An APL program for calculating signal detection indices

Abstract

Since Green and Swets' Signal Detection Theory and Psychophysics (1966), numerous books and articles have developed statistical decision or signal detection theory (SOT), for example, Egan (1975), Egan and Clarke (1966), Green and Swets (1966jI974), McNicol (1972), and Swets (1973). In addition, the. model has been applied to diverse areas of research: an~al as well as human psychophysics, memory, personality, learning, medicine, and behavioral pharmacology (Aiken, 1969; Appel & Dykstra, 1977; Lloyd & Appel, 1976; Price, 1966;Swets, 1969; Terman, 1970). In brief, SOT attempts to differentiate statistically between effects on discrimination of variables related to physical properties of the stimulus (sensitivity) and effects of variables related to characteristics of the response (criterion or bias). In this attempt, numerous parametric as well as nonparametric indices of both sensitivity and bias estimation have been developed (Dusoir, 1975; Green & Swets, 1966jI974;Grier, 1971; Hodos, 1970; Pollack, 1970; Pollack & Hsieh, 1969; Pollack & Norman, 1964). Of these, the most familiar parametric measures are d' (sensitivity) and (3 or In{3 (bias). The most familiar nonparametric measures are A' or P(I) (sensitivity) and B'H (bias). In applications of SOT, a yes-no procedure is often employed. In this paradigm a subject reports either that a stimulus has (R+) or has not (R-) occurred, given that the stimulus has (S+) or has not (S-) been presented. All possible outcomes can be represented as four relative frequencies, that is, HIT = fr(R+jS+), MISS = fr(R-jS+), False Alarm (FA) = fr(R+jS-), and Correct Rejection (CR) = fr(R-jS-). From these frequencies, conditioned probabilities, that is, p(R+/S+) and p(R+jS-), can be determined. When sample size is not too large or the number of observations is limited, indices of both sensitivity and bias can be calculated in a reasonable amount of time; moreover, tables of both d' and {3 are available for some, but not all, conditional probabilities (Freeman, 1973). A serious problem arises when parametric indices are used and the data a!e inconsistent with the assumptions of the model, that IS, Thurstone's case V of underlying normal distribution