On Computing the Key Probability in the Stochastically Curtailed Sequential Probability Ratio Test

Abstract

The Stochastically Curtailed Sequential Probability Ratio Test (SCSPRT) is a termination criterion for computerized classification tests (CCTs) that has been shown to be more efficient than the well-known Sequential Probability Ratio Test (SPRT). The performance of the SCSPRT depends on computing the probability that at a given stage in the test, an examinee's current interim classification status will not change before the end of the test. Previous work discusses two methods of computing this probability, an exact method in which all potential responses to remaining items are considered and an approximation based on the central limit theorem (CLT) requiring less computation. Generally, the CLT method should be used early in the test when the number of remaining items is large, and the exact method is more appropriate at later stages of the test when few items remain. However, there is currently a dearth of information as to the performance of the SCSPRT when using the two methods. For the first time, the exact and CLT methods of computing the crucial probability are compared in a simulation study to explore whether there is any effect on the accuracy or efficiency of the CCT. The article is focused toward practitioners and researchers interested in using the SCSPRT as a termination criterion in an operational CCT.