A nonrandomized minimax solution for passing scores in the binomial error model

A nonrandomized minimax solution is presented for passing scores in the binomial error model. The computation does not require prior knowledge regarding an individual examinee or group test data for a population of examinees. The optimum passing score minimizes the maximum risk which would be incurred by misclassifications. A closed-form solution is provided for the case of constant losses, and tables are presented for a variety of situations including linear and quadratic losses. A scheme which allows for correction for guessing is also described.This work was performed pursuant to Grant No. 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 position or policy and no official endorsement should be inferred. The editorial assistance and comments of Anthony J. Nitko and of Joseph C. Saunders are gratefully acknowledged.