Theoretical vs. empirical discriminability: the application of ROC methods to eyewitness identification

Receiver operating characteristic (ROC) analysis was introduced to the field of eyewitness identification 5 years ago. Since that time, it has been both influential and controversial, and the debate has raised an issue about measuring discriminability that is rarely considered. The issue concerns the distinction between empirical discriminability (measured by area under the ROC curve) vs. underlying/theoretical discriminability (measured by d’ or variants of it). Under most circumstances, the two measures will agree about a difference between two conditions in terms of discriminability. However, it is possible for them to disagree, and that fact can lead to confusion about which condition actually yields higher discriminability. For example, if the two conditions have implications for real-world practice (e.g., a comparison of competing lineup formats), should a policymaker rely on the area-under-the-curve measure or the theory-based measure? Here, we illustrate the fact that a given empirical ROC yields as many underlying discriminability measures as there are theories that one is willing to take seriously. No matter which theory is correct, for practical purposes, the singular area-under-the-curve measure best identifies the diagnostically superior procedure. For that reason, area under the ROC curve informs policy in a way that underlying theoretical discriminability never can. At the same time, theoretical measures of discriminability are equally important, but for a different reason. Without an adequate theoretical understanding of the relevant task, the field will be in no position to enhance empirical discriminability.