n as a statistical estimate of a sensory threshold. In psychology, the curve relating percentage of signals detected to signal strength is called the psychometric function. There had been some earlier concern in psychology for the eﬀect of the observer’s attitude on the measured threshold, e.g., Graham’s (1951) call for quantiﬁcation of instruction stimuli in the psychophysical equation, but no good way to deal with non-sensory factors had emerged.
In 1952, Tanner and Swets joined Peterson and Birdsall as staﬀ in a laboratory of the electrical engineering department called the Electronic Defense Group. They were aware of then-new conceptions of neural functioning in which stimulus inputs found an already active nervous system and neurons were not lying quiescent till ﬁred at full force. In short, neural noise as well as environmental noise was likely to be a factor in detection and then the observer’s task is readily conceived as a choice between statistical hypotheses. Though a minority idea in the history of psychophysics (see Corso 1963), the possibility that the observer deliberately sets a cutpoint on a continuous variable (weight of evidence) seemed likely to Tanner and Swets. A budding cognitive psychology (e.g., ‘new look’ in perception) supported the notion of extrasensory determinants of perceptual phenomena, as represented in SDT by expectancies (prior probabilities) and motivation (beneﬁts and costs).
6. Psychophysical Experiments
The new SDT was ﬁrst tested in Swets’s doctoral thesis in Blackwell’s vision laboratory (Tanner and Swets
1954; Swets et al. 1961–see Swets 1964, Chap. 1). It was then tested with greater control of the physical signal and noise parameters in new facilities for auditory research in the electrical engineering laboratory. Suﬃciently neat empirical ROCs were obtained in the form of the curved arc speciﬁed by SDT. ROCs found to be predicted by Blackwell’s ‘high-threshold’ theory—straight lines extending from some point along the left axis, that depended on signal strength, to the upper right hand corner—clearly did not ﬁt the data. Other threshold theories, e.g., ‘low-threshold’ theories, did not fare much better in experimental tests (Swets 1961–see Swets 1964, Chap. 4). It was recognized later that linear ROCs of slope 1, intersecting left and upper edges of the graph symmetrically, were predicted by several other measures and their implicit models (Swets 1996, Chap. 3) and also gave very poor ﬁts to sensory data (and other ROC data to be described; Swets 1996, Chap. 2). After a stint as observer in Swets’s thesis studies, David M. Green joined the engineering laboratory as an under- graduate research assistant. He soon became a full partner in research, and co-authored a laboratory technical report with Tanner and Swets in 1956 that included the ﬁrst auditory studies testing SDT. Birdsall has collaborated in research with the psychologists over the following decades and commented on a draft of this research paper.
The measure of discrimination performance used ﬁrst was denoted d’ (‘d prime’) and deﬁned as the diﬀerence between the means of two implicit, over- lapping, normal (Gaussian) functions for signal-plus- noise and noise-alone, of equal variance, divided by their common standard deviation. A value of d’ can be calculated for each ROC point, using the so-called single-stimulus yes–no method of data collection. Similarly, a value of d’ can be calculated for an observer’s performance under two other methods of data collection: the multiple-stimulus forced-choice method (one stimulus being signal-plus noise and the rest noise-alone) and the single-stimulus conﬁdence-rating method. Experimental tests showed that when the same signal and nonsignal stimuli were used with the three methods, essentially the same values of d’ were obtained. The measures speciﬁed by threshold theories had not achieved that degree of consistency or internal validity.
For many, the most conclusive evidence favoring SDT’s continuous decision variable and rejecting the high-threshold theory came from an expe