Passing score and length of a mastery test: An old problem appraoched anew

A classical problem in mastery testing is the choice of passing score and test length so that the mastery decisions are optimal. This problem has been addressed several times from a variety of viewpoints. In this paper, the usual indifference zone approach is adopted, with a new criterion for optimizing the passing score. Specifically, manipulation of probabilities of misclassification of masters versus non-masters is not incorporated into the scheme. Rather, explicit parameters are introduced to account for differences in loss between misclassifying a true master and a non-master. It appears that, under the assumption of the binomial error model, this approach yields a linear relationship between the optimal passing score and test length. The means by which different losses for both decision errors and a known base rate can be incorporated in the procedure are outlined, and the means by which a correction for guessing can be applied are described. Results are related to findings obtained in sequential probability ratio testing for binomial populations and in the latent class approach to mastery testing.