Using ROC Analysis to Refine Cut Scores Following a Standard Setting Process

Abstract

In educational assessment, cut scores are often defined through standard setting by a group of subject matter experts. This study aims to investigate the impact of several factors on classification accuracy using the receiver operating characteristic (ROC) analysis to provide statistical and theoretical evidence when the cut score needs to be refined. Factors examined in the study include the sample distribution relative to the cut score, prevalence of the positive event, and cost ratio. Forty item responses were simulated for examinees of four sample distributions. In addition, the prevalence and cost ratio between false negatives and false positives were manipulated to examine their impacts on classification accuracy. The optimal cut score is identified using the Youden Index J. The results showed that the optimal cut score identified by the evaluation criterion tended to pull the cut score closer to the mode of the proficiency distribution. In addition, depending on the prevalence of the positive event and cost ratio, the optimal cut score shifts accordingly. With the item parameters used to simulate the data and the simulated sample distributions, it was found that when passing the exam is a low-prevalence event in the population, increasing the cut score operationally improves the classification; when passing the exam is a high-prevalence event, then cut score should be reduced to achieve optimality. As the cost ratio increases, the optimal cut score suggested by the evaluation criterion decreases. In three out of the four sample distributions examined in this study, increasing the cut score enhanced the classification, irrespective of the cost ratio when the prevalence in the population is 50%. This study provides statistical evidence when the cut score needs to be refined for policy reasons.