Administrative problems such as computer malfunction and power outage occasionally lead to missing item scores and hence to incomplete data on mastery tests such as the AP and U.S. Medical Licensing examinations. Investigators are often interested in estimating the probabilities of passing of the examinees with incomplete data on mastery tests.…

Two types of classification error are possible in competency tests: erroneous classification of an individual as a "master" of the subject (Type II error), and erroneous classification of a master as a "nonmaster" of the subject (Type I). If steps are taken to minimize Type II errors, an artificially high number of true masters…

A solution is offered to problems associated with the inequality in the manipulability of probabilities of classification errors of masters versus nonmasters, based on competency test results. Eschewing the typical arbitrary establishment of observed-score standards below 100 percent, the solution incorporates a self-correction of wrong answers.…

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,…

The setting of a cut-off score on a mastery test usually involves a consideration of one or more of the following elements: (1) the distribution of observed test scores; (2) the type of mastery criterion used; (3) the level of acceptable risks of mis-classification; (4) the loss of functions of mis-classifications; and (5) the distribution of true…