Recently there has been interest in the problem of determining an optimal passing score for a mastery test when the purpose of the test is to predict success or failure on an external criterion. For the case of constant losses for the two error types, a method of determining an optimal passing score is readily derived using standard techniques. The purpose of this note is to describe a lower bound to the probability of identifying an optimal passing score based on a random sample of N examinees.

Using variance stabilizing transformations, this note describes approximate solutions to the ranking and selection problem of selecting the best binomial population or the bivariate normal population with the largest correlation coefficient.

When comparing examinees to a control, the examiner usually does not know the probability of correctly classifying the examinees based on the number of items used and the number of examinees tested. Using ranking and selection techniques, a general framework is described for deriving a lower bound on this probability. We illustrate how these techniques can be applied to the binomial error model. New exact results are given for normal populations having unknown and unequal variances.