Applications of Bayesian Decision Theory to Sequential Mastery Testing

Abstract

The purpose of this paper is to formulate optimal sequential rules for mastery tests. The framework for this approach is derived from empirical Bayesian decision theory. Both a threshold and linear loss structure are considered. The binomial probability distribution is adopted as the psychometric model involved. Conditions sufficient for sequentially setting optimal cutting scores are presented. Optimal sequential rules will be derived for the case of a beta distribution representing prior true level functioning. An empirical example of sequential mastery testing for concept-learning in medicine concludes the paper.