View source for Correlation does not imply causation

{{Short description|Refutation of a logical fallacy}}
The phrase "'''correlation does not imply causation'''" refers to the inability to legitimately deduce a [[Causality|cause-and-effect]] relationship between two events or  variables solely on the basis of an observed association or [[Correlation|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 }}</ref> The idea that "correlation implies causation" is an example of a [[Philosophy: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 ''[[Philosophy:Post hoc ergo propter hoc|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 [[Philosophy:Conflation|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 [[Philosophy: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|convergent cross mapping]]. The [[Philosophy:Bradford Hill criteria|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==

=== "Imply"===
In casual use, the word "implies" loosely means ''suggests'', rather than ''requires''. However, in [[Logic|logic]], the technical use of the word "implies" means "is a ''sufficient condition'' for."<ref name="sufficient">{{cite web
 |url=http://mathworld.wolfram.com/Sufficient.html
 |title=Sufficient
 |date=2019-12-02
 |website=Wolfram
 |access-date=2019-12-03
 }}</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|material conditional]]: ''if p then q'' symbolized as ''p&nbsp;→&nbsp;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"===
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).

If 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. Correlation is often used to infer causation because it is a ''necessary'' condition: that is, if A causes B, then A and B must necessarily be correlated. However it is not a ''sufficient'' condition.

[[File:Illiterate Dinos.jpg|thumb|upright|Dinosaur illiteracy and extinction may be correlated, but that would not mean the variables had a causal relationship.]]

==Causal analysis==
{{excerpt|Causal analysis}}

==Examples of illogically inferring causation from correlation==
===B causes A (reverse causation or reverse causality)===
'''Reverse causation''' or '''reverse causality''' or '''wrong direction''' is an [[Informal fallacy|informal fallacy]] of [[Philosophy:Questionable cause|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
:Subjects with low cholesterol correlate with an increase in mortality.
:Therefore, low cholesterol increases your risk of mortality.
It is the other way around since the disease, such as cancer, causes a low cholesterol because of a myriad of factors, such as weight loss, and 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>
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.

'''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 [[Engineering:Television|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|confusion of the inverse]]''). Indeed, in the [[Social:Social science|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/[[Finance:Signalling (economics)|signaling]] and [[Social:Human capital|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 [[History:Middle Ages|Middle Ages]] believed that [[Medicine: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 [[Medicine:Fever|fever]], makes the lice look for another host. The medical [[Physics:Thermometer|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>

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===
{{Main|Spurious relationship}}

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|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 ''[[Philosophy:Post hoc ergo propter hoc|post hoc ergo propter hoc]]'' fallacy and a member of the [[Philosophy:Questionable cause|questionable cause]] group of fallacies.

All of those examples deal with a lurking variable, which is simply a hidden third variable that affects both causes of the correlation. 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 [[Medicine:Myopia|myopia]] in later life.
:Therefore, sleeping with the light on causes myopia.

This is a scientific example that resulted from a study at the [[Organization:University of Pennsylvania|University of Pennsylvania]] Medical Center. Published in the May 13, 1999, issue of ''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 [[Organization:Ohio State University|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.<ref>[[Organization:Ohio State University|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.

;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.<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>
: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 "[[Correlation does not imply causation#A causes B and B causes A (bidirectional causation)|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 [[Chemistry:Carbon dioxide|CO<sub>2</sub>]] level and obesity levels have increased sharply.
:Hence, atmospheric CO<sub>2</sub> causes obesity.

Richer populations tend to eat more food and produce more CO<sub>2</sub>.

;Example 6
:[[Medicine:High-density lipoprotein|HDL]] ("good") [[Chemistry:Cholesterol|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<ref>Ornish, Dean. "Cholesterol: The good, the bad, and the truth" [http://www.huffingtonpost.com/dr-dean-ornish/cholesterol-the-good-the-_b_870655.html] (retrieved 3 June 2011)</ref> 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===
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 [[Earth: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
  | last = Dons
  | first = E
  | title = Transport mode choice and body mass index: Cross-sectional and longitudinal evidence from a European-wide study
  | journal = Environment International
  | volume =  119
 | issue = 119
  | pages = 109–116
 | year = 2018
  | doi =  10.1016/j.envint.2018.06.023
  | pmid = 29957352
| hdl = 10044/1/61061
 | s2cid = 49607716
 | url = http://spiral.imperial.ac.uk/bitstream/10044/1/61061/2/Dons2018%20preprint_BMI.pdf
  | hdl-access = free
  }}</ref>

===The relationship between A and B is coincidental===
{{Main|Spurious relationship}}

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 [[Philosophy:Bald–hairy|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 [[Unsolved:Bible code|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==
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 often 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.<ref name="Steven"/> Since it may be difficult or ethically impossible to run controlled double-blind studies, 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? &#124; 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 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 [[Biography:Ronald Fisher|Ronald Fisher]] (frequently on the industry's behalf).{{refn|group=list|name=Fisher refs|<ref>{{Citation|last=Silver|first=Nate|title=The Signal and the Noise: Why So Many Predictions Fail – But Some Don't|publisher=Penguin Books|place={{wipe|New York City}}|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=[[Medicine:The BMJ|The British Medical Journal]]|volume=2|issue=5035|publisher=British Medical Association|place=[[Place:London|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=[[Medicine:The BMJ|The British Medical Journal]]|volume=2|issue=5039|publisher=British Medical Association|place=[[Place:London|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|volume=182|issue=4628|publisher=[[Company:Nature Publishing Group|Nature Publishing Group]]|place=[[Place:London|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|volume=182|issue=4635|publisher=[[Company:Nature Publishing Group|Nature Publishing Group]]|place=[[Place:London|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>}}

Correlation is a valuable type of [[Scientific evidence|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"/>

==See also==
*{{annotated link|Philosophy:Affirming the consequent}}
*{{annotated link|Astronomy:Alignments of random points}}
*{{annotated link|Anecdotal evidence}}
*{{annotated link|Apophenia}}
**{{annotated link|Post hoc analysis}}
**{{annotated link|Multiple comparisons problem}}
**{{annotated link|Look-elsewhere effect}}
**{{annotated link|Data dredging}}
**{{annotated link|Testing hypotheses suggested by the data}}
*{{annotated link|Unsolved:Bible code}}
* [[Philosophy:Bradford Hill criteria|Bradford Hill criteria]]
*{{annotated link|Confounding}}
*{{annotated link|Confusion of the inverse}}
*{{annotated link|Medicine:French paradox}}
*{{annotated link|Design of experiments}}
*{{annotated link|Mediation (statistics)}}
*{{annotated link|Reproducibility}}
*{{annotated link|Spurious relationship}}
*{{annotated link|Philosophy:Teleology}}

==References==
{{Reflist|30em}}

; Bundled references
{{reflist|group=list}}

===Bibliography===
* {{cite book|last1=Beebee|first1=Helen|last2=Hitchcock|first2=Christopher|last3=Menzies|first3=Peter|title=The Oxford Handbook of Causation|url=https://books.google.com/books?id=yWWEIvNgUQ4C|year=2009|publisher=Oxford University Press|isbn=978-0-19-162946-4}}
* {{Cite book|last=Tufte |first=Edward R. |title=The Cognitive Style of PowerPoint: Pitching Out Corrupts Within |publisher=Graphics Press |location=Cheshire, Connecticut |year=2006|edition=2nd|isbn=978-0-9613921-5-4 |url=http://www.edwardtufte.com/tufte/powerpoint}}

{{Fallacies}}

{{DEFAULTSORT:Correlation Does Not Imply Causation}}
[[Category:Causal fallacies]]
[[Category:Causal inference]]
[[Category:Covariance and correlation]]

{{Sourceattribution|Correlation does not imply causation}}