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referred to as Green and Swets; see Figure 3). The SDT was originally developed by the Electronic Defense Group (EDG) at the University of Michigan, Ann Arbor, in the 1950s. Wesley Peterson and Ted Birdsall at the EDG wrote mathematical papers about ideal signal detec- tors. Spike Tanner applied those ideas to psychophysical issues. At this time, Dave (a graduate student) and Swets (a starting assistant professor; see Swets’ autobiography, 2010) helped advance the SDT in general, but over time, they extended Tanner’s ideas and developed a general psychophysical theory of detection and discrimination of sensory stimuli, especially sound. One of the first audi- tory papers was a detailed technical report by Tanner, Swets, and Green in 1956 (available at bit.ly/2PSvLiG).
Although the SDT was developed mainly to deal with behavioral experimental design and results, it was also applied to other decision tasks (see Swets, 2010), such as decisions radar operators have to make. A radar operator must decide if a “blip” on a noisy radar screen is a “signal” representing a plane that may pose a danger (“Yes,” there is a plane) or is merely “noise” not indicating any danger (“No,” there is no plane).
Similarly, subjects in hearing experiments are often asked to decide (Yes or No) if a sound presented on a trial is one that contains a target signal mixed with noise (Signal plus Noise [SN]) or is only the noise (Noise Alone [NA]). In detection based on sonar stimuli and on sound in a hearing experiment, one has to “trust” the operator’s/sub- ject’s response (Yes or No) regarding the occurrence of a signal. That is, to what extent does the response represent the observer’s sensitivity to the signal (e.g., a radar blip representing a plane, a sound representing a particular tone)? If the detection response is not a reliable estimate of sensitivity, then an enemy plane may go undetected and responses indicating that a particular sound occurred may not provide useful information about auditory process- ing (e.g., a person’s hearing loss may be missed). The SDT provides a theory for reliably estimating an observer’s sen- sitivity in making detection decisions when a weak signal is presented in a noisy background.
Although Dave has not been “active” in the field since his retirement, Greenfest triggered a return to SDT. Dave published a Letter to the Editor of JASA (Green, 2020) in what he referred to as a “homily.” Dave’s “complaint” was,
“I am somewhat disappointed about how SDT commonly
is portrayed and taught.” In his homily, Dave refers to the history of psychophysical measurements. The term psychophysics (psychoacoustics is the application of psy- chophysics to acoustics) was used by Gustave Fechner in his two-volume book Elemente der Psychophysik (1860) to define quantifiable functional relationships between objective measures of psychological sensations/percep- tions and physical stimulus variables that might excite the senses. Fechner argued that there are procedures (psychophysical procedures, cataloged in his book) that allow for objective behavioral measures of sensations and perceptions that can be measured similarly to those of the physical objects themselves.
However, in Dave’s words (Green, 2020), “The sensations produced by the stimuli were subjective; they were pri- vate or covert. The only objective fact was the observer’s response on that particular trial.” In detecting weak signals occurring in noisy backgrounds (i.e., differen- tiating between SN and NA), we might know, using a psychophysical procedure described by Fechner, that an observer says he/she detected the signal. The psychophys- ical procedures cataloged by Fechner (1860) provided ways to estimate correctly detecting the signal when it was presented (Hits), and Hits were used as a measure of sensitivity. However, what happens when the signal is not presented (when a response indicates that a signal was presented when it was not; a False Alarm)? Clearly, being able to avoid False Alarms would be important in obtaining an estimate of sensitivity. Fechner and many after him suggested ways to estimate observers’ sensi- tivity in indicating that they detected a signal when it was presented (Hits) and when it was not (False Alarms). False Alarms were then used in various ways to “correct” Hits as a measure of sensitivity, although such “correc- tions” were only approximations.
SDT starts with the simple idea that combining Hits and False Alarms provides measures of sensitivity in a more reliable and objective manner than just measuring Hits, even if Hits are corrected by False Alarms. A stimulus- response table (Figure 4) describes the raw data from a detection task. The four cells indicate the four condi- tional probabilities (P; “Response”/Stimulus), indicating an observer’s responses (Yes or No, a signal was presented) as a function of the stimulus (either SN or NA). Hit and Miss probabilities sum to one as do False Alarm and Cor- rect Rejection probabilities, and, as a result, SDT only uses
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