Correlation does not imply causation: Difference between revisions
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{{Short description|Refutation of a logical fallacy}} |
{{Short description|Refutation of a logical fallacy}} |
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{{Distinguish|Illusory correlation|Conflation}} |
{{Distinguish|Illusory correlation|Conflation}} |
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⚫ | The phrase "'''correlation does not imply causation'''" refers to the inability to legitimately deduce a [[Causality|cause-and-effect]] relationship between two events or [[Variable (research)|variables]] solely on the basis of an observed association or [[correlation]] between them.<ref name="Tufte 2006 5">{{harvnb|Tufte|2006|p=5}}</ref><ref name="Aldrich1995">{{Cite journal|last=Aldrich |first=John |journal=Statistical Science |volume=10 |year=1995 |pages=364–376 |title=Correlations Genuine and Spurious in Pearson and Yule |jstor=2246135 |doi=10.1214/ss/1177009870 |issue=4 |doi-access=free |url=https://eprints.soton.ac.uk/32919/1/1177009870.pdf }}</ref> The idea that "correlation implies causation" is an example of a [[questionable cause|questionable-cause]] [[Fallacy#logical|logical fallacy]], in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase '''''cum hoc ergo propter hoc''''' ('with this, therefore because of this'). This differs from the fallacy known as ''[[post hoc ergo propter hoc]]'' ("after this, therefore because of this"), in which an event following another is seen as a [[Logical consequence|necessary consequence]] of the former event, and from [[conflation]], the errant merging of two events, ideas, databases, etc., into one. |
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⚫ | As with any logical fallacy, identifying that the reasoning behind an argument is flawed [[Argument from fallacy|does not necessarily imply]] that the resulting conclusion is false. [[Statistics|Statistical]] methods have been proposed that use correlation as the basis for [[Statistical hypothesis testing|hypothesis tests]] for causality, including the [[Granger causality|Granger causality test]] and [[convergent cross mapping]]. The [[Bradford Hill criteria]], also known as Hill's criteria for causation, are a group of nine principles that can be useful in establishing epidemiologic evidence of a causal relationship. |
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⚫ | The phrase ''' |
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⚫ | As with any logical fallacy, identifying that the reasoning behind an argument is flawed [[Argument from fallacy|does not necessarily imply]] that the resulting conclusion is false. [[Statistics|Statistical]] methods have been proposed that use correlation as the basis for [[Statistical hypothesis testing|hypothesis tests]] for causality, including the [[Granger causality|Granger causality test]] and [[convergent cross mapping]]. |
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=== "Imply"=== |
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In casual use, the word "implies" loosely means ''suggests'' rather than ''requires''. However, in [[logic]], the technical use of the word "implies" means "is a ''[[sufficient condition]]'' for |
In casual use, the word "implies" loosely means ''suggests'', rather than ''requires''. However, in [[logic]], the technical use of the word "implies" means "is a ''[[sufficient condition]]'' for."<ref name="sufficient">{{cite web |
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|url=http://mathworld.wolfram.com/Sufficient.html |
|url=http://mathworld.wolfram.com/Sufficient.html |
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|title=Sufficient |
|title=Sufficient |
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|website=Wolfram |
|website=Wolfram |
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|access-date=2019-12-03 |
|access-date=2019-12-03 |
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}}</ref> |
}}</ref> That is the meaning intended by statisticians when they say causation is not certain. Indeed, ''p implies q'' has the technical meaning of the [[material conditional]]: ''if p then q'' symbolized as ''p → q''. That is, "if circumstance ''p'' is true, then ''q'' follows." In that sense, it is always correct to say "Correlation does not ''imply'' causation." |
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=== "Cause"=== |
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Where there is causation, there is correlation, but also a sequence in time from cause to effect, a plausible mechanism, and sometimes common and intermediate causes. While correlation is often used when inferring causation because it is a necessary condition, it is not a sufficient condition. |
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The word "[[Causality|cause]]" (or "causation") has multiple meanings in English. In philosophical terminology, "cause" can refer to [[Causality#Necessary and sufficient_causes|necessary, sufficient, or contributing]] causes. In examining correlation, "cause" is most often used to mean "one contributing cause" (but not necessarily the only contributing cause). |
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[[File:Illiterate Dinos.jpg|thumb|upright|Dinosaur illiteracy and extinction may be correlated, but |
[[File:Illiterate Dinos.jpg|thumb|upright|Dinosaur illiteracy and extinction may be correlated, but that would not mean the variables had a causal relationship.]] |
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==Causal analysis== |
==Causal analysis== |
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{{ |
{{excerpt|Causal analysis}} |
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Causal analysis is the field of [[experimental design]] and [[statistics]] pertaining to establishing cause and effect.<ref>{{cite journal |last1=Rohlfing |first1=Ingo |last2=Schneider |first2=Carsten Q. |title=A Unifying Framework for Causal Analysis in Set-Theoretic Multimethod Research |journal=Sociological Methods & Research |date=2018 |volume=47 |issue=1 |pages=37–63 |doi=10.1177/0049124115626170 |s2cid=124804330 |url=https://publications.ceu.edu/sites/default/files/publications/0049124115626170.pdf |access-date=29 February 2020}}</ref><ref>{{cite journal |last1=Brady |first1=Henry E. |title=Causation and Explanation in Social Science |journal=The Oxford Handbook of Political Science |date=7 July 2011 |doi=10.1093/oxfordhb/9780199604456.013.0049 |url=https://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199604456.001.0001/oxfordhb-9780199604456-e-049 |access-date=29 February 2020 |language=en}}</ref> For any two correlated events, A and B, their possible relationships include: |
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* A causes B (direct causation); |
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* B causes A (reverse causation); |
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*A and B are both caused by C (common causation); |
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* A causes B and B causes A (bidirectional or cyclic causation); |
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* There is no connection between A and B; the correlation is a [[coincidence]]. |
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Thus there can be no conclusion made regarding the ''existence'' or the ''direction'' of a cause-and-effect relationship only from the fact that A and B are correlated. Determining whether there is an actual cause-and-effect relationship requires further investigation, even when the relationship between ''A'' and ''B'' is [[statistical significance|statistically significant]], a large [[effect size]] is observed, or a large part of the [[Coefficient of determination|variance is explained]]. |
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===In philosophy and physics=== |
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{{Main|Causality|Causality (physics)}} |
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The nature of causality is systematically investigated in several [[discipline (specialism)|academic disciplines]], including [[philosophy]] and [[physics]]. |
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In academia, there are a significant number of theories on causality; ''The Oxford Handbook of Causation'' {{harv|Beebee|Hitchcock|Menzies|2009}} encompasses 770 pages. Among the more influential theories within [[philosophy]] are [[Aristotle]]'s [[Four causes]] and [[Al-Ghazali]]'s [[occasionalism]].<ref name=Beebee2009>{{harvnb|Beebee|Hitchcock|Menzies|2009}}</ref> [[David Hume]] argued that beliefs about causality are based on experience, and experience similarly based on the assumption that the future models the past, which in turn can only be based on experience – leading to [[circular logic]]. In conclusion, he asserted that [[problem of induction|causality is not based on actual reasoning]]: only correlation can actually be perceived.<ref name="StanfordHume">{{cite journal|last=Morris|first= William Edward |url=http://plato.stanford.edu/archives/spr2001/entries/hume/#CausationN|year=2001|title=David Hume|journal=The Stanford Encyclopedia of Philosophy}}</ref> [[Immanuel Kant]], according to {{harvtxt|Beebee|Hitchcock|Menzies|2009}}, held that "a causal principle according to which every event has a cause, or follows according to a causal law, cannot be established through induction as a purely empirical claim, since it would then lack strict universality, or necessity". |
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Outside the field of philosophy, theories of causation can be identified in [[classical mechanics]], [[statistical mechanics]], [[quantum mechanics]], [[spacetime]] theories, [[biology]], [[social science]]s, and [[law]].<ref name=Beebee2009 /> To establish a correlation as causal within [[physics]], it is normally understood that the cause and the effect must connect through a local [[mechanism (philosophy)|mechanism]] (cf. for instance the concept of [[impact (mechanics)|impact]]) or a [[wikt:nonlocality|nonlocal]] mechanism (cf. the concept of [[field (physics)|field]]), in accordance with known [[Physical law|laws of nature]]. |
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From the point of view of [[thermodynamics]], universal properties of causes as compared to effects have been identified through the [[second law of thermodynamics]], confirming the ancient, medieval and [[Descartes|Cartesian]]<ref name="Lloyd1976">{{cite journal|last=Lloyd|first= A.C.|title=The principle that the cause is greater than its effect|journal=Phronesis|volume=21|issue=2|pages= 146–156|year=1976|jstor=4181986|doi=10.1163/156852876x00101}}</ref> view that "the cause is greater than the effect" for the particular case of [[thermodynamic free energy]]. This, in turn, is challenged{{dubious|date=November 2017}} by popular interpretations of the concepts of [[nonlinear system]]s and the [[butterfly effect]], in which small events cause large effects due to, respectively, unpredictability and an unlikely triggering of large amounts of [[potential energy]]. |
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===Causality construed from counterfactual states=== |
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{{See also|Verificationism}} |
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Intuitively, causation seems to require not just a correlation, but a [[counterfactual]] dependence. Suppose that a student performed poorly on a test and guesses that the cause was his not studying. To prove this, one thinks of the counterfactual – the same student writing the same test under the same circumstances but having studied the night before. If one could rewind history, and change only one small thing (making the student study for the exam), then causation could be observed (by comparing version 1 to version 2). Because one cannot rewind history and replay events after making small controlled changes, causation can only be inferred, never exactly known. This is referred to as the Fundamental Problem of Causal Inference – it is impossible to directly observe causal effects.<ref>{{cite journal |first=Paul W. |last=Holland |title=Statistics and Causal Inference |journal=[[Journal of the American Statistical Association]] |volume=81 |issue=396 |year=1986 |pages=945–960 |doi= 10.1080/01621459.1986.10478354 }}</ref> |
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A major goal of scientific [[experiment]]s and statistical methods is to approximate as best possible the counterfactual state of the world.<ref>{{cite book |first=Judea |last=Pearl |year=2000 |title=Causality: Models, Reasoning, and Inference |url=https://archive.org/details/causalitymodelsr0000pear |url-access=registration |publisher=Cambridge University Press |isbn=9780521773621 }}</ref> For example, one could run an [[Twin study|experiment on identical twins]] who were known to consistently get the same grades on their tests. One twin is sent to study for six hours while the other is sent to the amusement park. If their test scores suddenly diverged by a large degree, this would be strong evidence that studying (or going to the amusement park) had a causal effect on test scores. In this case, correlation between studying and test scores would almost certainly imply causation. |
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Well-designed [[experiment|experimental studies]] replace equality of individuals as in the previous example by equality of groups. The objective is to construct two groups that are similar except for the treatment that the groups receive. This is achieved by selecting subjects from a single population and randomly assigning them to two or more groups. The likelihood of the groups behaving similarly to one another (on average) rises with the number of subjects in each group. If the groups are essentially equivalent except for the treatment they receive, and a difference in the outcome for the groups is observed, then this constitutes evidence that the treatment is responsible for the outcome, or in other words the treatment causes the observed effect. However, an observed effect could also be caused "by chance", for example as a result of random perturbations in the population. Statistical tests exist to quantify the likelihood of erroneously concluding that an observed difference exists when in fact it does not (for example see [[P-value]]). |
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===Causality predicted by an extrapolation of trends=== |
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{{unreferenced section|date=February 2020}} |
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{{See also|Inertia|Life-time of correlation}} |
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When experimental studies are impossible and only pre-existing data are available, as is usually the case for example in [[economics]], [[regression analysis]] can be used. Factors other than the potential causative variable of interest are controlled for by including them as [[Dependent and independent variables#Statistics|regressors]] in addition to the regressor representing the variable of interest. False inferences of causation due to reverse causation (or wrong estimates of the magnitude of causation due to the presence of bidirectional causation) can be avoided by using explanators (regressors) that are necessarily [[exogenous variable|exogenous]], such as physical explanators like rainfall amount (as a determinant of, say, futures prices), lagged variables whose values were determined before the dependent variable's value was determined, [[instrumental variables]] for the explanators (chosen based on their known exogeneity), etc. See [[Causality#Statistics and economics|causality in statistics and economics]]. [[Spurious relationship|Spurious correlation]] due to mutual influence from a third, common, causative variable, is harder to avoid: the model must be specified such that there is a theoretical reason to believe that no such underlying causative variable has been omitted from its analysis. |
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==Examples of illogically inferring causation from correlation== |
==Examples of illogically inferring causation from correlation== |
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===B causes A (reverse causation or reverse causality)=== |
===B causes A (reverse causation or reverse causality)=== |
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'''Reverse causation''' or '''reverse causality''' or '''wrong direction''' is an [[informal fallacy]] of [[questionable cause]] where cause and effect are reversed. The cause is said to be the effect and vice versa. |
'''Reverse causation''' or '''reverse causality''' or '''wrong direction''' is an [[informal fallacy]] of [[questionable cause]] where cause and effect are reversed. The cause is said to be the effect and vice versa. |
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;Example 2 |
;Example 2 |
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:Low cholesterol is associated with an increase in mortality. |
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:Therefore, low cholesterol increases your risk of mortality. |
:Therefore, low cholesterol increases your risk of mortality. |
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Causality is actually the other way around, since some diseases, such as cancer, cause low cholesterol due to a myriad of factors, such as weight loss, and they also cause an increase in mortality.<ref>{{cite journal |author=Naveed Sattar |author2=David Preiss | title = Reverse Causality in Cardiovascular Epidemiological Research | journal = Circulation | volume = 135 | issue = 24 | pages = 2369–2372 | date = 13 Jun 2017 | pmid = 28606949 | doi = 10.1161/CIRCULATIONAHA.117.028307 | doi-access = free }}</ref> |
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This is also seen with ex-smokers. Ex-smokers are more likely to die of lung cancer than current smokers.<ref>{{cite journal | |
This is also seen with ex-smokers. Ex-smokers are more likely to die of lung cancer than current smokers.<ref>{{cite journal |author=Richard Doll |author2=Richard Peto |author3=Jillian Boreham |author4=Isabelle Sutherland | title = Mortality in relation to smoking: 50 years' observations on male British doctors | journal = The BMJ | volume = 328 | issue = 7455 | pages = 1239–49 | date = 24 Jun 2004 | pmid = 15213107 | doi = 10.1136/bmj.38142.554479.AE | pmc = 437139 }}</ref> When lifelong smokers are told they have lung cancer, many quit smoking. This change can make it seem as if ex-smokers are more likely to die of lung cancer than current smokers. This can also be seen in alcoholics. As alcoholics become diagnosed with cirrhosis of the liver, many quit drinking. However, they also experience an increased risk of mortality. In these instances, it is the diseases that cause an increased risk of mortality, but the increased mortality is attributed to the beneficial effects that follow the diagnosis, making healthy changes look unhealthy. |
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In other cases it may simply be unclear which is the cause and which is the effect. For example: |
In other cases it may simply be unclear which is the cause and which is the effect. For example: |
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:''Children that watch a lot of [[television|TV]] are the most violent. Clearly, TV makes children more violent''. |
:''Children that watch a lot of [[television|TV]] are the most violent. Clearly, TV makes children more violent''. |
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This could easily be the other way round; that is, violent children like watching more TV than less violent ones. |
This could easily be the other way round; that is, violent children like watching more TV than less violent ones. |
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'''Example 4''' |
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A correlation between [[recreational drug use]] and [[psychiatric disorder]]s might be either way around: perhaps the drugs cause the disorders, or perhaps people use drugs to [[self medication|self medicate]] for preexisting conditions. [[Gateway drug theory]] may argue that [[marijuana]] usage leads to usage of harder drugs, but hard drug usage may lead to marijuana usage (see also ''[[confusion of the inverse]]''). Indeed, in the [[social science]]s where controlled experiments often cannot be used to discern the direction of causation, this fallacy can fuel long-standing scientific arguments. One such example can be found in [[education economics]], between the [[Screening (economics)|screening]]/[[Signalling (economics)|signaling]] and [[human capital]] models: it could either be that having innate ability enables one to complete an education, or that completing an education builds one's ability. |
A correlation between [[recreational drug use]] and [[psychiatric disorder]]s might be either way around: perhaps the drugs cause the disorders, or perhaps people use drugs to [[self medication|self medicate]] for preexisting conditions. [[Gateway drug theory]] may argue that [[marijuana]] usage leads to usage of harder drugs, but hard drug usage may lead to marijuana usage (see also ''[[confusion of the inverse]]''). Indeed, in the [[social science]]s where controlled experiments often cannot be used to discern the direction of causation, this fallacy can fuel long-standing scientific arguments. One such example can be found in [[education economics]], between the [[Screening (economics)|screening]]/[[Signalling (economics)|signaling]] and [[human capital]] models: it could either be that having innate ability enables one to complete an education, or that completing an education builds one's ability. |
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'''Example 5''' |
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A historical example of this is that Europeans in the [[Middle Ages]] believed that [[ |
A historical example of this is that Europeans in the [[Middle Ages]] believed that [[louse|lice]] were beneficial to health since there would rarely be any lice on sick people. The reasoning was that the people got sick because the lice left. The real reason however is that lice are extremely sensitive to [[body temperature]]. A small increase of body temperature, such as in a [[fever]], makes the lice look for another host. The medical [[thermometer]] had not yet been invented and so that increase in temperature was rarely noticed. Noticeable symptoms came later, which gave the impression that the lice had left before the person became sick.<ref>{{Cite web|url=https://blogs.scientificamerican.com/guest-blog/of-lice-and-men-an-itchy-history/|title=Of lice and men: An itchy history|last=Willingham|first=Emily|website=Scientific American Blog Network|language=en|access-date=2019-02-26}}</ref> |
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In other cases, two phenomena can each be a partial cause of the other; consider poverty and lack of education, or procrastination and poor self-esteem. One making an argument based on these two phenomena must however be careful to avoid the fallacy of [[circular cause and consequence]]. Poverty is ''a'' cause of lack of education, but it is not the ''sole'' cause, and vice versa. |
In other cases, two phenomena can each be a partial cause of the other; consider poverty and lack of education, or procrastination and poor self-esteem. One making an argument based on these two phenomena must however be careful to avoid the fallacy of [[circular cause and consequence]]. Poverty is ''a'' cause of lack of education, but it is not the ''sole'' cause, and vice versa. |
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{{Main|Spurious relationship}} |
{{Main|Spurious relationship}} |
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The '''third-cause fallacy''' (also known as ''ignoring a common cause''<ref name="labossiere">Labossiere, M.C., [http://www.opifexphoenix.com/reasoning/fallacies/ignorecc.htm ''Dr. LaBossiere's Philosophy Pages''] {{Webarchive|url=https://web.archive.org/web/20090522103015/http://www.opifexphoenix.com/reasoning/fallacies/ignorecc.htm |date=2009-05-22 |
The '''third-cause fallacy''' (also known as ''ignoring a common cause''<ref name="labossiere">Labossiere, M.C., [http://www.opifexphoenix.com/reasoning/fallacies/ignorecc.htm ''Dr. LaBossiere's Philosophy Pages''] {{Webarchive|url=https://web.archive.org/web/20090522103015/http://www.opifexphoenix.com/reasoning/fallacies/ignorecc.htm |date=2009-05-22}}</ref> or ''questionable cause''<ref name="labossiere"/>) is a [[Informal fallacy|logical fallacy]] in which a [[spurious relationship]] is confused for [[Causality|causation]]. It asserts that X causes Y when in reality, both X and Y are caused by Z. It is a variation on the ''[[post hoc ergo propter hoc]]'' fallacy and a member of the [[questionable cause]] group of fallacies. |
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All of |
All of those examples deal with a [[lurking variable]], which is simply a hidden third variable that affects both of the variables observed to be correlated. That third variable is also known as a [[confounding]] variable, with the slight difference that confounding variables need not be hidden and may thus be corrected for in an analysis. Note that the Wikipedia link to lurking variable redirects to confounding. A difficulty often also arises where the third factor, though fundamentally different from A and B, is so closely related to A and/or B as to be confused with them or very difficult to scientifically disentangle from them (see Example 4). |
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;Example 1 |
;Example 1 |
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:Therefore, sleeping with the light on causes myopia. |
:Therefore, sleeping with the light on causes myopia. |
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This is a scientific example that resulted from a study at the [[University of Pennsylvania]] [[Penn Presbyterian Medical Center|Medical Center]]. Published in the May 13, 1999, issue of ''[[Nature (journal)|Nature]]'',<ref name="QuinnMyopiaNature">{{cite journal |last1=Quinn|first1=Graham E.|last2=Shin|first2=Chai H.|last3=Maguire|first3=Maureen G.|last4=Stone|first4=Richard A.|title=Myopia and ambient lighting at night |journal=Nature |volume=399 |issue=6732 |pages=113–114 |date=May 1999 |pmid=10335839 |doi=10.1038/20094|bibcode=1999Natur.399..113Q|s2cid=4419645}}</ref> the study received much coverage at the time in the popular press.<ref>[[CNN]], May 13, 1999. [http://www.cnn.com/HEALTH/9905/12/children.lights/index.html Night-light may lead to nearsightedness]</ref> However, a later study at [[Ohio State University]] did not find that [[infant]]s sleeping with the light on caused the development of myopia. It did find a strong link between parental myopia and the development of child myopia, also noting that myopic parents were more likely to leave a light on in their children's bedroom.<ref>[[Ohio State University]] Research News, March 9, 2000. [http://researchnews.osu.edu/archive/nitelite.htm Night lights don't lead to nearsightedness, study suggests] {{Webarchive|url=https://web.archive.org/web/20060901152949/http://researchnews.osu.edu/archive/nitelite.htm |date=2006-09-01 }}</ref><ref name="ZadnikJones2000">{{cite journal|last1=Zadnik|first1=Karla|last2=Jones|first2=Lisa A.|last3=Irvin|first3=Brett C.|last4=Kleinstein|first4=Robert N.|last5=Manny|first5=Ruth E.|last6=Shin|first6=Julie A.|last7=Mutti|first7=Donald O.|title=Vision: Myopia and ambient night-time lighting|journal=Nature|volume=404|issue=6774|year=2000|pages=143–144|doi=10.1038/35004661|pmid=10724157|bibcode=2000Natur.404..143Z|s2cid=4399332}}</ref><ref name="GwiazdaOng2000">{{cite journal|last1=Gwiazda|first1=J.|last2=Ong|first2=E.|last3=Held|first3=R.|last4=Thorn|first4=F.|title=Vision: Myopia and ambient night-time lighting|journal=Nature|volume=404|issue=6774|year=2000| |
This is a scientific example that resulted from a study at the [[University of Pennsylvania]] [[Penn Presbyterian Medical Center|Medical Center]]. Published in the May 13, 1999, issue of ''[[Nature (journal)|Nature]]'',<ref name="QuinnMyopiaNature">{{cite journal |last1=Quinn|first1=Graham E.|last2=Shin|first2=Chai H.|last3=Maguire|first3=Maureen G.|last4=Stone|first4=Richard A.|title=Myopia and ambient lighting at night |journal=Nature |volume=399 |issue=6732 |pages=113–114 |date=May 1999 |pmid=10335839 |doi=10.1038/20094|bibcode=1999Natur.399..113Q|s2cid=4419645}}</ref> the study received much coverage at the time in the popular press.<ref>[[CNN]], May 13, 1999. [http://www.cnn.com/HEALTH/9905/12/children.lights/index.html Night-light may lead to nearsightedness]</ref> However, a later study at [[Ohio State University]] did not find that [[infant]]s sleeping with the light on caused the development of myopia. It did find a strong link between parental myopia and the development of child myopia, also noting that myopic parents were more likely to leave a light on in their children's bedroom.<ref>[[Ohio State University]] Research News, March 9, 2000. [http://researchnews.osu.edu/archive/nitelite.htm Night lights don't lead to nearsightedness, study suggests] {{Webarchive|url=https://web.archive.org/web/20060901152949/http://researchnews.osu.edu/archive/nitelite.htm |date=2006-09-01 }}</ref><ref name="ZadnikJones2000">{{cite journal|last1=Zadnik|first1=Karla|last2=Jones|first2=Lisa A.|last3=Irvin|first3=Brett C.|last4=Kleinstein|first4=Robert N.|last5=Manny|first5=Ruth E.|last6=Shin|first6=Julie A.|last7=Mutti|first7=Donald O.|title=Vision: Myopia and ambient night-time lighting|journal=Nature|volume=404|issue=6774|year=2000|pages=143–144|doi=10.1038/35004661|pmid=10724157|bibcode=2000Natur.404..143Z|s2cid=4399332}}</ref><ref name="GwiazdaOng2000">{{cite journal|last1=Gwiazda|first1=J.|last2=Ong|first2=E.|last3=Held|first3=R.|last4=Thorn|first4=F.|title=Vision: Myopia and ambient night-time lighting|journal=Nature|volume=404|issue=6774|year=2000|page=144|doi=10.1038/35004663|pmid=10724158|bibcode=2000Natur.404..144G|doi-access=free}}</ref><ref name="StoneMaguire2000">{{cite journal|last1=Stone|first1=Richard A.|last2=Maguire|first2=Maureen G.|last3=Quinn|first3=Graham E.|title=Vision: reply: Myopia and ambient night-time lighting|journal=Nature|volume=404|issue=6774|year=2000|page=144|doi=10.1038/35004665|pmid=10724158|bibcode=2000Natur.404..144S|doi-access=free}}</ref> In this case, the cause of both conditions is parental myopia, and the above-stated conclusion is false. |
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;Example 3 |
;Example 3 |
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:As ice cream sales increase, the rate of drowning deaths increases sharply. |
:As ice cream sales increase, the rate of drowning deaths increases sharply. |
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:Therefore, ice cream consumption causes drowning. |
:Therefore, ice cream consumption causes drowning. |
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;Example 4 |
;Example 4 |
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:A hypothetical study shows a relationship between test anxiety scores and shyness scores, with a statistical ''r'' value (strength of correlation) of +.59.<ref name="Carducci2009">{{cite book|last=Carducci|first=Bernardo J.|title=The Psychology of Personality: Viewpoints, Research, and Applications|url=https://books.google.com/books?id=1gJPXv5wQbIC|edition=2nd|year=2009|publisher=John Wiley & Sons|isbn=978-1-4051-3635-8}}</ref> |
:A hypothetical study shows a relationship between test anxiety scores and shyness scores, with a statistical ''r'' value (strength of correlation) of +.59.<ref name="Carducci2009">{{cite book|last=Carducci|first=Bernardo J.|title=The Psychology of Personality: Viewpoints, Research, and Applications|url=https://books.google.com/books?id=1gJPXv5wQbIC|edition=2nd|year=2009|publisher=John Wiley & Sons|isbn=978-1-4051-3635-8}}</ref> |
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:Therefore, it may be simply concluded that shyness, in some part, causally influences test anxiety. |
:Therefore, it may be simply concluded that shyness, in some part, causally influences test anxiety. |
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;Example 5 |
;Example 5 |
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:Since the 1950s, both the atmospheric [[carbon dioxide|CO<sub>2</sub>]] level and [[obesity]] levels have increased sharply. |
:Since the 1950s, both the atmospheric [[carbon dioxide|CO<sub>2</sub>]] level and [[obesity]] levels have increased sharply. |
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:Hence, atmospheric CO<sub>2</sub> causes obesity. |
:Hence, atmospheric CO<sub>2</sub> causes obesity. |
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;Example 6 |
;Example 6 |
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:[[High-density lipoprotein|HDL]] ("good") [[cholesterol]] is negatively correlated with incidence of heart attack. |
:[[High-density lipoprotein|HDL]] ("good") [[cholesterol]] is negatively correlated with incidence of heart attack. |
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:Therefore, taking medication to raise HDL decreases the chance of having a heart attack. |
:Therefore, taking medication to raise HDL decreases the chance of having a heart attack. |
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===Bidirectional causation: A causes B, and B causes A=== |
===Bidirectional causation: A causes B, and B causes A=== |
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Causality is not necessarily one-way;{{dubious|date=November 2020}}<!--needs qualification, such as "when considering statistical ensembles" or similar. When causality is understood in a fundamental physical sense of relationships between points in spacetime, it is, in fact, necessarily one-way (or causality breaks down altogether).--> |
Causality is not necessarily one-way;{{dubious|date=November 2020}}<!--needs qualification, such as "when considering statistical ensembles" or similar. When causality is understood in a fundamental physical sense of relationships between points in spacetime, it is, in fact, necessarily one-way (or causality breaks down altogether).--> |
||
in a [[Predation|predator-prey relationship]], predator numbers affect prey numbers, but prey numbers, i.e. food supply, also affect predator numbers. Another well-known example is that cyclists have a lower [[Body mass index|Body Mass Index]] than people who do not cycle. This is often explained by assuming that cycling increases [[physical activity]] levels and therefore decreases BMI. Because results from prospective studies on people who increase their bicycle use show a smaller effect on BMI than cross-sectional studies, there may be some reverse causality as well |
in a [[Predation|predator-prey relationship]], predator numbers affect prey numbers, but prey numbers, i.e. food supply, also affect predator numbers. Another well-known example is that cyclists have a lower [[Body mass index|Body Mass Index]] than people who do not cycle. This is often explained by assuming that cycling increases [[physical activity]] levels and therefore decreases BMI. Because results from prospective studies on people who increase their bicycle use show a smaller effect on BMI than cross-sectional studies, there may be some reverse causality as well. For example, people with a lower BMI may be more likely to want to cycle in the first place. <ref name="Dons">{{cite journal |
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| last = Dons |
| last = Dons |
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| first = E |
| first = E |
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==Use of correlation as scientific evidence== |
==Use of correlation as scientific evidence== |
||
Much of scientific evidence is based upon a correlation of variables<ref name="Steven">{{cite web|last=Novella|title=Evidence in Medicine: Correlation and Causation|url=http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/|work=Science and Medicine|date=18 November 2009|publisher=Science-Based Medicine}}</ref> |
Much of scientific evidence is based upon a correlation of variables<ref name="Steven">{{cite web|last=Novella|title=Evidence in Medicine: Correlation and Causation|url=http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/|work=Science and Medicine|date=18 November 2009|publisher=Science-Based Medicine}}</ref> that are observed to occur together. Scientists are careful to point out that correlation does not necessarily mean causation. The assumption that A causes B simply because A correlates with B is not accepted as a legitimate form of argument. |
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However, sometimes people commit the opposite fallacy |
However, sometimes people commit the opposite fallacy of dismissing correlation entirely. That would dismiss a large swath of important scientific evidence.<ref name="Steven"/> Since it may be difficult or ethically impossible to run controlled [[double-blind]] studies to address certain questions, correlational evidence from several different angles may be useful for ''prediction'' despite failing to provide evidence for ''causation''. For example, social workers might be interested in knowing how child abuse relates to academic performance. Although it would be unethical to perform an experiment in which children are randomly assigned to receive or not receive abuse, researchers can look at existing groups using a non-experimental correlational design. If in fact a negative correlation exists between abuse and academic performance, researchers could potentially use this knowledge of a statistical correlation to make predictions about children outside the study who experience abuse even though the study failed to provide causal evidence that abuse decreases academic performance.<ref>{{cite web|last=Nielsen |first=Michael |url=http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/ |title=If correlation doesn't imply causation, then what does? | DDI |publisher=Michaelnielsen.org |date=2012-01-23 |access-date=2017-10-08}}</ref> The combination of limited available methodologies with the dismissing correlation fallacy has on occasion been used to counter a scientific finding. For example, the [[tobacco industry]] has historically relied on a dismissal of correlational evidence to reject a link between [[Health effects of tobacco|tobacco smoke and lung cancer]],<ref name="Sciencebasedmedicine.org">{{cite web|url=http://www.sciencebasedmedicine.org/evidence-in-medicine-correlation-and-causation/ |title=Evidence in Medicine: Correlation and Causation – Science-Based Medicine |publisher=Sciencebasedmedicine.org |date=2009-11-18 |access-date=2017-10-08}}</ref> as did biologist and statistician [[Ronald Fisher]] (frequently on the industry's behalf).{{refn|group=list|name=Fisher refs|<ref>{{Citation|last=Silver|first=Nate|author-link=Nate Silver|title=The Signal and the Noise: Why So Many Predictions Fail – But Some Don't|publisher=[[Penguin Books]]|place=[[New York City|New York]]|edition=2nd|year=2015|pages=254–255|title-link=The Signal and the Noise}}</ref><ref>{{Citation|last=Fisher|first=Ronald|author-link=Ronald Fisher|title=Dangers Of Cigarette-Smoking|journal=[[The BMJ|The British Medical Journal]]|volume=2|issue=5035|publisher=[[British Medical Association]]|place=[[London]]|date=July 6, 1957|page=43|jstor=25383068|doi=10.1136/bmj.2.5035.43|pmc=1961750}}</ref><ref>{{Citation|last=Fisher|first=Ronald|author-link=Ronald Fisher|title=Dangers Of Cigarette-Smoking|journal=[[The BMJ|The British Medical Journal]]|volume=2|issue=5039|publisher=[[British Medical Association]]|place=[[London]]|date=August 3, 1957|pages=297–298|jstor=25383439|doi=10.1136/bmj.2.5039.297-b|pmc=1961712}}</ref><ref>{{Citation|last=Fisher|first=Ronald|author-link=Ronald Fisher|title=Cigarettes, Cancer, and Statistics|journal=The Centennial Review of Arts & Science|volume=2|publisher=[[Michigan State University Press]]|place=[[East Lansing, Michigan]]|year=1958|pages=151–166|url=https://www.york.ac.uk/depts/maths/histstat/fisher274.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.york.ac.uk/depts/maths/histstat/fisher274.pdf |archive-date=2022-10-09 |url-status=live}}</ref><ref>{{Citation|last=Fisher|first=Ronald|author-link=Ronald Fisher|title=The Nature of Probability|journal=The Centennial Review of Arts & Science|volume=2|publisher=[[Michigan State University Press]]|place=[[East Lansing, Michigan]]|year=1958|pages=261–274|url=https://www.york.ac.uk/depts/maths/histstat/fisher272.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.york.ac.uk/depts/maths/histstat/fisher272.pdf |archive-date=2022-10-09 |url-status=live}}</ref><ref>{{Citation|last=Fisher|first=Ronald|author-link=Ronald Fisher|title=Lung Cancer and Cigarettes|journal=[[Nature (journal)|Nature]]|volume=182|issue=4628|publisher=[[Nature Publishing Group]]|place=[[London]]|date=July 12, 1958|page=108|url=https://www.york.ac.uk/depts/maths/histstat/fisher275.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.york.ac.uk/depts/maths/histstat/fisher275.pdf |archive-date=2022-10-09 |url-status=live |doi=10.1038/182108a0|pmid=13566198|bibcode=1958Natur.182..108F|doi-access=free}}</ref><ref>{{Citation|last=Fisher|first=Ronald|author-link=Ronald Fisher|title=Cancer and Smoking|journal=[[Nature (journal)|Nature]]|volume=182|issue=4635|publisher=[[Nature Publishing Group]]|place=[[London]]|date=August 30, 1958|page=596|url=https://www.york.ac.uk/depts/maths/histstat/fisher276.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.york.ac.uk/depts/maths/histstat/fisher276.pdf |archive-date=2022-10-09 |url-status=live |doi=10.1038/182596a0|pmid=13577916|bibcode=1958Natur.182..596F|doi-access=free}}</ref>}} |
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Correlation is a valuable type of scientific evidence in fields such as medicine, psychology, and sociology. Correlations must first be confirmed as real, |
Correlation is a valuable type of [[scientific evidence]] in fields such as medicine, psychology, and sociology. Correlations must first be confirmed as real, and every possible causative relationship must then be systematically explored. In the end, correlation alone cannot be used as evidence for a cause-and-effect relationship between a treatment and benefit, a risk factor and a disease, or a social or economic factor and various outcomes. It is one of the most abused types of evidence because it is easy and even tempting to come to premature conclusions based upon the preliminary appearance of a correlation.<ref name="Sciencebasedmedicine.org"/> |
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==See also== |
==See also== |
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{{columns-list|colwidth=30em| |
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*{{annotated link|Affirming the consequent}} |
*{{annotated link|Affirming the consequent}} |
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*{{annotated link|Alignments of random points}} |
*{{annotated link|Alignments of random points}} |
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*{{annotated link|Anecdotal evidence}} |
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*{{annotated link|Apophenia}} |
*{{annotated link|Apophenia}} |
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**{{annotated link|Post hoc analysis}} |
**{{annotated link|Post hoc analysis}} |
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**{{annotated link|Testing hypotheses suggested by the data}} |
**{{annotated link|Testing hypotheses suggested by the data}} |
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*{{annotated link|Bible code}} |
*{{annotated link|Bible code}} |
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* [[Bradford Hill criteria]] |
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*{{annotated link|Coincidence# |
*{{annotated link|Coincidence#Causality}} |
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*{{annotated link|Confounding}} |
*{{annotated link|Confounding}} |
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*{{annotated link|Confusion of the inverse}} |
*{{annotated link|Confusion of the inverse}} |
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*{{annotated link|Design of experiments}} |
*{{annotated link|Design of experiments}} |
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*{{annotated link|Joint effect}} |
*{{annotated link|Joint effect}} |
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*{{annotated link|Mediation (statistics)}} |
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*{{annotated link|Normally distributed and uncorrelated does not imply independent}} |
*{{annotated link|Normally distributed and uncorrelated does not imply independent}} |
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*{{annotated link|Pirates in terms of global warming|Pirates and global warming}} |
*{{annotated link|Pirates in terms of global warming|Pirates and global warming}} |
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*{{annotated link|Reproducibility}} |
*{{annotated link|Reproducibility}} |
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*{{annotated link|Spurious relationship}} |
*{{annotated link|Spurious relationship}} |
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*{{annotated link| |
*{{annotated link|Teleology}} |
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}} |
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==References== |
==References== |
Latest revision as of 01:30, 12 August 2024
The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them.[1][2] The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase cum hoc ergo propter hoc ('with this, therefore because of this'). This differs from the fallacy known as post hoc ergo propter hoc ("after this, therefore because of this"), in which an event following another is seen as a necessary consequence of the former event, and from conflation, the errant merging of two events, ideas, databases, etc., into one.
As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not necessarily imply that the resulting conclusion is false. Statistical methods have been proposed that use correlation as the basis for hypothesis tests for causality, including the Granger causality test and convergent cross mapping. The Bradford Hill criteria, also known as Hill's criteria for causation, are a group of nine principles that can be useful in establishing epidemiologic evidence of a causal relationship.
Usage and meaning of terms
[edit]"Imply"
[edit]In casual use, the word "implies" loosely means suggests, rather than requires. However, in logic, the technical use of the word "implies" means "is a sufficient condition for."[3] That is the meaning intended by statisticians when they say causation is not certain. Indeed, p implies q has the technical meaning of the material conditional: if p then q symbolized as p → q. That is, "if circumstance p is true, then q follows." In that sense, it is always correct to say "Correlation does not imply causation."
"Cause"
[edit]The word "cause" (or "causation") has multiple meanings in English. In philosophical terminology, "cause" can refer to necessary, sufficient, or contributing causes. In examining correlation, "cause" is most often used to mean "one contributing cause" (but not necessarily the only contributing cause).
Causal analysis
[edit]Examples of illogically inferring causation from correlation
[edit]B causes A (reverse causation or reverse causality)
[edit]Reverse causation or reverse causality or wrong direction is an informal fallacy of questionable cause where cause and effect are reversed. The cause is said to be the effect and vice versa.
- Example 1
- The faster that windmills are observed to rotate, the more wind is observed.
- Therefore, wind is caused by the rotation of windmills. (Or, simply put: windmills, as their name indicates, are machines used to produce wind.)
In this example, the correlation (simultaneity) between windmill activity and wind velocity does not imply that wind is caused by windmills. It is rather the other way around, as suggested by the fact that wind does not need windmills to exist, while windmills need wind to rotate. Wind can be observed in places where there are no windmills or non-rotating windmills—and there are good reasons to believe that wind existed before the invention of windmills.
- Example 2
- Low cholesterol is associated with an increase in mortality.
- Therefore, low cholesterol increases your risk of mortality.
Causality is actually the other way around, since some diseases, such as cancer, cause low cholesterol due to a myriad of factors, such as weight loss, and they also cause an increase in mortality.[6] This is also seen with ex-smokers. Ex-smokers are more likely to die of lung cancer than current smokers.[7] When lifelong smokers are told they have lung cancer, many quit smoking. This change can make it seem as if ex-smokers are more likely to die of lung cancer than current smokers. This can also be seen in alcoholics. As alcoholics become diagnosed with cirrhosis of the liver, many quit drinking. However, they also experience an increased risk of mortality. In these instances, it is the diseases that cause an increased risk of mortality, but the increased mortality is attributed to the beneficial effects that follow the diagnosis, making healthy changes look unhealthy.
Example 3
In other cases it may simply be unclear which is the cause and which is the effect. For example:
- Children that watch a lot of TV are the most violent. Clearly, TV makes children more violent.
This could easily be the other way round; that is, violent children like watching more TV than less violent ones.
Example 4
A correlation between recreational drug use and psychiatric disorders might be either way around: perhaps the drugs cause the disorders, or perhaps people use drugs to self medicate for preexisting conditions. Gateway drug theory may argue that marijuana usage leads to usage of harder drugs, but hard drug usage may lead to marijuana usage (see also confusion of the inverse). Indeed, in the social sciences where controlled experiments often cannot be used to discern the direction of causation, this fallacy can fuel long-standing scientific arguments. One such example can be found in education economics, between the screening/signaling and human capital models: it could either be that having innate ability enables one to complete an education, or that completing an education builds one's ability.
Example 5
A historical example of this is that Europeans in the Middle Ages believed that lice were beneficial to health since there would rarely be any lice on sick people. The reasoning was that the people got sick because the lice left. The real reason however is that lice are extremely sensitive to body temperature. A small increase of body temperature, such as in a fever, makes the lice look for another host. The medical thermometer had not yet been invented and so that increase in temperature was rarely noticed. Noticeable symptoms came later, which gave the impression that the lice had left before the person became sick.[8]
In other cases, two phenomena can each be a partial cause of the other; consider poverty and lack of education, or procrastination and poor self-esteem. One making an argument based on these two phenomena must however be careful to avoid the fallacy of circular cause and consequence. Poverty is a cause of lack of education, but it is not the sole cause, and vice versa.
Third factor C (the common-causal variable) causes both A and B
[edit]The third-cause fallacy (also known as ignoring a common cause[9] or questionable cause[9]) is a logical fallacy in which a spurious relationship is confused for causation. It asserts that X causes Y when in reality, both X and Y are caused by Z. It is a variation on the post hoc ergo propter hoc fallacy and a member of the questionable cause group of fallacies.
All of those examples deal with a lurking variable, which is simply a hidden third variable that affects both of the variables observed to be correlated. That third variable is also known as a confounding variable, with the slight difference that confounding variables need not be hidden and may thus be corrected for in an analysis. Note that the Wikipedia link to lurking variable redirects to confounding. A difficulty often also arises where the third factor, though fundamentally different from A and B, is so closely related to A and/or B as to be confused with them or very difficult to scientifically disentangle from them (see Example 4).
- Example 1
- Sleeping with one's shoes on is strongly correlated with waking up with a headache.
- Therefore, sleeping with one's shoes on causes headache.
The above example commits the correlation-implies-causation fallacy, as it prematurely concludes that sleeping with one's shoes on causes headache. A more plausible explanation is that both are caused by a third factor, in this case going to bed drunk, which thereby gives rise to a correlation. So the conclusion is false.
- Example 2
- Young children who sleep with the light on are much more likely to develop myopia in later life.
- Therefore, sleeping with the light on causes myopia.
This is a scientific example that resulted from a study at the University of Pennsylvania Medical Center. Published in the May 13, 1999, issue of Nature,[10] the study received much coverage at the time in the popular press.[11] However, a later study at Ohio State University did not find that infants sleeping with the light on caused the development of myopia. It did find a strong link between parental myopia and the development of child myopia, also noting that myopic parents were more likely to leave a light on in their children's bedroom.[12][13][14][15] In this case, the cause of both conditions is parental myopia, and the above-stated conclusion is false.
- Example 3
- As ice cream sales increase, the rate of drowning deaths increases sharply.
- Therefore, ice cream consumption causes drowning.
This example fails to recognize the importance of time of year and temperature to ice cream sales. Ice cream is sold during the hot summer months at a much greater rate than during colder times, and it is during these hot summer months that people are more likely to engage in activities involving water, such as swimming. The increased drowning deaths are simply caused by more exposure to water-based activities, not ice cream. The stated conclusion is false.
- Example 4
- A hypothetical study shows a relationship between test anxiety scores and shyness scores, with a statistical r value (strength of correlation) of +.59.[16]
- Therefore, it may be simply concluded that shyness, in some part, causally influences test anxiety.
However, as encountered in many psychological studies, another variable, a "self-consciousness score", is discovered that has a sharper correlation (+.73) with shyness. This suggests a possible "third variable" problem, however, when three such closely related measures are found, it further suggests that each may have bidirectional tendencies (see "bidirectional variable", above), being a cluster of correlated values each influencing one another to some extent. Therefore, the simple conclusion above may be false.
- Example 5
- Since the 1950s, both the atmospheric CO2 level and obesity levels have increased sharply.
- Hence, atmospheric CO2 causes obesity.
Richer populations tend to eat more food and produce more CO2.
- Example 6
- HDL ("good") cholesterol is negatively correlated with incidence of heart attack.
- Therefore, taking medication to raise HDL decreases the chance of having a heart attack.
Further research[17] has called this conclusion into question. Instead, it may be that other underlying factors, like genes, diet and exercise, affect both HDL levels and the likelihood of having a heart attack; it is possible that medicines may affect the directly measurable factor, HDL levels, without affecting the chance of heart attack.
Bidirectional causation: A causes B, and B causes A
[edit]Causality is not necessarily one-way;[dubious – discuss] in a predator-prey relationship, predator numbers affect prey numbers, but prey numbers, i.e. food supply, also affect predator numbers. Another well-known example is that cyclists have a lower Body Mass Index than people who do not cycle. This is often explained by assuming that cycling increases physical activity levels and therefore decreases BMI. Because results from prospective studies on people who increase their bicycle use show a smaller effect on BMI than cross-sectional studies, there may be some reverse causality as well. For example, people with a lower BMI may be more likely to want to cycle in the first place. [18]
The relationship between A and B is coincidental
[edit]The two variables are not related at all, but correlate by chance. The more things are examined, the more likely it is that two unrelated variables will appear to be related. For example:
- The result of the last home game by the Washington Commanders prior to the presidential election predicted the outcome of every presidential election from 1936 to 2000 inclusive, despite the fact that the outcomes of football games had nothing to do with the outcome of the popular election. This streak was finally broken in 2004 (or 2012 using an alternative formulation of the original rule).
- The Mierscheid law, which correlates the Social Democratic Party of Germany's share of the popular vote with the size of crude steel production in Western Germany.
- Alternating bald–hairy Russian leaders: A bald (or obviously balding) state leader of Russia has succeeded a non-bald ("hairy") one, and vice versa, for nearly 200 years.
- The Bible code, Hebrew words predicting historical events supposedly hidden within the Torah: the huge number of combinations of letters makes appearances of any word in sufficiently lengthy text statistically insignificant.
Use of correlation as scientific evidence
[edit]Much of scientific evidence is based upon a correlation of variables[19] that are observed to occur together. Scientists are careful to point out that correlation does not necessarily mean causation. The assumption that A causes B simply because A correlates with B is not accepted as a legitimate form of argument.
However, sometimes people commit the opposite fallacy of dismissing correlation entirely. That would dismiss a large swath of important scientific evidence.[19] Since it may be difficult or ethically impossible to run controlled double-blind studies to address certain questions, correlational evidence from several different angles may be useful for prediction despite failing to provide evidence for causation. For example, social workers might be interested in knowing how child abuse relates to academic performance. Although it would be unethical to perform an experiment in which children are randomly assigned to receive or not receive abuse, researchers can look at existing groups using a non-experimental correlational design. If in fact a negative correlation exists between abuse and academic performance, researchers could potentially use this knowledge of a statistical correlation to make predictions about children outside the study who experience abuse even though the study failed to provide causal evidence that abuse decreases academic performance.[20] The combination of limited available methodologies with the dismissing correlation fallacy has on occasion been used to counter a scientific finding. For example, the tobacco industry has historically relied on a dismissal of correlational evidence to reject a link between tobacco smoke and lung cancer,[21] as did biologist and statistician Ronald Fisher (frequently on the industry's behalf).[list 1]
Correlation is a valuable type of scientific evidence in fields such as medicine, psychology, and sociology. Correlations must first be confirmed as real, and every possible causative relationship must then be systematically explored. In the end, correlation alone cannot be used as evidence for a cause-and-effect relationship between a treatment and benefit, a risk factor and a disease, or a social or economic factor and various outcomes. It is one of the most abused types of evidence because it is easy and even tempting to come to premature conclusions based upon the preliminary appearance of a correlation.[21]
See also
[edit]- Affirming the consequent – Type of fallacious argument (logical fallacy)
- Alignments of random points – Phenomenon in statistics
- Anecdotal evidence – Evidence relying on personal testimony
- Apophenia – Tendency to perceive connections between unrelated things
- Post hoc analysis – Statistical analyses that were not specified before the data were seen
- Multiple comparisons problem – Statistical interpretation with many tests
- Look-elsewhere effect – Statistical analysis phenomenon
- Data dredging – Misuse of data analysis
- Testing hypotheses suggested by the data – Problem of circular reasoning in statistics
- Bible code – Purported set of secret messages encoded within the Hebrew text of the Torah
- Bradford Hill criteria
- Coincidence#Causality – Concurrence of events with no connection
- Confounding – Variable or factor in causal inference
- Confusion of the inverse – Logical fallacy
- French paradox – Observation that amount heart diseases French people have is much less than is expected
- Design of experiments – Design of tasks
- Joint effect – Apparent, but false, correlation between causally-independent variables
- Mediation (statistics) – Statistical model
- Normally distributed and uncorrelated does not imply independent
- Pirates and global warming – Satirical deity
- Reproducibility – Aspect of scientific research
- Spurious relationship – Apparent, but false, correlation between causally-independent variables
- Teleology – Thinking in terms of destiny or purpose
References
[edit]- ^ Tufte 2006, p. 5
- ^ Aldrich, John (1995). "Correlations Genuine and Spurious in Pearson and Yule" (PDF). Statistical Science. 10 (4): 364–376. doi:10.1214/ss/1177009870. JSTOR 2246135.
- ^ "Sufficient". Wolfram. 2019-12-02. Retrieved 2019-12-03.
- ^ Rohlfing, Ingo; Schneider, Carsten Q. (2018). "A Unifying Framework for Causal Analysis in Set-Theoretic Multimethod Research" (PDF). Sociological Methods & Research. 47 (1): 37–63. doi:10.1177/0049124115626170. S2CID 124804330. Retrieved 29 February 2020.
- ^ Brady, Henry E. (7 July 2011). "Causation and Explanation in Social Science". The Oxford Handbook of Political Science. doi:10.1093/oxfordhb/9780199604456.013.0049. Retrieved 29 February 2020.
- ^ Naveed Sattar; David Preiss (13 Jun 2017). "Reverse Causality in Cardiovascular Epidemiological Research". Circulation. 135 (24): 2369–2372. doi:10.1161/CIRCULATIONAHA.117.028307. PMID 28606949.
- ^ Richard Doll; Richard Peto; Jillian Boreham; Isabelle Sutherland (24 Jun 2004). "Mortality in relation to smoking: 50 years' observations on male British doctors". The BMJ. 328 (7455): 1239–49. doi:10.1136/bmj.38142.554479.AE. PMC 437139. PMID 15213107.
- ^ Willingham, Emily. "Of lice and men: An itchy history". Scientific American Blog Network. Retrieved 2019-02-26.
- ^ a b Labossiere, M.C., Dr. LaBossiere's Philosophy Pages Archived 2009-05-22 at the Wayback Machine
- ^ Quinn, Graham E.; Shin, Chai H.; Maguire, Maureen G.; Stone, Richard A. (May 1999). "Myopia and ambient lighting at night". Nature. 399 (6732): 113–114. Bibcode:1999Natur.399..113Q. doi:10.1038/20094. PMID 10335839. S2CID 4419645.
- ^ CNN, May 13, 1999. Night-light may lead to nearsightedness
- ^ Ohio State University Research News, March 9, 2000. Night lights don't lead to nearsightedness, study suggests Archived 2006-09-01 at the Wayback Machine
- ^ Zadnik, Karla; Jones, Lisa A.; Irvin, Brett C.; Kleinstein, Robert N.; Manny, Ruth E.; Shin, Julie A.; Mutti, Donald O. (2000). "Vision: Myopia and ambient night-time lighting". Nature. 404 (6774): 143–144. Bibcode:2000Natur.404..143Z. doi:10.1038/35004661. PMID 10724157. S2CID 4399332.
- ^ Gwiazda, J.; Ong, E.; Held, R.; Thorn, F. (2000). "Vision: Myopia and ambient night-time lighting". Nature. 404 (6774): 144. Bibcode:2000Natur.404..144G. doi:10.1038/35004663. PMID 10724158.
- ^ Stone, Richard A.; Maguire, Maureen G.; Quinn, Graham E. (2000). "Vision: reply: Myopia and ambient night-time lighting". Nature. 404 (6774): 144. Bibcode:2000Natur.404..144S. doi:10.1038/35004665. PMID 10724158.
- ^ Carducci, Bernardo J. (2009). The Psychology of Personality: Viewpoints, Research, and Applications (2nd ed.). John Wiley & Sons. ISBN 978-1-4051-3635-8.
- ^ Ornish, Dean. "Cholesterol: The good, the bad, and the truth" [1] (retrieved 3 June 2011)
- ^ Dons, E (2018). "Transport mode choice and body mass index: Cross-sectional and longitudinal evidence from a European-wide study" (PDF). Environment International. 119 (119): 109–116. doi:10.1016/j.envint.2018.06.023. hdl:10044/1/61061. PMID 29957352. S2CID 49607716.
- ^ a b Novella (18 November 2009). "Evidence in Medicine: Correlation and Causation". Science and Medicine. Science-Based Medicine.
- ^ Nielsen, Michael (2012-01-23). "If correlation doesn't imply causation, then what does? | DDI". Michaelnielsen.org. Retrieved 2017-10-08.
- ^ a b "Evidence in Medicine: Correlation and Causation – Science-Based Medicine". Sciencebasedmedicine.org. 2009-11-18. Retrieved 2017-10-08.
- ^ Silver, Nate (2015), The Signal and the Noise: Why So Many Predictions Fail – But Some Don't (2nd ed.), New York: Penguin Books, pp. 254–255
- ^ Fisher, Ronald (July 6, 1957), "Dangers Of Cigarette-Smoking", The British Medical Journal, 2 (5035), London: British Medical Association: 43, doi:10.1136/bmj.2.5035.43, JSTOR 25383068, PMC 1961750
- ^ Fisher, Ronald (August 3, 1957), "Dangers Of Cigarette-Smoking", The British Medical Journal, 2 (5039), London: British Medical Association: 297–298, doi:10.1136/bmj.2.5039.297-b, JSTOR 25383439, PMC 1961712
- ^ Fisher, Ronald (1958), "Cigarettes, Cancer, and Statistics" (PDF), The Centennial Review of Arts & Science, 2, East Lansing, Michigan: Michigan State University Press: 151–166, archived (PDF) from the original on 2022-10-09
- ^ Fisher, Ronald (1958), "The Nature of Probability" (PDF), The Centennial Review of Arts & Science, 2, East Lansing, Michigan: Michigan State University Press: 261–274, archived (PDF) from the original on 2022-10-09
- ^ Fisher, Ronald (July 12, 1958), "Lung Cancer and Cigarettes" (PDF), Nature, 182 (4628), London: Nature Publishing Group: 108, Bibcode:1958Natur.182..108F, doi:10.1038/182108a0, PMID 13566198, archived (PDF) from the original on 2022-10-09
- ^ Fisher, Ronald (August 30, 1958), "Cancer and Smoking" (PDF), Nature, 182 (4635), London: Nature Publishing Group: 596, Bibcode:1958Natur.182..596F, doi:10.1038/182596a0, PMID 13577916, archived (PDF) from the original on 2022-10-09
- Bundled references
Bibliography
[edit]- Beebee, Helen; Hitchcock, Christopher; Menzies, Peter (2009). The Oxford Handbook of Causation. Oxford University Press. ISBN 978-0-19-162946-4.
- Tufte, Edward R. (2006). The Cognitive Style of PowerPoint: Pitching Out Corrupts Within (2nd ed.). Cheshire, Connecticut: Graphics Press. ISBN 978-0-9613921-5-4.