What's under the ROC? An Introduction to Receiver Operating Characteristics Curves

It is often necessary to dichotomize a continuous scale to separate respondents into normal and abnormal groups. However, because the distributions of the scores in these 2 groups most often overlap, any cut point that is chosen will result in 2 types of errors: false negatives (that is, abnormal cases judged to be normal) and false positives (that is, normal cases placed in the abnormal group). Changing the cut point will alter the numbers of erroneous judgments but will not eliminate the problem. A technique called receiver operating characteristic (ROC) curves allows us to determine the ability of a test to discriminate between groups, to choose the optimal cut point, and to compare the performance of 2 or more tests. We discuss how to calculate and compare ROC curves and the factors that must be considered in choosing an optimal cut point.