Regression toward the mean in a two-stage selection program. II. Correlated within-subject observations.

A model for a two-stage selection program based upon normally distributed variables is examined. The within-subject variation is described by a stationary first-order autoregressive process. The expected regression toward the mean and the mean and variance of the distribution of retained subjects are given as functions of the classification points in each stage, the number of observations, the autocorrelation coefficient, and the time interval between observations. Because the time interval between observations affects the within-subject correlation, this interval must be considered in designing selection programs. If high autocorrelation is present, an investigator should space the observations more widely to decrease the correlation and thereby obtain more information from a given number of observations.