Applying the Minimax Principle to Sequential Mastery Testing

The purpose of this paper is to derive optimal rules for sequential mastery tests. In a sequential mastery test, the decision is to classify a subject as a master, a nonmaster, or to continue sampling and administering another random item. The framework of minimax sequential decision theory (minimum information approach) is used; that is, optimal rules are obtained by minimizing the maximum expected losses associated with all possible decision rules at each stage of sampling. The main advantage of this approach is that costs of sampling can be explicitly taken into account. The binomial model is assumed for the probability of a correct response given the true level of functioning, whereas threshold loss is adopted for the loss function involved. Monotonicity conditions are derived, that is, conditions sufficient for optimal rules to be in the form of sequential cutting scores. The paper concludes with a simulation study, in which the minimax sequential strategy is compared with other procedures that exist for similar classification decision problems in the literature.