d o′ : Sensitivity at the optimal criterion location

Abstract

Signal detection theory (SDT) was developed to provide a measure of the discriminability of a signal against background noise, independently of response bias. However, equal discriminability over a range of bias is only achieved by the traditional signal detection measure d′ under a narrow set of conditions – i.e., binormal noise and signal distributions of equal variance and base rates. In response to observed departures from these conditions, more robust alternative measures of d′ have been developed, including da and, more recently, dp′. Each of these alternatives addresses some, but not all, of the difficulties that arise when the assumptions of SDT are violated. Moreover, none of these measures directly follow from a central idea of discriminability by an observer that adopts a minimize error count (MEC) strategy. I propose a new d′ alternative, do′, that is robust to violations of the standard signal detection assumptions, remains consistent with varying bias, and is grounded in the principle of discriminability following a MEC strategy. Simulations illustrate how do′ is similar to the recently developed dp′ when the observer optimizes their criterion placement to minimize the number of errors but, unlike dp′, remains consistent irrespective of the observer’s criterion placement Moreover, unlike da, do′ reflects changes in discriminability related to base rates of signal vs. noise presentations. The use of do′ also has implications for the interpretation of bias metrics, such as β and c, which are examined at the optimal criterion under a variety of conditions.