Correlation does not imply causation

"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.

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