e 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 experiment suggested by Robert Z. Norman, a Michigan mathematics student. Carried out with visual stimuli, the critical ﬁnding was that a second choice made in a four alternative forced-choice test, when the ﬁrst choice was incorrect, was correct with probability greater than 1/3 and that the probability of it being correct increased with signal strength (Swets et al. 1961, Swets 1964, Chap. 1).
Validating the rating method, as mentioned above, had the important eﬀect of providing an eﬃcient method for obtaining empirical ROCs. Whereas under the yes–no method the observer is induced to set a diﬀerent cutpoint in each of several observing sessions (each providing an ROC point), under the rating method the observer eﬀectively maintains several decision cutpoints simultaneously (the boundaries of the rating categories) so that several empirical ROC points (enough to deﬁne a curve) can be obtained in one observing session.
7. Dissemination Of SDT In Psychology
Despite the growing evidence for it, acceptance of SDT was not rapid or broad in psychophysical circles. This was partly due to threshold theory having been ingrained in the ﬁeld for a century (as a concept and a collection of methods and measures), and probably because SDT arose in an engineering context (and retained the engineers’ terminology), the early visual data were noisy, and the ﬁrst article (Tanner and Swets 1954) was cryptic. Dissemination was assisted when J. C. R. Licklider brought Swets and Green to the Massachusetts Institute of Technology where they participated in Cambridge’s hotbed of psychophysics and mathematical psychology, and where oﬀering a special summer course for postgraduates led to a published collection of approximately 35 of the articles on SDT in psychology that had appeared by then, along with tables of d’ (Swets 1964). Licklider also hired both of them part-time at the research ﬁrm of Bolt Beranek and Newman Inc., where they obtained contract support from the National Aeronautics and Space Administration to write a systematic text