The Latin phrase “post hoc ergo propter hoc” means, literally, “after this therefore because of this.” The post hoc fallacy is committed when it is assumed that because one thing occurred after another, it must have occurred as a result of it. Mere temporal succession, however, does not entail causal succession. Just because one thing follows another does not mean that it was caused by it. This fallacy is closely related to the cum hoc fallacy.
Example
(1) Most people who are read the last rites die shortly afterwards.
Therefore:
(2) Priests are going around killing people with magic words!
This argument commits the post hoc fallacy because it infers a causal connection based solely on temporal order.
Real-World Examples
One example of the post hoc flaw is the evidence often given for the efficacy of prayer. When someone reasons that as they prayed for something and it then happened, it therefore must have happened because they prayed for it, they commit the post hoc fallacy. The correlation between the prayer and the event could result from coincidence, rather than cause, so does not prove that prayer works.
Superstitions often arise from people committing the post hoc fallacy. Consider, for example, a sportsman who adopts a pre-match ritual because one time he did something before a game he got a good result. The reasoning here is presumably that on the first occasion the activity preceded the success, so the activity must have contributed to the success, so repeating the activity is likely to lead to a recurrence of the success. This is a classic example of the post hoc fallacy in action.