A Guide for Setting the Cut-Scores to Minimize Weighted Classification Errors in Test Batteries

Abstract

In this article, we extend the methodology of the Cut-Score Operating Function that we introduced previously and apply it to a testing scenario with multiple independent components and different testing policies. We derive analytically the overall classification error rate for a test battery under the policy when several retakes are allowed for individual components and also for when one is required to retake the whole battery. We derive the overall classification error rate using a flexible cost function defined by weights assigned to false negative and false positive errors. The result, shown graphically, is that competing demands of minimizing both false positive and false negative errors yield a unique optimal value for the cut-score. This cut-score can be estimated numerically for any number of components and any number of retakes. Among the results we obtain is that the more lenient the retake policy the higher one must set the cut-score to minimize the error rate.