Compensatory Rules for Optimal Classification with Mastery Scores

Abstract

A model for simultaneous optimization of combinations of test-based decisions in education and psychology is proposed using Bayesian decision theory. To illustrate the approach, one classification decision with two treatments each followed by a mastery decision are combined into a decision network. An important decision is made between weak and strong decision rules. As opposed to strong rules, weak rules are allowed to be a function of prior test scores in the series. Conditions under which optimal rules take weak monotone forms are derived. Results from a well-known problem in The Netherlands of selecting optimal continuation schools on the basis of achievement test scores are presented.