Correlation does not imply Causation

One of the most fundamental principles students of the scientific method must recognize is what is known as the post hoc fallacy. A fallacy is, according to Dictionary.com, "a deceptive, misleading, or false notion, belief, etc.: That the world is flat was at one time a popular fallacy."

The words post hoc are Latin, meaning after this or after the event. The term "post hoc fallacy" is an abbreviation of the statement post hoc, ergo propter hoc. The full phrase means after this, therefore because of this. What this phrase refers to is the erroneous assumption that just because an event B reliably follows an event A, then B is caused by A. An almost equivalent phrase is cum hoc, ergo proctor hoc, which means with this, therefore because of this. Technically, though, since effects follow causes, cum hoc is not often used in this sense.

Just because an event often occurs after or with another event, one can not validly conclude that the first event causes the second. The experimental method is required to make causal conclusions. When two variables are correlated or associated, it is clear that they are in some way related. The value of one variable in any given observation predicts the value of the other. It is important to realize that there are three possible reasons two variables (named, say A & B) can be correlated. It may be that (1) A causes B, (2) B causes A, or (3) some variable C causes both A and B.

Many novice researchers fall victim to the post hoc fallacy when trying to design research. Advertisers and other people trying to promote an idea without evidence will often use correlation to suggest causation. They will attempt to suggest that A causes B simply because B is found with A, in the way fire is found with smoke. It is important in learning to make valid scientific statements to avoid this error.

Here is an example of how the error might work. A person trying to increase sales of umbrellas in a large general store discovers that umbrella sales are correlated with windshield wiper sales. That is, on days that umbrella sales are high, windshield wiper sales are also high. The person might commit the post hoc error by assuming that windshield wiper sales cause umbrella sales, and they may try to increase umbrella sales by running a sale on windshield wipers. Obviously, the plan will fail, because windshield wiper sales don't cause umbrella sales. Changing windshield wiper sales will not effect umbrella sales, even though sales of the two products are correlated. The truth is, both windshield wiper sales and umbrella sales are caused by a third variable the person has not even considered: rainfall.

Three Possible Explanations of Correlation: