Post hoc ergo propter hoc and/or cum hoc ergo propter hoc
From Wikipedia: Post hoc ergo propter hoc, Latin for “after this, therefore because of this”, is a logical fallacy (of the questionable cause variety) that states “Since that event followed this one, that event must have been caused by this one.” It is often shortened to simply post hoc and is also sometimes referred to as false cause, coincidental correlation, or correlation not causation. It is subtly different from the fallacy cum hoc ergo propter hoc (see below), in which two things or events occur simultaneously or the chronological ordering is insignificant or unknown.
Post hoc is a particularly tempting error because temporal sequence appears to be integral to causality. The fallacy lies in coming to a conclusion based solely on the order of events, rather than taking into account other factors that might rule out the connection.
Cum hoc ergo propert hoc – “Correlation does not imply causation” (related to “ignoring a common cause” and questionable cause) is a phrase used in science and statistics to emphasize that a correlation between two variables does not automatically imply that one causes the other (though correlation is necessary for linear causation in the absence of any third and countervailing causative variable, it can indicate possible causes or areas for further investigation; in other words, correlation is a hint).
The opposite belief, correlation proves causation, is a logical fallacy by which two events that occur together are claimed to have a cause-and-effect relationship. The fallacy is also known as cum hoc ergo propter hoc (Latin for “with this, therefore because of this”) and false cause. It is a common fallacy in which it is assumed that, because two things or events occur together, one must be the cause of the other. By contrast, the fallacy, post hoc ergo propter hoc, requires that one event occur after the other, and so may be considered a related fallacy.
In a widely studied example, numerous epidemiological studies showed that women who were 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 cause and effect, as had been supposed.