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Correlation does not imply causation is a phrase used in statistics to emphasize that a correlation between two variables does not imply that one causes the other. Many statistical tests calculate correlation between variables. A few go further, using correlation as a basis for testing a hypothesis of a true causal relationship; examples are the Granger causality test and convergent cross mapping. The counter-assumption, that ''correlation proves causation'', is considered a questionable cause 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 necessarily a consequence of the first event, is sometimes described as ''post hoc ergo propter hoc'' (Latin for "after this, therefore because of this"). For example, in a widely studied case, numerous epidemiological studies showed that women taking combined 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 groups (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 a direct cause and effect, as had been supposed. 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 does in fact have a negative incidence on the likelihood of coronary heart disease the assumption of causality would have been correct, although the logic behind the assumption would still have been flawed. ==Usage== In logic, the technical use of the word "implies" means "is a ''sufficient'' circumstance for". 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." However, in casual use, the word "implies" 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. 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.〔 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: * "Empirically observed covariation is a necessary but not sufficient condition for causality." * "Correlation is not causation but it sure is a hint." 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Correlation does not imply causation」の詳細全文を読む スポンサード リンク
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