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on a ROC contour, whereas the area under a ROC contour (PA) can be used as a bias- and distribution-free measure of sensitivity (e.g., as the Hit proportion increases and the FA proportion decreases, PA would increase independent of response bias, indicating an increase in sensitivity alone).
One way to test for the observer’s sensitivity is the two- interval AB test. In this test, observers are presented two successive sounds: the signal occurs in either the first or the second interval (NA followed by SN or SN followed by NA, randomly determined), and observers indicate which interval contained the signal. One hundred percent correct responses indicate that an observer clearly detected the signal, whereas 50% correct responses indicate that the signal was inaudible. In Green and Swets (1966) and in Dave’s homily (2020), Dave proves that the percentage of correct responses in the AB test is equal to the PA.
This proof is nonparametric, that is, it is independent of any assumptions about the form of the NA and SN distributions. In many papers on SDT, a common first assumption is that the underlying distributions are both Gaussian and of equal variance (see Egan, 1975). If we assume that the observer has no bias to favor one interval or the other, the AB test becomes a second measure of the observer’s sensitivity to the signal without having to make any assumptions about the form of the underlying NA and SN distributions. To paraphrase Green (2020), the moral of his homily is that although perceptual expe- riences are covert, percent correct and PA both provide objective measures of the observer’s sensitivity.
Dave often described SDT (e.g., Green, 1960, 1964) as “a combination of two distinct theoretical structures: decision theory and the theory of ideal observers.” Some
aspects of decision theory have been briefly described. Ideal observer theory (e.g., Green, 1960, 1964) “provides a collection of ideal mathematical models which relates the detectability of the signal to definite physical charac- teristics of the stimulus.”
In considering a particular ideal observer (a particular mathematical model), a detection model can be developed. In such a model, the form of the NA and SN probability density functions (the “definite physical characteristics of the stimulus”) is precisely defined. In many cases, Fourier series, bandlimited, white, Gaussian noise forms the NA dis- tribution, and the SN distribution is this noise distribution
plus a sinusoidal tone (see Green, 1960, 1964 for a detailed discussion of these assumptions). Using both the decision and ideal observer aspects of SDT, a detection model for describing the detection, discrimination, and identifica- tion of auditory signals presented in noisy backgrounds was developed, and Dave performed many psychoacoustic experiments testing the model (see Swets, 1964 for chapters describing some of these experiments, many authored by Dave). Papers published by Dave and many others estab- lished detection models as valuable for accounting for many aspects of human observers’ detection, discrimination, and identification of a variety of auditory signals often masked by noise (e.g., Swets, 1964; Green and Swets, 1966).
SDT has also been used to evaluate the performance of humans and other animals in different sensory tasks, to measure decisions based on memory and attention, and to characterize how neural elements respond to stimu- lation (e.g., Swets, 1964; Green and Swets, 1966). In addition, SDT has been used in many nonlaboratory situ- ations such as deciding when a radiological image may or may not indicate a tumor, when a jury may or may not decide that an innocent person is innocent, or when an alarm may or may not lead to a decision that there is a dangerous situation (e.g., see Swets, 2010). Thus, SDT is a powerful decision paradigm with wide application.
Dave and “Profile Analysis”
Although Dave published many experiments based on the SDT early in his career, he investigated a wide range of topics over the rest of his career. One of the many topics led to the publication of Profile Analysis: Auditory Intensity Discrimination (Green, 1988). This book is about auditory intensity discrimination in general and when changes in intensity across a sound’s spectrum can be discriminated, i.e., when there is a spectral “profile” that can be percep- tually “analyzed.” Most everyday sounds have complex spectra in which intensity varies as a function of frequency, and the perceptual differences between and among such sounds are often based on “spectral profiles.”
Dave’s interest in profile analysis was sparked by Murray Spiegel, a postdoc who received his PhD from Washing- ton University in St. Louis, Missouri, working with Chuck Watson. Murray worked with Chuck on “10-tone pattern” perception (Watson, 2005). In an attempt to generate complex stimuli that had many properties of real-world sounds but whose acoustics could be carefully controlled,
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