Statistical Reversion toward the Mean: More Universal than Regression toward the Mean

Schmittlein discussed the lack of universality of regression toward the mean. The present note emphasizes the universality of a similar effect, dubbed “reversion” toward the mean, defined as the shift in conditional expectation of the upper or lower portion of a distribution. Reversion toward the mean is a useful concept for statistical reasoning in applications and is more self-evidently plausible than regression toward the mean.