what varies or what remains the same. We vary the conditions for the acts of measurement, to help isolate what has changed. Mill's canons can then help us figure out what the important factor is. Factor analysis is one technique for discovering the important factor in an effect.
Depending on the predictions, the experiments can have different shapes. It could be a classical experiment in a laboratory setting, a double-blind study or an archaeological excavation. Even taking a plane from New York to Paris is an experiment that tests the aerodynamical hypotheses used for constructing the plane.
These institutions thereby reduce the research function to a cost/benefit, which is expressed as money, and the time and attention of the researchers to be expended, in exchange for a report to their constituents. Current large instruments, such as CERN's Large Hadron Collider (LHC), or LIGO, or the National Ignition Facility (NIF), or the International Space Station (ISS), or the James Webb Space Telescope (JWST), entail expected costs of billions of dollars, and timeframes extending over decades. These kinds of institutions affect public policy, on a national or even international basis, and the researchers would require shared access to such machines and their adjunct infrastructure.
Scientists assume an attitude of openness and accountability on the part of those experimenting. Detailed record-keeping is essential, to aid in recording and reporting on the experimental results, and supports the effectiveness and integrity of the procedure. They will also assist in reproducing the experimental results, likely by others. Traces of this approach can be seen in the work of Hipparchus (190120 BCE), when determining a value for the precession of the Earth, while controlled experiments can be seen in the works of al-Battani (853929 CE) and Alhazen (9651039 CE).
=== Communication and iteration ===
Watson and Crick then produced their model, using this information along with the previously known information about DNA's composition, especially Chargaff's rules of base pairing. After considerable fruitless experimentation, being discouraged by their superior from continuing, and numerous false starts, Watson and Crick were able to infer the essential structure of DNA by concrete modeling of the physical shapes of the nucleotides which comprise it. They were guided by the bond lengths which had been deduced by Linus Pauling and by Rosalind Franklin's X-ray diffraction images.
The scientific method is iterative. At any stage, it is possible to refine its accuracy and precision, so that some consideration will lead the scientist to repeat an earlier part of the process. Failure to develop an interesting hypothesis may lead a scientist to re-define the subject under consideration. Failure of a hypothesis to produce interesting and testable predictions may lead to reconsideration of the hypothesis or of the definition of the subject. Failure of an experiment to produce interesting results may lead a scientist to reconsider the experimental method, the hypothesis, or the definition of the subject.
This manner of iteration can span decades and sometimes centuries. Published papers can be built upon. For example: By 1027, Alhazen, based on his measurements of the refraction of light, was able to deduce that outer space was less dense than air, that is: "the body of the heavens is rarer than the body of air". In 1079 Ibn Mu'adh's Treatise On Twilight was able to infer that Earth's atmosphere was 50 miles thick, based on atmospheric refraction of the sun's rays.
This is why the scientific method is often represented as circular new information leads to new characterisations, and the cycle of science continues. Measurements collected can be archived, passed onwards and used by others. Other scientists may start their own research and enter the process at any stage. They might adopt the characterization and formulate their own hypothesis, or they might adopt the hypothesis and deduce their own predictions. Often the experiment is not done by the person who made the prediction, and the characterization is based on experiments done by someone else. Published results of experiments can also serve as a hypothesis predicting their own reproducibility.
=== Confirmation ===

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Science is a social enterprise, and scientific work tends to be accepted by the scientific community when it has been confirmed. Crucially, experimental and theoretical results must be reproduced by others within the scientific community. Researchers have given their lives for this vision; Georg Wilhelm Richmann was killed by ball lightning (1753) when attempting to replicate the 1752 kite-flying experiment of Benjamin Franklin.
If an experiment cannot be repeated to produce the same results, this implies that the original results might have been in error. As a result, it is common for a single experiment to be performed multiple times, especially when there are uncontrolled variables or other indications of experimental error. For significant or surprising results, other scientists may also attempt to replicate the results for themselves, especially if those results would be important to their own work. Replication has become a contentious issue in social and biomedical science where treatments are administered to groups of individuals. Typically an experimental group gets the treatment, such as a drug, and the control group gets a placebo. John Ioannidis in 2005 pointed out that the method being used has led to many findings that cannot be replicated.
Peer review—anonymous expert evaluation of research—assesses experimental soundness rather than certifying correctness. Some journals request that the experimenter provide lists of possible peer reviewers, especially if the field is highly specialized. Specialists review methodology and design; if approved (sometimes requiring additional experiments), the prestige of the journal where the work is published indicates perceived quality.
Scientists typically are careful in recording their data, a requirement promoted by Ludwik Fleck (18961961) and others. Though not typically required, they might be requested to supply this data to other scientists who wish to replicate their original results (or parts of their original results), extending to the sharing of any experimental samples that may be difficult to obtain. To protect against bad science and fraudulent data, government research-granting agencies such as the National Science Foundation, and science journals, including Nature and Science, have a policy that researchers must archive their data and methods so that other researchers can test the data and methods and build on the research that has gone before. Scientific data archiving can be done at several national archives in the U.S. or the World Data Center.
== Foundational principles ==
=== Honesty, openness, and falsifiability ===
The unfettered principles of science are to strive for accuracy and the creed of honesty; openness already being a matter of degrees. Openness is restricted by the general rigour of scepticism. And of course the matter of non-science.
Smolin, in 2013, espoused ethical principles rather than giving any potentially limited definition of the rules of inquiry. His ideas stand in the context of the scale of datadriven and big science, which has seen increased importance of honesty and consequently reproducibility. His thought is that science is a community effort by those who have accreditation and are working within the community. He also warns against overzealous parsimony.
Popper previously took ethical principles even further, going as far as to ascribe value to theories only if they were falsifiable. Popper used the falsifiability criterion to demarcate a scientific theory from a theory like astrology: both "explain" observations, but the scientific theory takes the risk of making predictions that decide whether it is right or wrong:
"Those among us who are unwilling to expose their ideas to the hazard of refutation do not take part in the game of science."
=== Theory's interactions with observation ===
Science has limits. Those limits are usually deemed to be answers to questions that aren't in science's domain, such as faith. Science has other limits as well, as it seeks to make true statements about reality. The nature of truth and the discussion on how scientific statements relate to reality is best left to the article on the philosophy of science here. More immediately topical limitations show themselves in the observation of reality.
It is the natural limitations of scientific inquiry that there is no pure observation as theory is required to interpret empirical data, and observation is therefore influenced by the observer's conceptual framework. As science is an unfinished project, this does lead to difficulties. Namely, that false conclusions are drawn, because of limited information.
An example here are the experiments of Kepler and Brahe, used by Hanson to illustrate the concept. Despite observing the same sunrise the two scientists came to different conclusions—their intersubjectivity leading to differing conclusions. Johannes Kepler used Tycho Brahe's method of observation, which was to project the image of the Sun on a piece of paper through a pinhole aperture, instead of looking directly at the Sun. He disagreed with Brahe's conclusion that total eclipses of the Sun were impossible because, contrary to Brahe, he knew that there were historical accounts of total eclipses. Instead, he deduced that the images taken would become more accurate, the larger the aperture—this fact is now fundamental for optical system design. Another historic example here is the discovery of Neptune, credited as being found via mathematics because previous observers didn't know what they were looking at.

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=== Empiricism, rationalism, and more pragmatic views ===
Scientific endeavour can be characterised as the pursuit of truths about the natural world or as the elimination of doubt about the same. The former is the direct construction of explanations from empirical data and logic, the latter the reduction of potential explanations. It was established above how the interpretation of empirical data is theory-laden, so neither approach is trivial.
The ubiquitous element in the scientific method is empiricism, which holds that knowledge is created by a process involving observation; scientific theories generalize observations. This is in opposition to stringent forms of rationalism, which holds that knowledge is created by the human intellect; later clarified by Popper to be built on prior theory. The scientific method embodies the position that reason alone cannot solve a particular scientific problem; it unequivocally refutes claims that revelation, political or religious dogma, appeals to tradition, commonly held beliefs, common sense, or currently held theories pose the only possible means of demonstrating truth.
In 1877, C. S. Peirce characterized inquiry in general not as the pursuit of truth per se but as the struggle to move from irritating, inhibitory doubts born of surprises, disagreements, and the like, and to reach a secure belief, the belief being that on which one is prepared to act. His pragmatic views framed scientific inquiry as part of a broader spectrum and as spurred, like inquiry generally, by actual doubt, not mere verbal or "hyperbolic doubt", which he held to be fruitless. This "hyperbolic doubt" Peirce argues against here is of course just another name for Cartesian doubt associated with René Descartes. It is a methodological route to certain knowledge by identifying what can't be doubted.
A strong formulation of the scientific method is not always aligned with a form of empiricism in which the empirical data is put forward in the form of experience or other abstracted forms of knowledge as in current scientific practice the use of scientific modelling and reliance on abstract typologies and theories is normally accepted. In 2010, Hawking suggested that physics' models of reality should simply be accepted where they prove to make useful predictions. He calls the concept model-dependent realism.
== Rationality ==
The following section will first explore beliefs and biases, and then get to the rational reasoning most associated with the sciences.
=== Beliefs and biases ===
Scientific methodology often directs that hypotheses be tested in controlled conditions wherever possible. This is frequently possible in certain areas, such as in the biological sciences, and more difficult in other areas, such as in astronomy.
The practice of experimental control and reproducibility can have the effect of diminishing the potentially harmful effects of circumstance, and to a degree, personal bias. For example, pre-existing beliefs can alter the interpretation of results, as in confirmation bias; this is a heuristic that leads a person with a particular belief to see things as reinforcing their belief, even if another observer might disagree (in other words, people tend to observe what they expect to observe).
[T]he action of thought is excited by the irritation of doubt, and ceases when belief is attained.
A historical example is the belief that the legs of a galloping horse are splayed at the point when none of the horse's legs touch the ground, to the point of this image being included in paintings by its supporters. However, the first stop-action pictures of a horse's gallop by Eadweard Muybridge showed this to be false, and that the legs are instead gathered together.
Another important human bias that plays a role is a preference for new, surprising statements (see Appeal to novelty), which can result in a search for evidence that the new is true. Poorly attested beliefs can be believed and acted upon via a less rigorous heuristic.
Goldhaber and Nieto published in 2010 the observation that if theoretical structures with "many closely neighboring subjects are described by connecting theoretical concepts, then the theoretical structure acquires a robustness which makes it increasingly hard though certainly never impossible to overturn". When a narrative is constructed its elements become easier to believe.
Fleck (1979), p. 27 notes "Words and ideas are originally phonetic and mental equivalences of the experiences coinciding with them. ... Such proto-ideas are at first always too broad and insufficiently specialized. ... Once a structurally complete and closed system of opinions consisting of many details and relations has been formed, it offers enduring resistance to anything that contradicts it". Sometimes, these relations have their elements assumed a priori, or contain some other logical or methodological flaw in the process that ultimately produced them. Donald M. MacKay has analyzed these elements in terms of limits to the accuracy of measurement and has related them to instrumental elements in a category of measurement.
=== Deductive and inductive reasoning ===
The idea of there being two opposed justifications for truth has shown up throughout the history of scientific method as analysis versus synthesis, non-ampliative/ampliative, or even confirmation and verification. (And there are other kinds of reasoning.) One to use what is observed to build towards fundamental truths and the other to derive from those fundamental truths more specific principles.
Deductive reasoning derives specific conclusions from established general principles—if the premises are true, the conclusion must be true. Inductive reasoning builds general principles from observations—conclusions are probable but not guaranteed. Scientific inquiry employs both: induction generates hypotheses from observations; deduction predicts testable consequences. This process requires stringent scepticism regarding observed phenomena, because cognitive assumptions can distort the interpretation of initial perceptions.

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An example for how inductive and deductive reasoning works can be found in the history of gravitational theory. It took thousands of years of measurements, from the Chaldean, Indian, Persian, Greek, Arabic, and European astronomers, to fully record the motion of planet Earth. Kepler(and others) were then able to build their early theories by generalizing the collected data inductively, and Newton was able to unify prior theory and measurements into the consequences of his laws of motion in 1727.
Another common example of inductive reasoning is the observation of a counterexample to current theory inducing the need for new ideas. Le Verrier in 1859 pointed out problems with the perihelion of Mercury that showed Newton's theory to be at least incomplete. The observed difference of Mercury's precession between Newtonian theory and observation was one of the things that occurred to Einstein as a possible early test of his theory of relativity. His relativistic calculations matched observation much more closely than Newtonian theory did. Though, today's Standard Model of physics suggests that we still do not know at least some of the concepts surrounding Einstein's theory, it holds to this day and is being built on deductively.
A theory being assumed as true and subsequently built on is a common example of deductive reasoning. Theory building on Einstein's achievement can simply state that 'we have shown that this case fulfils the conditions under which general/special relativity applies, therefore its conclusions apply also'. If it was properly shown that 'this case' fulfils the conditions, the conclusion follows. An extension of this is the assumption of a solution to an open problem. This weaker kind of deductive reasoning will get used in current research, when multiple scientists or even teams of researchers are all gradually solving specific cases in working towards proving a larger theory. This often sees hypotheses being revised again and again as new proof emerges.
This way of presenting inductive and deductive reasoning shows part of why science is often presented as being a cycle of iteration. It is important to keep in mind that that cycle's foundations lie in reasoning, and not wholly in the following of procedure.
=== Certainty, probabilities, and statistical inference ===
Claims of scientific truth can be opposed in three ways: by falsifying them, by questioning their certainty, or by asserting the claim itself to be incoherent. Incoherence, here, means internal errors in logic, like stating opposites to be true; falsification is what Popper would have called the honest work of conjecture and refutation — certainty, perhaps, is where difficulties in telling truths from non-truths arise most easily.
Scientific measurements include uncertainty estimates, calculated through repeated measurements, error propagation from underlying quantities, or sampling limitations. uncertainty. Counts of things may represent a sample of desired quantities, with an uncertainty that depends upon the sampling method used and the number of samples taken.
In the case of measurement imprecision, there will simply be a 'probable deviation' expressing itself in a study's conclusions. Statistics are different. Inductive statistical generalisation will take sample data and extrapolate more general conclusions, which has to be justified — and scrutinised. It can even be said that statistical models are only ever useful, but never a complete representation of circumstances.
In statistical analysis, expected and unexpected bias is a large factor. Research questions, the collection of data, or the interpretation of results, all are subject to larger amounts of scrutiny than in comfortably logical environments. Statistical models go through a process for validation, for which one could even say that awareness of potential biases is more important than the hard logic; errors in logic are easier to find in peer review, after all. More general, claims to rational knowledge, and especially statistics, have to be put into their appropriate context. Simple statements such as '9 out of 10 doctors recommend' are therefore of unknown quality because they do not justify their methodology.
Lack of familiarity with statistical methodologies can result in erroneous conclusions. Foregoing the easy example, multiple probabilities interacting is where, for example medical professionals, have shown a lack of proper understanding. Bayes' theorem is the mathematical principle lining out how standing probabilities are adjusted given new information. The boy or girl paradox is a common example. In knowledge representation, Bayesian estimation of mutual information between random variables is a way to measure dependence, independence, or interdependence of the information under scrutiny.
Beyond commonly associated survey methodology of field research, the concept together with probabilistic reasoning is used to advance fields of science where research objects have no definitive states of being. For example, in statistical mechanics.
== Methods of inquiry ==

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=== Hypothetico-deductive method ===
The hypothetico-deductive model, or hypothesis-testing method, or "traditional" scientific method is, as the name implies, based on the formation of hypotheses and their testing via deductive reasoning. A hypothesis stating implications, often called predictions, that are falsifiable via experiment is of central importance here, as not the hypothesis but its implications are what is tested. Basically, scientists will look at the hypothetical consequences a (potential) theory holds and prove or disprove those instead of the theory itself. If an experimental test of those hypothetical consequences shows them to be false, it follows logically that the part of the theory that implied them was false also. If they show as true however, it does not prove the theory definitively.
The logic of this testing is what affords this method of inquiry to be reasoned deductively. The formulated hypothesis is assumed to be 'true', and from that 'true' statement implications are inferred. If the following tests show the implications to be false, it follows that the hypothesis was false also. If test show the implications to be true, new insights will be gained. It is important to be aware that a positive test here will at best strongly imply but not definitively prove the tested hypothesis, as deductive inference (A ⇒ B) is not equivalent like that; only (¬B ⇒ ¬A) is valid logic. Their positive outcomes however, as Hempel put it, provide "at least some support, some corroboration or confirmation for it". This is why Popper insisted on fielded hypotheses to be falsifieable, as successful tests imply very little otherwise. As Gillies put it, "successful theories are those that survive elimination through falsification".
Deductive reasoning in this mode of inquiry will sometimes be replaced by abductive reasoning—the search for the most plausible explanation via logical inference. For example, in biology, where general laws are few, as valid deductions rely on solid presuppositions.
=== Inductive method ===
The inductivist approach to deriving scientific truth first rose to prominence with Francis Bacon and particularly with Isaac Newton and those who followed him. After the establishment of the HD-method, it was often put aside as something of a "fishing expedition" though. It is still valid to some degree, but today's inductive method is often far removed from the historic approach—the scale of the data collected lending new effectiveness to the method. It is most-associated with data-mining projects or large-scale observation projects. In both these cases, it is often not at all clear what the results of proposed experiments will be, and thus knowledge will arise after the collection of data through inductive reasoning.
Where the traditional method of inquiry does both, the inductive approach usually formulates only a research question, not a hypothesis. Following the initial question instead, a suitable "high-throughput method" of data-collection is determined, the resulting data processed and 'cleaned up', and conclusions drawn after. "This shift in focus elevates the data to the supreme role of revealing novel insights by themselves".
The advantage the inductive method has over methods formulating a hypothesis that it is essentially free of "a researcher's preconceived notions" regarding their subject. On the other hand, inductive reasoning is always attached to a measure of certainty, as all inductively reasoned conclusions are. This measure of certainty can reach quite high degrees, though. For example, in the determination of large primes, which are used in encryption software.
=== Mathematical modelling ===
Mathematical modelling, or allochthonous reasoning, typically is the formulation of a hypothesis followed by building mathematical constructs that can be tested in place of conducting physical laboratory experiments. This approach has two main factors: simplification/abstraction and secondly a set of correspondence rules. The correspondence rules lay out how the constructed model will relate back to reality-how truth is derived; and the simplifying steps taken in the abstraction of the given system are to reduce factors that do not bear relevance and thereby reduce unexpected errors. These steps can also help the researcher in understanding the important factors of the system, how far parsimony can be taken until the system becomes more and more unchangeable and thereby stable. Parsimony and related principles are further explored below.
Once this translation into mathematics is complete, the resulting model, in place of the corresponding system, can be analysed through purely mathematical and computational means. The results of this analysis are of course also purely mathematical in nature and get translated back to the system as it exists in reality via the previously determined correspondence rules—iteration following review and interpretation of the findings. The way such models are reasoned will often be mathematically deductive—but they don't have to be. An example here are Monte-Carlo simulations. These generate empirical data "arbitrarily", and, while they may not be able to reveal universal principles, they can nevertheless be useful.

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== Scientific inquiry ==
Scientific inquiry generally aims to obtain knowledge in the form of testable explanations that scientists can use to predict the results of future experiments. This allows scientists to gain a better understanding of the topic under study, and later to use that understanding to intervene in its causal mechanisms (such as to cure disease). The better an explanation is at making predictions, the more useful it frequently can be, and the more likely it will continue to explain a body of evidence better than its alternatives. The most successful explanations those that explain and make accurate predictions in a wide range of circumstances are often called scientific theories.
Most experimental results do not produce large changes in human understanding; improvements in theoretical scientific understanding typically result from a gradual process of development over time, sometimes across different domains of science. Scientific models vary in the extent to which they have been experimentally tested and for how long, and in their acceptance in the scientific community. In general, explanations become accepted over time as evidence accumulates on a given topic, and the explanation in question proves more powerful than its alternatives at explaining the evidence. Often subsequent researchers re-formulate the explanations over time, or combined explanations to produce new explanations.
=== Properties of scientific inquiry ===
Scientific knowledge is closely tied to empirical findings and can remain subject to falsification if new experimental observations are incompatible with what is found. That is, no theory can ever be considered final since new problematic evidence might be discovered. If such evidence is found, a new theory may be proposed, or (more commonly) it is found that modifications to the previous theory are sufficient to explain the new evidence. The strength of a theory relates to how long it has persisted without major alteration to its core principles.
Theories can also become subsumed by other theories. For example, Newton's laws explained thousands of years of scientific observations of the planets almost perfectly. However, these laws were then determined to be special cases of a more general theory (relativity), which explained both the (previously unexplained) exceptions to Newton's laws and predicted and explained other observations such as the deflection of light by gravity. Thus, in certain cases independent, unconnected, scientific observations can be connected, unified by principles of increasing explanatory power.
Since new theories might be more comprehensive than what preceded them, and thus be able to explain more than previous ones, successor theories might be able to meet a higher standard by explaining a larger body of observations than their predecessors. For example, the theory of evolution explains the diversity of life on Earth, how species adapt to their environments, and many other patterns observed in the natural world; its most recent major modification was unification with genetics to form the modern evolutionary synthesis. In subsequent modifications, it has also subsumed aspects of many other fields such as biochemistry and molecular biology.
== Heuristics ==
=== Confirmation theory ===
During the course of history, one theory has succeeded another, and some have suggested further work while others have seemed content just to explain the phenomena. The reasons why one theory has replaced another are not always obvious or simple. The philosophy of science includes the question: What criteria are satisfied by a 'good' theory. This question has a long history, and many scientists, as well as philosophers, have considered it. The objective is to be able to choose one theory as preferable to another without introducing cognitive bias. Though different thinkers emphasize different aspects, good theories are accurate, internally consistent, explanatory beyond required data, unifying of disparate phenomena, and fruitful for research. When empirical evidence is limited, scientists favor parsimony and invariant observations. Scientists will sometimes also list the very subjective criteria of "formal elegance" which can indicate multiple different things.
The goal here is to make the choice between theories less arbitrary. Nonetheless, these criteria contain subjective elements, and should be considered heuristics rather than a definitive. Also, criteria such as these do not necessarily decide between alternative theories. Quoting Bird:
"[Such criteria] cannot determine scientific choice. First, which features of a theory satisfy these criteria may be disputable (e.g. does simplicity concern the ontological commitments of a theory or its mathematical form?). Secondly, these criteria are imprecise, and so there is room for disagreement about the degree to which they hold. Thirdly, there can be disagreement about how they are to be weighted relative to one another, especially when they conflict."
It also is debatable whether existing scientific theories satisfy all these criteria, which may represent goals not yet achieved. For example, explanatory power over all existing observations is satisfied by no one theory at the moment.
==== Parsimony ====
The desiderata of a "good" theory have been debated for centuries, going back perhaps even earlier than Occam's razor, which is often taken as an attribute of a good theory. Science tries to be simple. When gathered data supports multiple explanations, the most simple explanation for phenomena or the most simple formation of a theory is recommended by the principle of parsimony. Scientists go as far as to call simple proofs of complex statements beautiful.

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We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
The concept of parsimony should not be held to imply complete frugality in the pursuit of scientific truth. The general process starts at the opposite end of there being a vast number of potential explanations and general disorder. An example can be seen in Paul Krugman's process, who makes explicit to "dare to be silly". He writes that in his work on new theories of international trade he reviewed prior work with an open frame of mind and broadened his initial viewpoint even in unlikely directions. Once he had a sufficient body of ideas, he would try to simplify and thus find what worked among what did not. Specific to Krugman here was to "question the question". He recognised that prior work had applied erroneous models to already present evidence, commenting that "intelligent commentary was ignored". Thus touching on the need to bridge the common bias against other circles of thought.
==== Elegance ====
Occam's razor might fall under the heading of "simple elegance", but it is arguable that parsimony and elegance pull in different directions. Introducing additional elements could simplify theory formulation, whereas simplifying a theory's ontology might lead to increased syntactical complexity.
Sometimes ad-hoc modifications of a failing idea may also be dismissed as lacking "formal elegance". This appeal to what may be called "aesthetic" is hard to characterise, but essentially about a sort of familiarity. Though, argument based on "elegance" is contentious and over-reliance on familiarity will breed stagnation.
==== Invariance ====
Principles of invariance have been a theme in scientific writing, and especially physics, since at least the early 20th century. The basic idea here is that good structures to look for are those independent of perspective, an idea that has featured earlier of course for example in Mill's Methods of difference and agreement—methods that would be referred back to in the context of contrast and invariance. But as tends to be the case, there is a difference between something being a basic consideration and something being given weight. Principles of invariance have only been given weight in the wake of Einstein's theories of relativity, which reduced everything to relations and were thereby fundamentally unchangeable, unable to be varied. As David Deutsch put it in 2009: "the search for hard-to-vary explanations is the origin of all progress".
An example here can be found in one of Einstein's thought experiments. The one of a lab suspended in empty space is an example of a useful invariant observation. He imagined the absence of gravity and an experimenter free floating in the lab. — If now an entity pulls the lab upwards, accelerating uniformly, the experimenter would perceive the resulting force as gravity. The entity however would feel the work needed to accelerate the lab continuously. Through this experiment Einstein was able to equate gravitational and inertial mass; something unexplained by Newton's laws, and an early but "powerful argument for a generalised postulate of relativity".
The feature, which suggests reality, is always some kind of invariance of a structure independent of the aspect, the projection.
The discussion on invariance in physics is often had in the more specific context of symmetry. The Einstein example above, in the parlance of Mill would be an agreement between two values. In the context of invariance, it is a variable that remains unchanged through some kind of transformation or change in perspective. And discussion focused on symmetry would view the two perspectives as systems that share a relevant aspect and are therefore symmetrical.
Related principles here are falsifiability and testability. The opposite of something being hard-to-vary are theories that resist falsification—a frustration that was expressed colourfully by Wolfgang Pauli as them being "not even wrong". The importance of scientific theories to be falsifiable finds especial emphasis in the philosophy of Karl Popper. The broader view here is testability, since it includes the former and allows for additional practical considerations.
== Philosophy and discourse ==
Philosophy of science looks at the underpinning logic of the scientific method, at what separates science from non-science, and the ethic that is implicit in science. There are basic assumptions, derived from philosophy by at least one prominent scientist, that form the base of the scientific method namely, that reality is objective and consistent, that humans have the capacity to perceive reality accurately, and that rational explanations exist for elements of the real world. These assumptions from methodological naturalism form a basis on which science may be grounded. Logical positivist, empiricist, falsificationist, and other theories have criticized these assumptions and given alternative accounts of the logic of science, but each has also itself been criticized.
There are several kinds of modern philosophical conceptualizations and attempts at definitions of the method of science. The one attempted by the unificationists, who argue for the existence of a unified definition that is useful (or at least 'works' in every context of science). The pluralists, arguing degrees of science being too fractured for a universal definition of its method to by useful. And those, who argue that the very attempt at definition is already detrimental to the free flow of ideas.
Additionally, there have been views on the social framework in which science is done, and the impact of the sciences social environment on research. Also, there is 'scientific method' as popularised by Dewey in How We Think (1910) and Karl Pearson in Grammar of Science (1892), as used in fairly uncritical manner in education.
=== Pluralism ===