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Wily regression to the mean

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Regression to the mean is like the cicada, just as you forget about it, you hear its buzz. The man who taught DSN the history of statistics, Prof. Steve Stigler of the University of Chicago, said this of it:

“Galton’s completion of his discovery of this phenomenon [regression to the mean] in the 1880s should rank should rank with the greatest individual events in the history of science—at a level with William Harvey’s discovery of the circulation of blood and with Isaac Newton’s of the separation of light.”

A nice example of a manager not appreciating regression to the mean is found in Tversky & Kahneman’s famous 1974 Science article:

“The failure to recognize the import of regression can have pernicious consequences, as illustrated by the following observation. In a discussion of flight training, experienced instructors noted that praise for an exceptionally smooth landing is typically followed by a poorer landing on the next try, while harsh criticism after a rough landing is usually followed by an improvement on the next try. The instructors concluded that verbal rewards are detrimental to learning, while verbal punishments are beneficial, contrary to accepted psychological doctrine. This conclusion is unwarranted because of the presence of regression toward the mean. As in other cases of repeated examination, an improvement will usually follow a poor performance and a deterioration will usually follow an outstanding performance, even if the instructor does not respond to the trainee’s achievement on the first attempt. Because the instructors had praised their trainees after good landings and admonished them after poor ones, they reached the erroneous and potentially harmful conclusion that punishment is more effective than reward.”

Thanks for Ralph Hertwig of Basel for the reference.

Tversky, A., & Kahneman, D. Judgment under uncertainty: Heuristics and biases. Science, 1974, 185, 1124-1131.