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Signal detection
the question For most of the nineteenth century the working idea was the threshold: below some intensity a stimulus is not felt, above it it is. Fechner built a science of sensation on this idea (Fechner, 1860), and measured it with the methods that still carry his name. The trouble was that thresholds would not sit still. The same observer, on the same day, would give different answers to the same faint light, and the answer moved when you changed what a "yes" was worth. the classic finding The fix came from radar engineering. Peterson, Birdsall & Fox (1954) worked out how an ideal receiver should decide whether a noisy trace contains a target. Tanner & Swets (1954) carried the same mathematics to a human looking for a dim spot of light. In the model, every trial produces some internal evidence. Noise alone produces a spread of values; signal plus noise produces a spread shifted upward. The observer sets a criterion and says yes whenever the evidence exceeds it. Two numbers come out. d′ is the distance between the two spreads in standard units: how detectable the signal is for this person. The criterion is where they put the line: how willing they are to say yes. Change the payoffs, or tell people that signals are common, and the criterion moves while d′ stays put. Plot hits against false alarms as the criterion moves and you get the ROC curve, whose bow measures sensitivity independent of bias.
Swets (1961) then asked the pointed question in his title: is there a sensory threshold at all? His answer, from the data then available, was that the results looked like a continuous decision on noisy evidence, and that the classical "threshold" was largely a criterion in disguise [paraphrase, not a quotation]. The full treatment is the textbook by (Green & Swets, 1966). what held up, and what did not The separation of sensitivity from bias held up and spread far beyond the lab: to memory ("old" versus "new"), to radiology, to eyewitness line-ups, to any task where a person or a test says yes or no. Macmillan & Creelman is the standard working guide. What did not survive intact is the simplest version of the model. The two spreads often have unequal variances, which shows up as an asymmetric ROC, and the single number d′ is then a summary that depends on where you measured. Whether some low-level "high threshold" exists under the noise is still argued over in the memory literature; the ROC shape is the main evidence on both sides. in machines Every binary classifier is a signal detector with a criterion someone chose. Moving the decision threshold on a model's score traces the same ROC, and the area under it is the field's most-reported number. The lesson Swets drew for people carries over unchanged: a model that "finds more" may simply have moved its line. Ask for both rates. live debates One process or two in recognition memory? Confidence-rating ROCs for recognition are asymmetric. Yonelinas (1994) read this as two processes: a threshold-like recollection plus graded familiarity. Wixted (2007) argued that an unequal-variance signal detection model, in which remembered items have more variable strength, fits as well and more simply [paraphrase, not a quotation]. Because the two accounts predict similar curves over much of the range, the debate turns on the shape of zROCs and on assumptions about how confidence maps onto strength (Ratcliff, Sheu & Gronlund, 1992). Lineups. Applied to eyewitness identification, ROC analysis overturned a policy consensus. Wixted & Mickes (2014) proposed a diagnostic-feature-detection model in which comparing faces side by side helps, and Wixted, Mickes & Fisher (2018) argued that an initial, high-confidence identification under fair conditions is far more reliable than the field had taught. Critics question whether lab ROCs carry over to real cases. Metacognition. Maniscalco & Lau (2012) introduced meta-d′, the sensitivity of confidence ratings expressed in the units of d′, so that how well someone knows when they are right can be separated from how well they perform. methodological critiques Measure choice is a theory choice. Rotello, Heit & Dubé (2015) showed how replications using a measure with the wrong implicit model, for example percent correct or d′ when variances are unequal, can repeat an erroneous conclusion more confidently with every new sample [paraphrase, not a quotation]. Stanislaw & Todorov (1999) remain the practical guide to computing the measures, including the corrections needed when hit or false-alarm rates hit 0 or 1. the open problem Where does the criterion come from, inside a person? Payoffs and base rates move it, but people move it less than an ideal observer would, and they carry it from one task to the next. A good account of how criteria are learned, and why they are sticky, is still missing. The same question, asked of a model, is the problem of choosing an operating point that the people who use it can understand. In the tour there is a room about thresholds where the light is turned down on purpose. It is the same question, asked with your own eyes. Walk the tour or read the plain list of rooms. Reading list
see also
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hen someone says "yes, I saw it", two things have happened. Something reached them, and they decided it was enough to report. Signal detection theory is the bookkeeping that keeps those two apart. It is the reason a psychologist will not accept a hit rate on its own.
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rev. Oct 24 2026