Regression to the Mean

Historical Background

Sir Francis Galton was the first to document regression to the mean. His grandfather Erasmus Darwin, one of the leading intellectuals of that time, and cousin Charles Darwin were both geniuses. Galton wondered if geniality was hereditary and studied famous families of geniuses such as the Darwins and the Mozarts. He noted that the children of geniuses were almost all less brilliant than their parents and that the grandchildren were even less brilliant. Children and grandchildren of geniuses, on the average, are clearly gifted but invariably closer to the general population average than their (grand)parents. More numerical evidence of this effect was provided in his studies on comparing the heights of adult children and their parents. He noted that whenever parents are well above or below average in height, their children are also likely to be similarly above or below average in height, but not by as much. He observed that the same phenomenon was true for mother sweet peas and daughter sweet peas and published a paper with the title “Regression Toward Mediocrity in Hereditary Stature.” Karl Pearson, Galton's biographer and a brilliant statistician, was the first to note that Galton had created “a revolution in the scientific ideas,” not the least because this phenomenon creates the false impression that all phenomena after a sufficient number of regressions will be reduced to a boring, mediocre average, with no room for individual brilliance.

Description of the Phenomenon

Regression to the mean predicts that more extreme (deviant) measures tend to be closer to the [Page 971]population's average when a follow-up measurement is taken. The less reliable the measurement is, the stronger the regression. For perfectly reliable measures, there is no regression to the mean. For instance, if you measure the length of a very large stone, that stone will, in all likelihood, not have “shrunk” the next morning. For totally unreliable measures, the regression is complete; the best prediction of the next measurement is the average. If you measure blood pressure by asking, “Did you enjoy last night's television show?” an extremely high blood pressure measurement after watching the worst show of the year will almost certainly be followed by a much lower blood pressure measurement the next day. The more extreme the measurement result, the more likely noise or error terms have played a role in the measurement. So the more extreme a measurement, the more likely and stronger the regression effect will be. The chance of regression toward the mean also increases when the two measurement instruments are less than perfectly correlated and when the groups are selected on a nonrandom basis (i.e., extreme groups). It is important to note that regression is not an artifact or an observable process. It is the direct consequence of the unreliability of two (pre- and post-) measurements. It is a measurement problem.

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