A bayesian procedure for mastery decisions based on multivariate normal test data

A Bayesian framework for making mastery/nonmastery decisions based on multivariate test data is described in this study. Overall, mastery is granted (or denied) if the posterior expected loss associated with such action is smaller than the one incurred by the denial (or grant) of mastery. An explicit form for the cutting contour which separates mastery and nonmastery states in the test score space is given for multivariate normal test scores and for a constant loss ratio. For multiple cutting scores in the true ability space, the test score cutting contour will resemble the boundary defined by multiple test cutting scores when the test reliabilities are reasonably close to unity. For tests with low reliabilities, decisions may very well be based simply on a suitably chosen composite score.This work was performed pursuant to Grant NIE-G-78-0087 with the National Institute of Education, Department of Health, Education, and Welfare, Huynh Huynh, Principal Investigator. Points of view or opinions stated do not necessarily reflect NIE positions or policy and no official endorsement should be inferred. The assistance of Joseph C. Saunders is gratefully acknowledged. The author is indebted to an anonymous referee who pointed out several computational errors in the earlier versions of the paper.