A Backward Induction Computational Procedure to Sequential Mastery Testing

Summary

In a sequential mastery test, the decision is to classify a student as a master, a non-master, or to continue testing and administering another random item. Sequential mastery tests are designed with the goal of maximizing the probability of making correct classification decisions (i.e., mastery and non-mastery) while at the same time minimizing test length. The purpose of this paper is to derive optimal rules for sequential mastery tests. The framework of Bayesian sequential decision theory is used; that is, optimal rules are obtained by minimizing the posterior expected losses associated with all possible decision rules at each stage of testing. The main advantage of this approach is that costs of testing can be explicitly taken into account. Techniques of backward induction (i.e., dynamic programming) are used for computing optimal rules that minimize the posterior expected loss at each stage of testing. This technique starts by considering the final stage of testing and then works backward to the first stage of testing. For given maximum number of items to be administered, it is shown how the appropriate action can be computed at each stage of testing for different number-correct score.