Correlation does not imply causation

[[File:Variable interactions.png|thumb|right|It could be causal. Or it could be any of these.]]
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[[File:Correlations not causally related.png|thumb|right|6 examples of correlation not implying causation.]]
{{cquote|I used to think I could [[Psychic|control ducks with my mind]] but it turns out ducks & I just have very similar ideas about what stuff ducks should do.|||Jacy Catlin<ref>https://twitter.com/ieatanddrink/status/709590592293113858</ref>}}
'''Correlation does not imply causation''' is the logically valid idea that events which [[Coincidence|coincide]] with each other are not necessarily [[Causality|caused]] by each other. The form of [[logical fallacy|fallacy]] that it addresses is known as ''[[post hoc, ergo propter hoc]]''. For example: Both vaccination rates and [[autism]] rates are rising (perhaps even correlated), [[Anti-vaccination movement#Autism|but that does not mean that vaccines cause autism any more than it means that autism causes vaccines]]. The [[reality]] is that cause and effect can be indirect due to a third factor known as a [[confounding variable]] — or that causality can be the reverse of what is assumed.

The assumption of causation is false when the only evidence available is simple correlation. However: It is not true that correlation ''cannot'' imply causation. (Obviously, if two things have no correlation, then it is near impossible for one to cause the other.) In a [[Control group|controlled]] [[Scientific method|scientific]] [[experiment]], causation can be teased out of a correlation by removing all possible confounding variables. (Often, several identical experiments are run with different levels of the experimental variable, such as temperature or drug dosage.) If there's still a correlation, then causation is very, very likely.

==Explanations and examples==
[[File:Autism Causes Vaccines.png|thumb|right|More logical than the converse, indeed. ([http://smbc-comics.com/index.php?id=4033 Source])]]
[[File:5G causes Coronavirus.jpeg|thumb|right|5G causes… Taco Bell?]]
For any given correlation, there are four basic possibilities. Let's assume that autism rates are correlated with vaccination rates:
#It's genuinely causal: [X] causes [Z]. (Vaccination cause autism.)
#The causality is reversed: [Z] causes [X]. (Autism causes vaccination.)
#A confounding variable is the cause: [X] is correlated with [Z]. [Y] (a confounding variable) is the true cause of [Z]. However, [Y] is highly correlated with [X] — making it appear as though [X] is the cause. (Both vaccination rates and the willingness of doctors to diagnose autism have risen over the years [not to mention that autism was not even named until 1910, albeit only as a symptom of [[schizophrenia]] at first, after [[Louis Pasteur]] introduced the second generation of vaccines].<ref group=note>Autism, once seen as utterly debilitating, has become more accepted and very widely known. In addition, the medical definition of autism has become broader over the years.</ref> This willingness explains most of the rise in autism rates.)
#It is simply [[coincidence]] or a statistical fluke (rare, but it does happen). (The [[Moon]] is just far enough away to be the same size as the [[Sun]] in the sky because it had to be somewhere.)

===Simple example===
{{cquote|100% of people who drink water die.|||Someone}}
Two events can consistently correlate with each other but not have any causal relationship. An example is the relationship between reading ability and shoe size across the whole population of the [[United States]]. If someone performed such a survey, they would find that the larger shoe sizes correlate with better reading ability, but this does not mean large shoes ''cause'' good reading skills. Instead, it's caused by the fact that young [[children]] have small feet and have not yet (or only recently) been taught to read. In this case, the two variables are more accurately correlated with a third: age.{{Nofact}}

The part age plays in this example is known as a "[[confounding variable]]" or "confounding factor", and is something that is not being controlled for in the [[experiment]]. In this case, age influences both reading ability and shoe size quite directly. A confounding variable can be what the actual cause of a correlation is, hence any studies must take these into account and find ways of dealing with them, usually by searching them out and trying to alter this variable directly.

The most common method to control confounding variables is with controlled studies. In these studies, the differences between the observations and the [[control group]] are minimised as best as possible, so that one can be more confident that a correlation is a valid indicator of causation. This is extremely important in compensating for the [[placebo effect]] in medical trials, but it is also important in other branches of [[science]]. In the age/shoe-size/reading-ability example, a controlled experiment would look for a correlation between reading ability and shoe size given a sample of people all the same age — or alternatively, the [[hypothesis]] could be further tested by correlating age and reading ability given a sample of similar shoe size.

===Risk factor===
The term "[[risk]] factor" is used in [[medicine]] to mean "something that is positively correlated". For instance, [[obesity]] is a risk factor for Type 2 diabetes. The term is often incorrectly understood to mean "cause" (e.g. "I'm at risk for diabetes? But I'm not fat!"). Alternatively, a clear risk factor can be disputed on the basis that it's not a definitive cause — a classic use of the [[uncertainty tactic]] (e.g. "I [[Tobacco smoking|smoke three packs a day]] and I don't have [[cancer]]!").

Even when there is a correlation, the risk factor does not necessarily go both ways: obesity is a risk for Type 2 diabetes, but untreated diabetes can, in certain situations, cause weight loss, as excess glucose is excreted in urine.<ref>{{cite web |url=http://www.mayoclinic.org/diseases-conditions/type-2-diabetes/basics/symptoms/con-20031902 |title=Type 2 diabetes: Symptoms and causes |author=Mayo Clinic Staff}}</ref> In other words, correlation combined with a specific temporal relationship does, in fact, imply causation.{{Citation needed}}{{efn|"Implying" causation is not meant to mean proving causation. However, when two things are correlated and one frequently precedes the other, that is evidence in favor of causation.}} Taking insulin can cause weight gain, as the previously wasted [[sugar]]s can now be metabolized, but that risk factor correlates to the treatment, not the [[disease]].<ref>[http://www.mayoclinic.org/diseases-conditions/diabetes/in-depth/insulin-and-weight-gain/art-20047836 Insulin and weight gain: Keep the pounds off]</ref>

===In science===
{{cquote|Correlation does not imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing "look over there."|||xkcd<ref>[http://xkcd.com/552/ xkcd — Correlation]</ref>}}
In science, correlation studies are often used to test for the existence of interesting patterns, but they are never used exclusively to claim a cause. In order to make a causal claim, you must run an experiment or series of experiments and further studies using the [[scientific method]] — i.e., test to see if it really is a cause by altering parameters and performing more experiments, making predictions and testing them. This is in order to validate that one event is indeed directly influencing the other and is the reason behind the detected correlation.  

Many [[woo]] and [[pseudoscience]] pushers conflate correlation with causation in order to make a claim of validity, but forget to attempt the later scientific steps of compensating for confounding variables and thoroughly testing the causal relationship. For example, if someone gets a cold, but takes [[Vitamin C|Vitamin C]], their cold will go away. The claim is then made that the Vitamin C caused the cold to go away. However, the cold [[Regression to the mean|would have gone away anyway]], whether or not the Vitamin C was taken, and so the validity of the claim is false. The [[placebo effect]] is another correlation with "treatment" that [[quack]]s use to create false validity. 

Correlations seem to tap into a deep part of human psychology. As [[pattern recognition]] machines, we are hyper-responsive to any potential [[signal detection theory|signal]] in our environment. People will often take two completely unrelated events and decide that they must cause each other because they seem to correlate. Someone may decide that when she wears a given shirt, she has good luck; this is often combined with a powerful [[confirmation bias]] to create [[magical thinking]] and [[superstition]].

===In parody===
[[File:Organicautism.png|thumb|left|Autism rates compared with [[organic food]] sales. Definitive proof that autism is caused by organic food?]][[File:PiratesVsTemp.png|thumb|Left|fighting piracy = global warming]]
[[File:Heatmap.png|thumb|left|Our site's users are [[Furry fandom|furries]]]]
[[File:NickCage.jpeg|thumb|right|Nicholas Cage movies cause deaths{{fact|joke}}]]
In the "Church of the [[Flying Spaghetti Monster]]", a key "belief" is that [[global warming]] is caused by a lack of pirates (not the modern kind, like in [[Somalia]], but the old-timey swashbuckling kind) sailing the oceans. This is shown by a graph correlating increasing surface temperatures of the [[Earth]] with a decline in the number of pirates.<ref>Church of the Flying Spaghetti Monster: [http://www.venganza.org/about/open-letter/ Open Letter To Kansas School Board]</ref> While it is certainly true that piracy has decreased and temperatures have gone up, there is nothing directly connecting the two trends. ''Or is there?''

==Fallacy engineering==
[[File:Correlation of correlation and causation.png|thumb|right|While correlation is only weakly correlated with causation, causation typically causes correlation.]]
Care should be taken not to assume that the opposite is impossible (that correlation ''never'' implies causation). Correlations implying causations are successfully postulated and tested every day. Most scientific theories would not exist without this particular process of the scientific method.

Woo spinners, when cornered and on the defensive, may try to claim that correlation never implies causation, in order to avoid [[statistical]] analysis (where the correlation's implication of causation is ''demonstrated''). They ignore the scientific analysis by claiming that correlation doesn't imply causation with an effortless [[handwave]]. By arguing this, they are arguing that they know the [[truth]] without any [[Evidence|evidential]] support, and your number magic be damned!

For example, when presented with evidence that use of a vaccine is followed by an ''almost complete'' reduction in infection rate, [[Anti-vaccination movement|anti-vaccine proponents]] often discount this change as mere correlation — which ignores the sound methodology, control of variables, extremely low probability that this is merely an extreme example (low ''p''-values), and generally clear-cut evidence that correlation is totally linked to a causal chain. Ironically, the antivaxers often, after casting doubt on this method, use that very method themselves (only without the hard work neccessary to support their case). They may cite their own statistics that show an increase of cases of [[autism]] (or some other terror ''du jour'') when a vaccine is introduced. If they search long enough, [[Anecdotal evidence|they may find some place at some time where this happened]] and then use this example as representative of everywhere always.

This tactic is also often used by [[climate change]] deniers ("the ''highly'' statistically significant association of greenhouse gases and global temperature does not imply causation") as well as every type of woo spinner you can imagine (shockingly including even some economists and scientists).

===In a nutshell===
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[[File:XKCD causation does not imply causation.png|center|frame|Maybe...]]
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==See also==

*[[Ecological fallacy]]
*[[Confusion of the inverse]]
*''[[Post hoc, ergo propter hoc]]''
*[[Freakonomics]]
*[[Essay:CAM Statistics]]

==External links==
*[https://tylervigen.com/ Spurious Correlations]
*[https://web.archive.org/web/20111129012141/http://dilbert.com/strips/comic/2011-11-28/ Dilbert, November 28, 2011]
*[https://slate.com/news-and-politics/2013/07/warm-weather-homicide-rates-when-ice-cream-sales-rise-homicides-rise-coincidence.html "When Ice Cream Sales Rise, So Do Homicides. Coincidence, or Will Your Next Cone Murder You?", ''Slate'']

==Notes==
{{reflist|group=note}}

==References==
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[[Category:Causation fallacies]]
[[Category:Philosophy of science]]
[[Category:Statistics]]
[[Category:Clichéed sayings]]

Categories: Causation fallacies, Philosophy of science, Statistics, Clichéed sayings