Regression to the mean

26 July, 2015 at 14:21 | Posted in Statistics & Econometrics | Leave a comment

I had one of the most satisfying eureka experiences of my career while teaching flight instructors … about the psychology of effective training. I was telling them about an important principle of skill training: rewards for improved performance work better than punishment of mistakes…

THINKING-FAST-AND-SLOWWhen I finished my enthusiastic speech, one of the most seasoned instructors in the group raised his hand and made a short speech of his own. He began by conceding that rewarding improved performance might be good for the birds, but he denied that it was optimal for flight cadets. This is what he said: “On many occasions I have praised flight the next time thy try the same maneuver they usually do worse. On the other hand, I have often screamed into a cadet’s earphone for bad execution, and in general he does better on his next try. So please don’t tell us that reward works and punishment does not, because the opposite is the case” …

What he had observed is known as regression to the mean, which in that case was due to random fluctuations in the quality of performance. Naturally, he praised only a cadet whose performance was far better than average. But the cadet was probably just lucky on that particular attempt and therefore likely to deteriorate regardless of whether or not he was praised. Similarly, the instructor would shout into a cadet’s earphones only when the cadet’s performance was unusually bad and therefore likely to improve regardless of what the instructor did. The instructor had attached a causal interpretation to the inevitable fluctuations of a random process …

I had stumbled onto a significant fact of the human condition: the feedback to which life exposes us is perverse. Because we tend to be nice to other people when they please us and nasty when they do not, we are statistically punished for being nice and rewarded for being nasty …

It took Francis Galton several years to figure out that correlation and regression are not two concepts – they are different perspectives on the same concept: whenever the correlation between two scores is imperfect, there will be regression to the mean …

Causal explanations will be evoked when regression is detected, but they will be wrong because the truth is that regression to the mean has an explanation but does not have a cause.

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