Regression fallacy

The regression (or regressive) fallacy is an informal fallacy. It assumes that something has returned to normal because of corrective actions taken while it was abnormal. This fails to account for natural fluctuations. It is frequently a special kind of the post hoc fallacy.

Things like golf scores, the earth's temperature, and chronic back pain fluctuate naturally and usually regress towards the mean. The logical flaw is to make predictions that expect exceptional results to continue as if they were average (see Representativeness heuristic). People are most likely to take action when variance is at its peak. Then after results become more normal they believe that their action was the cause of the change when in fact it was not causal.

This use of the word "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. In fact, in any situation where two variables are less than perfectly correlated, an exceptional score on one variable may not be matched by an equally exceptional score on the other variable. The imperfect correlation between parents and children (height is not entirely heritable) means that the distribution of heights of their children will be centered somewhere between the average of the parents and the average of the population as whole. Thus, any single child can be more extreme than the parents, but the odds are against it.

When his pain got worse, he went to a doctor, after which the pain subsided a little. Therefore, he benefited from the doctor's treatment.

The pain subsiding a little after it has gotten worse is more easily explained by regression towards the mean. Assuming the pain relief was caused by the doctor is fallacious.

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

Often exceptional performances are followed by more normal performances, so the change in performance might better be explained by regression towards the mean. Incidentally, some experiments 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.

The frequency of accidents on a road fell after a speed camera was installed. Therefore, the speed camera has improved road safety.

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