It has been known for over 40 years that there are two fundamentally different kinds of detection tasks in the theory of signal detectability. The Type 1 task is to distinguish between events defined independently of the observer; the Type 2 task is to distinguish between one's own correct and incorrect decisions about those Type 1 events. For the Type 1 task, the behavior of the detector can be summarized by the traditional receiver operating characteristic (ROC) curve. This curve can be compared with a theoretical ROC curve, which can be generated from overlapping probability functions conditional on the Type 1 events on an appropriate decision axis. We show how to derive the probability functions underlying Type 2 decisions from those for the Type 1 task. ROC curves and the usual measures of performance are readily obtained from those Type 2 functions, and some relationships among various Type 1 and Type 2 performance measures are presented. We discuss the relationship between Type 1 and Type 2 confidence ratings and caution against the practice of presenting transformed Type 2 ratings as empirical Type 1 ratings.

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Green's relationship, A SI =P(C) 2I , which equates the area, A SI , under the receiver operating characteristic (ROC) curve in the single-interval forcedchoice (SIFC) task with the proportion correct, P(C) 2I , in the two-interval forced-choice (2IFC) task, is rederived using the cross-correlation functions of the SIFC evidence distributions. The relationship is generalized to include discrete random variables, unidimensional decision axes that do not need to be monotonic with likelihood ratio, and arbitrary prior and guessing probabilities. A 2IFC difference decision rule is assumed. Further nonparametric relationships, including an equality between an entropy transform of A SI and the 2IFC channel capacity, nonparametric bounds on the area under the 2IFC ROC curve in terms of A SI , and methods for estimating 2IFC ROC curves based on information from the SIFC task, are developed. These relationships are investigated experimentally. Experiment I is a frequency-discrimination task where the evidence is known to be distributed as a discrete random variable. Experiment II is an amplitude-discrimination task where the theoretical evidence distributions are continuously distributed. The problem of observer inconsistency is addressed by repeating the experiments multiple times, using the same stimuli, then using group operating characteristic (GOC) analysis to remove unique noise. Results from Experiment I show excellent support for all the theoretical relationships, and results from Experiment II show partial support for the theoretical relationships.

While a visiting professor at the University of Texas, Egan (1967) showed us how power-law ROC curves can be derived from overlapping Rayleigh distributions. Such distributions suggest immediately that detection performance for narrow-band noise signals should differ markedly from that for sinusoidal signals. Accordingly, the psychometric function for Rayleigh signals was derived. The equations governing the probability of being correct in a 2AFC experiment for sinusoidal and noise signals are: P(c) = 1 − 12(exp− σs2/2σn2), which is another way of expressing Marill's famous equation, and P(c) = (σn2+σs2)/(2σn2+σs2), respectively; σn and σs are the rms voltages of the effective masking noise and the signal. For these signals, both rating-scale and 2AFC experiments, appropriate to the tenets of detection theory, show that the shapes of human psychometric functions are predicted in detail by the mathematical models. [Work supported by National Institute of Mental Health, Naval Ship Systems Command, and National Aeronautics and Space Administration.]

To analyze Vietnamese social organization, we must put aside ourimage of it as similar to that of China, with its patrilineal clans. Writings on Vietnam have portrayed a country molded by its northern neighbour in the “thousand years of Chinese domination” of the first millennium A.D. to such an extent that all things Vietnamese must needs be seen in a Chinese and indeed a Confucian light. Socially, this means domination by the male and the father, patrilineal succession, and clan organization, that is, a certain rigidity in social organization.