Wrong direction

In statistics, the phrase 'correlation does not imply causation' refers to the inability to legitimately deduce a cause-and-effect relationship between two variables solely on the basis of an observed association or correlation between them. The complementary idea that 'correlation implies causation' is an example of a questionable-cause 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 post hoc ergo propter hoc ('after this, therefore because of this'), in which an event following another is seen as a necessary consequence of the former event. In statistics, the phrase 'correlation does not imply causation' refers to the inability to legitimately deduce a cause-and-effect relationship between two variables solely on the basis of an observed association or correlation between them. The complementary idea that 'correlation implies causation' is an example of a questionable-cause 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 post hoc ergo propter hoc ('after this, therefore because of this'), in which an event following another is seen as a necessary consequence of the former event. In a widely studied example of the statistical fallacy, 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 later randomized controlled trials showed that use of HRT led to a small but statistically significant increase in the risk of CHD. Reanalysis of the data from the epidemiological studies showed that women undertaking HRT were more likely to be from higher socioeconomic groups (ABC1), with better-than-average diet and exercise regimens. Thus 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 one being a direct cause of the other, as had been supposed.