Regression toward the mean in a two-stage selection program

A model for a two-stage selection program based upon normally distributed variables is examined. Subjects in the upper part of the distribution of first-stage observations are retained and subsequently observed an additional number of times in a second stage. Subjects in the upper part of the distribution of second-stage observations are again retained. The first stage consists of n₁ observations and the second stage of n₂ subsequent observations. The effect of regression toward the mean and the mean and variance of the distribution of retained subjects are examined numerically as functions of the proportions eliminated at each stage and number of first- and second-stage observations.