Accuracy of d′ and A′ as estimates of sensitivity

Abstract

In signal detection theory, sensitivity can be indexed as either the distance between distributions or the area under the isosensitivity curve. The statistic d′ is usually identified as a distance measure of sensitivity, while A′ is an estimate of the area. This article considers both statistics as estimates. As such, they can be evaluated against actual distances and areas calculated under specific assumptions about the variances of the distributions. The analysis shows that d′ is a better estimate of distance than A′ is of area only under the assumption that the variances of the hypothetical distributions are equal (i.e., the slope of the z-coordinate ROC is 1.0). When the slope takes on values other than 1.0, A′ is generally a more accurate estimate of area than d′ is of distance. © 1993, Psychonomic Society, Inc.. All rights reserved.