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| | Hello! Allow me to start by saying my name - Kraig. For years she's been working as a cashier. The favorite hobby for her and her kids is collecting kites and is actually trying to create it a line of work. Texas has always been my family home. I'm useless at webdesign but you need to check my website: http://rayj5764.jimdo.com<br><br>my website :: forum ([http://rayj5764.jimdo.com linked internet page]) |
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| [[File:PiratesVsTemp(en).svg|thumb|300px|A chart that, according to [[Flying Spaghetti Monster|Bobby Henderson]], correlates the number of pirates with global temperature. The two variables are correlated, but one does not imply the other|alt=chart showing that in 1820 there were 25,000 pirates and the global average temperature was 14.2 degrees C, while in 2000 there were 17 pirates and the global average temperature was 15.9 degrees C.]]
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| '''Correlation does not imply causation''' is a phrase in [[science]] and [[statistics]] that emphasizes that a [[Correlation and dependence|correlation]] between two variables does not necessarily imply that one [[causality|causes]] the other.<ref name="Tufte 2006 5">{{Cite journal|last=Tufte |first=Edward R. |authorlink=Edward Tufte |title=The Cognitive Style of PowerPoint: Pitching Out Corrupts Within |publisher=[[Graphics Press]] |location=[[Cheshire, Connecticut]] |year=2006 |pages=5 |isbn=0-9613921-5-0 |url=http://www.edwardtufte.com/tufte/powerpoint}}</ref><ref>{{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 |url=http://www.economics.soton.ac.uk/staff/aldrich/spurious.pdf |jstor=2246135 |doi= 10.1214/ss/1177009870 |issue=4}}</ref> Many [[statistical tests]] calculate correlation between [[Variable (mathematics)|variables]]. A few go further and calculate the likelihood of a true causal relationship; examples are the [[Granger causality]] test and [[convergent cross mapping]].
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| The counter assumption, that ''correlation proves causation'', is considered a [[questionable cause]] [[Fallacy#logical|logical fallacy]] in that two events occurring ''together'' are taken to have a cause-and-effect relationship. This fallacy is also known as ''cum hoc ergo propter hoc'', Latin for "with this, therefore because of this", and "false cause". A similar fallacy, that an event that follows another was [[Logical consequence|necessarily a consequence]] of the first event, is sometimes described as ''[[post hoc ergo propter hoc]]'' ([[Latin]] for "after this, therefore because of this").
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| In a widely studied example, numerous [[epidemiological study|epidemiological studies]] showed that women who were taking combined [[Hormone replacement therapy (menopause)|hormone replacement therapy]] (HRT) also had a lower-than-average incidence of [[coronary heart disease]] (CHD), leading doctors to propose that HRT was protective against CHD. But [[randomized controlled trials]] showed that HRT caused a small but statistically significant ''increase'' in risk of CHD. Re-analysis of the data from the epidemiological studies showed that women undertaking HRT were more likely to be from higher [[socio-economic group]]s ([[NRS social grade|ABC1]]), with better-than-average diet and exercise regimens. The use of HRT and decreased incidence of coronary heart disease were coincident effects of a common cause (i.e. the benefits associated with a higher socioeconomic status), rather than cause and effect, as had been supposed.<ref>{{cite journal |author=Lawlor DA, Davey Smith G, Ebrahim S |title=Commentary: the hormone replacement-coronary heart disease conundrum: is this the death of observational epidemiology? |journal=Int J Epidemiol |volume=33 |issue=3 |pages=464–7 |year=2004 |month=June |pmid=15166201 |doi=10.1093/ije/dyh124}}</ref>
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| As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not imply that the resulting conclusion is false. In the instance above, if the trials had found that hormone replacement therapy caused a decrease in coronary heart disease, but not to the degree suggested by the epidemiological studies, the assumption of causality would have been correct, although the logic behind the assumption would still have been flawed.
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| ==Usage==
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| In [[logic]], the technical use of the word "implies" means "to be a ''[[Sufficient condition|sufficient]]'' circumstance". This 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 this sense, it is always correct to say "Correlation does not ''imply'' causation."
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| However, in casual use, the word "imply" loosely means ''suggests'' rather than ''requires''. The idea that correlation and causation are connected is certainly true; where there is causation, there is a likely correlation. Indeed, correlation is used when inferring causation; the important point is that such inferences are made after correlations are confirmed as real and all causational relationship are systematically explored using large enough data sets.
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| [[Edward Tufte]], in a criticism of the brevity of "correlation does not imply causation", deprecates the use of "is" to relate correlation and causation (as in "Correlation is not causation"), citing its inaccuracy as incomplete.<ref name="Tufte 2006 5"/> While it is not the case that correlation is causation, simply stating their nonequivalence omits information about their relationship. Tufte suggests that the shortest true statement that can be made about causality and correlation is one of the following:<ref>{{cite book|last=Tufte|first=Edward R.|authorlink=Edward Tufte|title=The Cognitive Style of PowerPoint|url=http://books.google.com/?id=3oNRAAAAMAAJ&q=%22Empirically+observed+covariation%22+necessary&dq=%22Empirically+observed+covariation%22+necessary|year=2003|publisher=Graphics Press|location=Cheshire, Connecticut|isbn=0-9613921-5-0|page=4}}</ref>
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| *"Empirically observed covariation is a necessary but not sufficient condition for causality."
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| *"Correlation is not causation but it sure is a hint."
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| ==General pattern==
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| For any two correlated events A and B, the following relationships are possible:
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| *A causes B;
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| *B causes A;
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| *A and B are consequences of a common cause, but do not cause each other;
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| *There is no connection between A and B; the correlation is coincidental.
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| Less clear-cut correlations are also possible. For example, causality is not necessarily one-way; in a [[Predation|predator-prey relationship]], predator numbers affect prey, but prey numbers, i.e. food supply, also affect predators.
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| The ''cum hoc ergo propter hoc'' logical fallacy can be expressed as follows:
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| # ''A'' occurs in correlation with ''B''.
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| # Therefore, ''A'' causes ''B''.
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| In this type of logical fallacy, one makes a premature conclusion about [[causality]] after observing only a [[correlation]] between two or more factors. Generally, if one factor (''A'') is observed to only be correlated with another factor (''B''), it is sometimes taken for granted that ''A'' is causing ''B'', even when no evidence supports it. This is a logical fallacy because there are at least five possibilities:
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| # ''A'' may be the cause of ''B''.
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| # ''B'' may be the cause of ''A''.
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| # some unknown third factor ''C'' may actually be the cause of both ''A'' and ''B''.
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| # there may be a combination of the above three relationships. For example, ''B'' may be the cause of ''A'' at the same time as ''A'' is the cause of ''B'' (contradicting that the only relationship between ''A'' and ''B'' is that ''A'' causes ''B''). This describes a [[self-reinforcement|self-reinforcing]] system.
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| # the "relationship" is a [[coincidence]] or so complex or indirect that it is more effectively called a coincidence (i.e. two events occurring at the same time that have no direct relationship to each other besides the fact that they are occurring at the same time). A larger [[sample size]] helps to reduce the chance of a coincidence, unless there is a [[systematic error]] in the experiment.
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| In other words, 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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| ==Examples of illogically inferring causation from correlation==
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| {{No footnotes|section|date=July 2012}}
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| ===B causes A (reverse causation)===
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| ;Example 1
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| :The faster windmills are observed to rotate, the more wind is observed to be.
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| :Therefore wind is caused by the rotation of windmills. (Or, simply put: windmills, as their name indicates, are machines used to produce wind.)
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| 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 doesn’t 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.
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| ===A and B cause C, which causes D (string of causation)===
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| :Lack of religion is associated with increased rates of depression. | |
| :Therefore, lack of religion directly causes increased rates of depression.
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| In this example, the correlation between lack of religion and depression does not imply that lack of religion causes depression. Depression is caused in part by how people are treated. Some cultures might be suspicious of people who have a lack of religion, so people who have a lack of religion are more likely to be discriminated against and to fall into depression. So the above conclusion is false.
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| ===A causes B and B causes A (bidirectional causation)===
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| :Increased pressure is associated with increased temperature.
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| :Therefore pressure causes temperature.
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| The [[ideal gas law]], <math>PV=nRT</math>, describes the direct relationship between pressure and temperature (along with other factors) to show that there is a direct correlation between the two properties. For a fixed volume and mass of gas, an increase in temperature causes an increase in pressure; likewise, increased pressure causes an increase in temperature. This demonstrates bidirectional causation. The conclusion that pressure causes temperature is true but is not logically guaranteed by the premise.
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| ===Third factor C (the common-causal variable) causes both A and B===
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| {{Main|Spurious relationship}}
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| All these examples deal with a [[lurking variable]], which is simply a hidden third variable that affects both causes of the correlation; for example, the fact that it is summer in Example 3. 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
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| :[[Sleeping]] with one's [[shoes]] on is strongly correlated with waking up with a [[headache]].
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| :Therefore, sleeping with one's shoes on causes headache.
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| 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 [[Drunkenness|drunk]], which thereby gives rise to a correlation. So the conclusion is false.
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| ;Example 2
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| :Young children who sleep with the light on are much more likely to develop [[myopia]] in later life.
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| :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 |author=Quinn GE, Shin CH, Maguire MG, Stone RA |title=Myopia and ambient lighting at night |journal=Nature |volume=399 |issue=6732 |pages=113–4 |year=1999 |month=May |pmid=10335839 |doi=10.1038/20094}}</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]</ref><ref>{{cite journal |author=Zadnik K, Jones LA, Irvin BC, ''et al.'' |title=Myopia and ambient night-time lighting |journal=Nature |volume=404 |issue=6774 |pages=143–4 |year=2000 |month=March |pmid=10724157 |doi=10.1038/35004661}}</ref><ref>{{cite journal |author=Gwiazda J, Ong E, Held R, Thorn F |title=Myopia and ambient night-time lighting |journal=Nature |volume=404 |issue=6774 |pages=144 |year=2000 |month=March |pmid=10724158 |doi=10.1038/35004663}}</ref><ref>{{Cite journal|journal=Nature|year=2000|volume=404|doi=10.1038/35004665|last2=et al.|last=Stone|title=Myopia and ambient night-time lighting|pages=144 |issue=6774 |month=March|pmid=<!--none-->|first1=J|first2=E|last3=Held|first3=R|last4=Thorn|first4=F|postscript=<!--None-->}}</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
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| :As [[ice cream]] sales increase, the rate of [[drowning]] deaths increases sharply.
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| :Therefore, ice cream consumption causes drowning.
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| The aforementioned example fails to recognize the importance of time and temperature in relationship 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 [[Human swimming|swimming]]. The increased drowning deaths are simply caused by more exposure to water-based activities, not ice cream. The stated conclusion is false.
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| ;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>The Psychology of Personality: Viewpoints, Research, and Applications. Carducci, Bernard J. 2nd Edition. Wiley-Blackwell: UK, 2009.</ref>
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| :Therefore, it may be simply concluded that shyness, in some part, causally influences test anxiety. | |
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| 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 .28bidirectional causation.29|bidirectional variable]]", above), being a cluster of correlated values each influencing one another to some extent. Therefore, the simple conclusion above may be false.
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| ;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.
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| :Hence, atmospheric CO<sub>2</sub> causes obesity.
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| Richer populations tend to eat more food and consume more energy
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| ;Example 6
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| :[[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.
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| 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.
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| ===The ecological fallacy===
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| There is a relation between this subject-matter and the [[ecological fallacy]], described in a 1950 paper by William S. Robinson.<ref>{{cite journal|author=Robinson, W.S.|year=1950|title=Ecological Correlations and the Behavior of Individuals|journal=American Sociological Review |volume=15 |issue=3 |pages=351–357 |doi=10.2307/2087176 |jstor=2087176 |publisher=American Sociological Review}}</ref> Robinson shows that ecological correlations, where the statistical object is a group of persons (i.e. an ethnic group), does not show the same behaviour as individual correlations, where the objects of inquiry are individuals: "The relation between ecological and individual correlations which is discussed in this paper provides a definite answer as to whether ecological correlations can validly be used as substitutes for individual correlations. They cannot." (...) "(a)n ecological correlation is almost certainly not equal to its corresponding individual correlation."
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| ==Determining causation==
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| ===In academia===
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| {{Main|Causality|Causality (physics)}}
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| The point of view that correlation implies causation may be regarded as a theory of [[causality]], which is somewhat inherent to the field of [[statistics]]. Within [[academia]] as a whole, the nature of causality is systematically investigated from several [[discipline (specialism)|academic disciplines]], including [[philosophy]] and [[physics]].
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| In academia, there is a significant number of theories on causality; ''The Oxford Handbook of Causation'' (Beebee et al. 2009) encompasses 770 pages. Among the more influential theories within [[philosophy]] are [[Aristotle]]'s [[Four causes]] and [[Al-Ghazali]]'s [[occasionalism]].<ref>Beebee et al., 2009</ref> [[David Hume]] argued that causality is 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>[http://plato.stanford.edu/entries/hume/#CausationN David Hume (Stanford Encyclopedia of Philosophy)]</ref> [[Immanuel Kant]], according to Beebee et al., 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".<ref name="Beebee et al. 2009">Beebee et al. 2009</ref>
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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="Beebee et al. 2009"/> 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|Descartian]]<ref>Lloyd, A.C., The principle that the cause is greater than its effect, Pronesis 21(2), 1976</ref> view that "the cause is greater than the effect" for the particular case of [[thermodynamic free energy]]. This, in turn, is challenged 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>Paul W. Holland. 1986. "Statistics and Causal Inference" Journal of the American Statistical Association, Vol. 81, No. 396. (Dec., 1986), pp. 945–960.</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>Judea Pearl. 2000. ''Causality: Models, Reasoning, and Inference,'' Cambridge University Press.</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. This is achieved by randomization of the subjects to two or more groups. Although not a perfect system, the likeliness of being equal in all aspects rises with the number of subjects placed randomly in the treatment/[[placebo]] groups. From the significance of the difference of the effect of the treatment vs. the placebo, one can conclude the likeliness of the treatment having a causal effect on the disease. This likeliness can be quantified in statistical terms by the [[P-value]] {{dubious|date=July 2012}}.
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| ===Causality predicted by an extrapolation of trends===
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| {{See also|Inertia}}
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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 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 the presence of bidirectional causation) can be avoided by using explanators ([[Dependent and independent variables#Use in statistics|regressors]]) that are necessarily [[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]]. [[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 the model. In particular, underlying time trends of both the dependent variable and the independent (potentially causative) variable must be controlled for by including time as another independent variable.{{Citation needed|date=April 2013}}
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| ==Use of correlation as scientific evidence==
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| 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|publisher=Science-Based Medicine}}</ref> – they 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 – dismissing correlation entirely, as if it does not suggest causation. This would dismiss a large swath of important scientific evidence.<ref name="Steven"/>
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| In conclusion, correlation is a valuable type of scientific evidence in fields such as medicine, psychology, and sociology. But first correlations must be confirmed as real, and then every possible causative relationship must be systematically explored. In the end correlation can be used as powerful 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. But it is also 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.
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| ==See also==
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| * [[Affirming the consequent]]
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| * [[Chain reaction]]
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| * [[Confirmation bias]]
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| * [[Confounding]]
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| * [[Design of experiments]]
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| * [[Domino effect]]
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| * [[Ecological fallacy]]
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| * [[Four causes]]
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| * [[Mierscheid Law]]
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| * [[Normally distributed and uncorrelated does not imply independent]]
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| * [[Observational study]]
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| * [[Occam's razor]]
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| * [[Flying Spaghetti Monster#Pirates and global warming|Pirates and global warming]]
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| * [[Synchronicity]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://singapore.cs.ucla.edu/LECTURE/lecture_sec1.htm "The Art and Science of cause and effect"]: a slide show and tutorial lecture by Judea Pearl
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| * [http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf Causal inference in statistics: An overview], by Judea Pearl (September 2009)
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| {{Informal Fallacy}}
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| {{Misuse of statistics}}
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| {{DEFAULTSORT:Correlation Does Not Imply Causation}}
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| [[Category:Causal fallacies]]
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| [[Category:Causal inference]]
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| [[Category:Covariance and correlation]]
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| [[Category:Misuse of statistics]]
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