Signal detection theory (SDT) is a model of perceptual DECISION MAKING whose central tenet is that cognitive performance, limited by inherent variability, requires a decision process. Applying a statistical-decision approach developed in studying radar reception, W. P. Tanner and J. A. Swets proposed in 1954 a "decision-making theory of visual detection," showing how sensory and decision processes could be separated in the simplest perceptual task. Extensive early application to detection problems accounts for the name of the theory, but SDT is now used widely in cognitive science as a modeling tool and for analyzing discrimination and classification data (see PSYCHOPHYSICS).

In detection, an observer attempts
to distinguish two stimuli, *noise (N)* and *signal plus
noise (S + N).* These stimuli evoke not single percepts,
but trial-to-trial distributions of effects on some relevant decision
axis, as in figure 1a. The observer's ability to tell the stimuli
apart depends on the overlap between the distributions, quantified
by *d",* the normalized difference between their
means. The goal of identifying each stimulus as an example of *N* or *S + N* as
accurately as possible can be accomplished with a simple decision
rule: Establish a *criterion* value of the decision axis
and choose one response for points below it, the other for points
above it. The placement of the criterion determines both the *hits* ("yes" responses
to signals) and the *false alarms* ("yes" responses
to noise). If the criterion is high (strict), the observer will
make few false alarms, but also not that many hits. By adopting
a lower (more lax) criterion (figure 1b), the number of hits is increased,
but at the expense of also increasing the false alarm rate. This
change in the decision strategy does not affect *d",* which
is therefore a measure of *sensitivity* that is independent
of *response bias.*

The statistic *d"* is
calculated by assuming that the underlying distributions in the
perceptual space are Gaussian and have equal variance. Both of these
assumptions can be tested by varying the location of the criterion
to construct an *ROC* (receiver operating characteristic) curve,
the hit rate as a function of the false-alarm rate (figure 2). ROCs
can be obtained by varying instructions to encourage criterion shifts;
or more efficiently by using *confidence ratings,* interpreting
each level of confidence as a different criterion location. Most
data are consistent with the assumption of normality (Swets 1986)
or the very similar predictions of logistic distributions, which arise
from choice theory (Luce 1963). For data sets that reveal unequal
variances, accuracy can be measured using the area under the ROC,
a statistic that is nonparametric (makes no assumptions about the
underlying distributions) when calculated from a full ROC rather
than a single hit/false-alarm pair (Macmillan and Creelman 1996).

The source of the variability in
the underlying distributions can be internal or external. When variability
is external (as, for example, when a tone is presented in random
noise), the statistics of the noise can be used to predict *d"* for *ideal
observers* (Green and Swets 1966: chap. 6). Similarly, the decision
rule adopted by the observer depends on experimental manipulations
such as the frequency of the signal, and the optimal criterion location
can be predicted using Bayes's rule. Ideal sensitivity and
response bias are often not found, but in some detection and discrimination
situations they provide a baseline against which observed performance
may be measured. The stimulus noise is much harder to characterize
in other perceptual situations, such as X-ray reading, where *N* is healthy
tissue and *S + N* diseased (Swensson and Judy 1981).
Most of the many applications of SDT to memory invoke only internal
variability. For example, in a recognition memory experiment (Snodgrass
and Corwin 1988) the *S + N* distribution arises
from old items and the *N* items from new ones. Klatzky and Erdelyi
(1985) argued that the effect of hypnosis on recognition memory
is to alter criterion rather than *d",* and that
distinguishing these possibilities requires presenting both.

The examples so far use a one-interval
experimental method for measuring discrimination: in a sequence
of trials, *N* or *S + N* is presented and
the observer attempts to identify the stimulus, with or without
a confidence rating. This paradigm has been widely used, but not
exclusively: In *forced-choice* designs, each trial contains *m* intervals,
one with *S + N* and the rest with *N*, and
the observer chooses the *S + N* interval; in *same-different,* two
stimuli are presented that may be the same (both *S + N* or
both *N*) or different (one of each); *oddity* is
like forced-choice, except that the "odd" interval
may contain either *S + N* or both *N*; and so
on. Workers in areas as diverse as SPEECH PERCEPTION and
food evaluation have argued that such designs are preferable to
the one-interval design in their fields.

In the absence of theory, it is difficult
to compare performance across paradigms, but SDT permits the abstraction
of the same statistic, *d"* or a derivative, from
all (Macmillan and Creelman 1991). The basis of comparison is that *d"* can
always be construed as a distance measure in a perceptual space
that contains multiple distributions. For the one-interval
design, this space is one-dimensional, as in figure 1, but for other
designs each interval corresponds to a dimension. According to SDT,
an unbiased observer with *d"* = 2 will
be correct 93 percent of the time in two-alternative forced-choice
but as low as 67 percent in same-different. Some tasks can be approached
with more than one decision rule; for example, the optimal strategy
in same-different is to make *independent observations* in
the two intervals, whereas in the *differencing* model the effects
of the two intervals are subtracted. By examining ROC curve shapes, Irwin
and Francis (1995) concluded that the differencing model was correct
for simple visual stimuli, the optimal model for complex ones.

Detection theory also provides a
bridge between discrimination and other types of judgment, particularly
identification (in which a distinct response is required for each
of *m* stimuli) and classification (in which stimuli are
sorted into subclasses). For sets of stimuli that differ along a
single dimension, such as sounds differing only in loudness, SDT allows
the estimation of *d"* for each pair of stimuli
in both identification and discrimination. The two tasks are roughly
equivalent when the range of stimuli is small, but increasingly
discrepant as range increases. Durlach and Braida's (1969)
theory of resolution describes both types of experiments and relates
them quantitatively under the assumption that resolution is limited
by both sensory and memory variance, the latter increasing with
range.

For more complex stimulus sets, a multidimensional
version of SDT is increasingly applied (Graham 1989; Ashby 1992).
In natural extensions of the unidimensional model, each stimulus
is assumed to give rise to a distribution in a multidimensional perceptual
space, distances between stimuli reflect resolution, and the observer
uses a decision boundary to divide the space into regions, one for
each response. The more complex representation raises new issues
about the perceptual interactions between dimensions, and about
the form of the decision boundary; many of these concepts have been
codified under the rubric of generalized recognition theory, or GRT
(Ashby and Townsend 1986). Multidimensional SDT can be used to determine
the optimal possible performance, given the MENTAL REPRESENTATION of
the observer (Sperling and Dosher 1986). For example, Palmer (1995)
accounted for the set-size effect in visual search without assuming
any processing limitations, and Graham, Kramer, and Yager (1987)
predicted performance in both uncertain detection (in which *S + N* can
take on one of several values) and summation (in which redundant
information is available) for several models. In a more complex
example of information integration, Sorkin, West, and Robinson (forthcoming) showed
how a group decision can be predicted from individual inputs without
assumptions about interaction among its members. In all of these
cases, as for the complex designs described earlier, SDT provides
a baseline analysis of the situation against which data can be compared
before specific processing assumptions are invoked.

- PATTERN RECOGNITION AND FEEDFORWARD NETWORKS
- PROBABILITY, FOUNDATIONS OF
- STATISTICAL TECHNIQUES IN NATURAL LANGUAGE PROCESSING

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