The mean and variance of the selection differential after top‐down selection from a mixture of normal samples

A procedure is presented for determining the mean and variance of the selection differential for top‐down selections in which the candidates come from populations that have a different average score on the selection measure. Although the procedure is based on the same stochastic model and requires identical data to the currently available method for estimating the mean selection differential, it has the advantage that the resulting expressions are valid for finite‐sample selection decisions and that the variance of the selection differential can also be assessed. The difference between the two procedures is illustrated by means of an example application, and it is shown how the present results are particularly helpful in determining the expected utility of personnel selection decisions.