Confusing correlation with causation

Consider two events A and B.  Event B closely follows Event A in time.  Does this mean that Event A caused Event B?  Possibly, but not necessarily.  Both events could have been cause by a third event C, or more likely, the close timing of Events A and B is a coincidence.  So not only is causation not the only explanation, it is not even the best explanation.

Post hoc ergo propter hoc (Latin: ‘after this, therefore because of this’ – often shortened to post hoc) is a logical fallacy that states ‘Since Event B followed Event A, Event B must have been caused by Event A.’ It is subtly different from the fallacy cum hoc ergo propter hoc (‘with this, therefore because of this’), in which two things or events occur simultaneously or the chronological ordering is insignificant or unknown. These fallacies are also known as ‘False cause’.

Post hoc is a particularly tempting error because temporal sequence appears to be integral to causality.  Indeed, if Event A did cause Event B, Event B would probably occur soon after Event A in time.  But the reverse connection is not necessarily true – temporal correlation does not imply 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.

The form of the post hoc fallacy can be expressed as follows:

Premise: A occurred, then B occurred.

Conclusion: Therefore, A caused B.

The following is a simple example: ‘The rooster crows immediately before sunrise, therefore the rooster causes the sun to rise’.  This conclusion is false, not just we happen to know that it is factually incorrect, but because the argument is fallacious.

When B is undesirable, this fallacy is often committed in reverse: Avoiding A will prevent B.  This is the basis of many superstitious beliefs, such as bad luck associated with Friday the 13^th or walking under ladders.

An example of the cum hoc fallacy is as follows.  Sleeping with one’s shoes on (A) is strongly correlated with waking up with a headache (B). Therefore, sleeping with one’s shoes on causes headache.  A more plausible explanation is that both are caused by a third factor (C), in this case going to bed drunk, which thereby gives rise to a correlation between A and B.  So the conclusion is false.

Another example, is that ice-cream sales are correlated with the level of house burglaries during warmer weather when more people are on holidays (vacation). But ice-cream doesn’t cause burglaries, nor vice versa.

Source: Wikimedia Commons

On the other hand, if A is often correlated with B, then although we still can’t logically conclude that A causes B (or vice versa), such a causal link may be a hypothesis worth testing via properly designed scientific experiments.

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