Statistical consideration of mastery scores

The kind of mastery score problem often encountered in educational and psychological testing may be roughly described as follows: given that a certain unit of instruction must be mastered by a subject, a test is administered at the end of this unit and, on the basis of the observed score or an estimate of the true score, a decision is made about the grant of the mastery status. If the subject is declared master of the unit, he will be allowed to proceed to the next unit of instruction. Otherwise, remedial work will be given. Given relevant consequences of misclassification, the problem is to determine an optimum decision rule.Part of this work was completed while the author was Visiting Researcher at the Learning Research and Development Center, University of Pittsburgh, in the summer of 1973. Gratitude is extended to Robert Glaser for the invitation and to Anthony Nitko for helpful comments and suggestions.