# Regression fallacy

The regression (or regressive) fallacy is a logical fallacy where regression towards the mean is seen not as a natural fluctuation but as being brought about by a specific cause. It is frequently a special kind of the post hoc fallacy.

Exceptional performances are usually followed by less-than-exceptional performances, and this is known in statistics as regression toward the mean. However, people tend to make non-regressive predictions that expect exceptional results to continue as if they were average. (See representativeness heuristic.) Additionally, people are most likely to undertake corrective action when variance is at its peak; then, after results become more normal infer that their corrective behavior was the cause of the change rather than a natural regression towards the mean.

The phrase ‘regression’ was coined by Sir Francis Galton in a study from 1885 called "Regression Toward Mediocrity in Hereditary Stature”. He showed that the height of children from very short or very tall parents would move towards the average.

## Examples

When his pain had gotten worse, he went to a witchdoctor, after which it subsided a little. Clearly, he benefitted from the witchdoctor's powers.

The pain subsiding a little after it has gotten worse was more easily explained by regression towards the mean, therefore assuming it was caused by the witchdoctor is fallacious.

After the new President was elected, the country had far fewer terrorist attacks. The citizens applauded this bold initiative.

Assuming that the severity of terrorist attacks under the previous president was unusually high, then its recession to more normal levels could be an example of statistical regression independent of who was president at the time. It would be difficult for terrorist attacks to only continue increasing even if the same president stayed in office over the next term and the next, or even for a remarkably high rate of occurrences to keep up over the next term with the same president.

The student did exceptionally poorly last semester, so I punished him. He did much better this semester. Clearly, punishment is effective in improving student's grades.

As a rule, exceptional performances tend to be followed by more normal performances, so the change in performance might better be explained by regression towards the mean. Incidentally, tests have shown that people may develop a systematic bias for punishment and against reward because of reasoning analogous to this example of the regression fallacy.

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