Signal detection theory is a theoretical framework for understanding how decisions are made under uncertainty. It applies whenever judgments must be based on noisy, imperfect evidence—such as deciding whether a faint stimulus was present, whether a face was seen before, whether a medical test result indicates disease, or whether a defendant is guilty. In such situations, observed accuracy reflects not only how well evidence from two states of the world can be distinguished (discriminability) but also how decisively or cautiously the decision maker sets their criterion for responding (response bias). Signal detection theory (SDT) provides principled measures that separate these two components, allowing performance to be conceptualized and quantified in a theoretically coherent way. Although the core ideas underlying SDT date back more than a century, they remain essential today because intuition and simple accuracy measures based on alternative theories often confound sensitivity and bias, leading researchers to draw misleading conclusions. This article reviews the central concepts of SDT, explains the computation and interpretation of its key measures, and considers its enduring foundational role across psychology, neuroscience, medicine, and related fields.

History

The historical roots of SDT lie in an insight that was foundational for experimental psychology: subjective experience can be treated as a noisy measurement. In his work on psychophysics, Gustav Fechner (1860/1966) proposed that when a person perceives a stimulus—such as the heaviness of a weight—the resulting sensation varies from trial to trial because of random noise in the nervous system. As a result, judgments are sometimes incorrect, and not because the observer is guessing but because the internal signal itself fluctuates. This way of thinking transformed errors from nuisances into informative data because the pattern of errors reveals how strongly two stimuli can be discriminated. SDT ultimately grew out of this realization, which provided a principled framework for measuring psychological sensitivity in the presence of unavoidable noise.

Fechner’s proposal was motivated by earlier work on measurement error in the physical sciences. In the early 1800s, the mathematician Carl Friedrich Gauss showed that repeated measurements of the same physical quantity tend to vary around a true value in a systematic way, forming what is now called the normal (or Gaussian) distribution, illustrated schematically in Figure 1A. The key insight was that variability is not merely random chaos but follows lawful statistical regularities that can be characterized by a mean and a dispersion. Although Gauss developed these ideas to understand error in physical measurement, they provided a natural model for thinking about variability in psychological measurements as well, from which internal signals cannot be observed directly. This statistical perspective made it possible to quantify differences between underlying signals in standardized units, laying the groundwork for later developments in psychophysics and, eventually, SDT.

Figure 1B illustrates the Gaussian distribution with the metric (gm in this case) replaced by $σ$. For example, as one usually learns in an introductory statistics class, ~68% of observations will fall within one standard deviation of the mean, and ~95% will fall within two standard deviations. The standard deviation is a special, universal metric because these percentages apply whether the distribution of scores reflects the measured weights of an object (in grams), the measured heights of males (in centimeters), or the cholesterol levels of a population (in milligrams per deciliter). The measurement scale is transformed from grams, centimeters, or milligrams per deciliter to standard deviations. All Gaussian distributions can be expressed in their individual measurement scales or, as illustrated in Figure 1B, in terms of the singular metric $σ$.

Fechner’s insight about noisy psychological measurement can be illustrated with a simple example involving the perception of weight. When you pick up a small weight, you immediately experience how heavy it feels. In a way, your brain just “measured” the heaviness of that weight. Even though we cannot see this measurement, it exists, and it has some magnitude. We might represent this unobservable quantity as $x_i^*$, with the asterisk indicating that this is a psychological measure, not a physical measure made using a scale in the observable world. Fechner’s insight was to assume that this psychological measure can also be usefully conceptualized in terms of Gaussian measurement error: $x_i^*=μ^*+e_i^*$ (Link, 1994). That is, a given weight (e.g., 25 gm) generates a true feeling of heaviness, $μ^*$, which is the average of the feelings it would generate over a large number of trials, plus random error on this particular trial, $e_i^*$. According to this idea, part of the heaviness that you subjectively experience on a given trial is simply random noise in your nervous system. Although we do not have a measurement scale for the mind (such as grams), variability in perception can nevertheless be discussed in terms of standard deviations from the mean.

Imagine that you pick up two small weights, one in each hand, that differ slightly in mass (e.g., weight A = 20 gm and weight B = 18 gm). The heavier weight A in your left hand might feel slightly heavier than weight B in your right hand. If you now repeat that comparison a number of times, you may discover that, occasionally, weight B feels heavier than weight A. The fact that you make an occasional error might seem utterly mundane. However, like Pavlov watching his dog salivate, Fechner thought about Gaussian measurement error and realized that something interesting was happening. Sometimes, random measurement error in the brain may be why the subjective heaviness of the two weights differ from their objective weights. And if the errors are large enough on a given trial, the weight in your right hand (the lighter weight) may subjectively feel heavier than the weight in your left hand. A subtle but important point is that, from the perspective of SDT, errors do not reflect random guesses. Instead, they reflect actual subjective perceptions that differ from objective reality because of random “noise” in the nervous system.

The feelings of heaviness generated by weight A can be conceptualized as a Gaussian distribution with mean $μ_A$, and the feelings of heaviness generated by weight B can be conceptualized as a Gaussian distribution with a lower mean, $μ_B$. For simplicity, it can further be assumed that the two distributions have the same standard deviation ($σ$). With this novel way of thinking, Fechner had a way to make theoretical sense of the errors people make when performing simple tasks like this. In addition, it offered something that had been missing: a measurement scale for subjective experience. Although the difference in how heavy the two weights feel cannot be directly measured, it is possible to indirectly measure the difference between them using the universal metric, namely, how far apart they are in standard deviation units ($σ$). Although it might seem like magic at first, this measure can easily be estimated from the percentage of trials that weight A is mistakenly reported as being the heavier weight. This is possible because Gauss had earlier worked out the mathematical properties of the normal distribution (Figure 1B).

Many years later, Louis Thurstone (1927) realized that this same approach could be used to scale the psychological distance between attributes that cannot even be measured in the observable world. For example, when presented with a choice between Brand A and Brand B, the proportion of a population expressing a preference for Brand B could be used to psychologically scale the magnitude of the difference between the two brands. A few decades later, experimental psychologists and statisticians realized that the psychological distance between two categories could be measured even if only one option was presented at a time—a yes/no task (Tanner & Swets, 1954)—rather than presenting both options simultaneously for a choice—a two-alternative forced-choice task. A real-world example is the criminal trial, in which the decision involves two underlying states of the world—guilty or innocent—but, unlike a forced-choice task, only a single option (the defendant, who is either innocent or guilty) is presented at a given time, and the decision is based on noisy and imperfect evidence (e.g., does the evidence indicate that the defendant is guilty, yes or no?). Many other examples of yes/no detection tasks can be found in the field of psychological science (e.g., did this word appear on an earlier list? Was a quiet tone played on this trial? Is this fake news?).

Core concepts

When using a simple yes/no signal detection task, it is important to conceptualize the data through the lens of SDT. Otherwise, a researcher will probably rely on an intuitive but theoretically incoherent measure to compute an accuracy score for each participant. And if the performance measure is theoretically incoherent, the ability to acquire a deeper theoretical understanding of the question addressed by the research will be on the wrong path from the start.

Every measure of accuracy implies a theory, and it is hard to overstate the importance of that point (Swets, 1986). Even a measure as seemingly straightforward as “percent correct” implies a theory about how the participant is using underlying (unobservable) signals to make a decision. The easiest way to appreciate this point is to consider a concrete example of a signal detection task in which different measures disagree about what the results imply.

Response bias

Consider a recognition memory task in which each participant studies a list of 25 faces randomly selected from a face database and later completes a recognition memory test [see Face Perception]. On this test, suppose that the participant is presented with those same 25 faces again, one at a time, and asked, “Was this one of the faces you saw earlier, yes or no?” If the participant says “Yes” to all 25 faces (100% correct), it might seem to reflect good memory for the studied faces. However, the truth is that you cannot tell if the participant’s memory for these faces is good or bad. The participant may have recognized all 25 faces as having been seen before (good memory), or the participant might be a complete amnesic who does not remember any of the faces but who tends to say “yes” to every presented face anyway (bad memory). In the latter case, we would say that the participant has a strong response bias to say “yes.” Response bias is an issue that must somehow be factored out of the performance score so as not to distort our assessment of a participant’s memory-based performance [see Computational Models of Memory].

This example illustrates how easy it can be to overlook the fact that this recognition task is a signal detection task, with two states of the world (old items that appeared on the list and new items that did not). Critically, in a signal detection task, items from both states must be tested to assess performance. To this day, presenting test items from only one state and computing an accuracy score is a surprisingly common mistake in the literature, a point that has been discussed explicitly in methodological critiques of measurement practices (e.g., Brady et al., 2023).

Suppose this mistake is fixed such that the recognition test now involves the 25 faces presented earlier (the old faces) plus 25 additional faces randomly selected from the same face database (new faces). These faces are then randomly intermixed and presented one at a time for a decision. Often, participants are asked to decide if the item is “old” or “new.” This example illustrates a more general point about signal detection tasks; what matters is not the specific response labels but whether the observer is attempting to distinguish between two underlying states of the world, namely, signal versus noise. In this case, even though the participant is asked to decide if a given test item is old or new, it is still a yes/no signal detection task.

On this much-improved test, a participant with perfect memory would say “old” to all 25 of the old faces and “new” to all 25 of the new faces (100% correct). At the other extreme, a participant with profound amnesia would have to guess and would therefore achieve a level of performance no better than random chance (50% correct). This would be true even with a strong response bias to say “old” to all 50 faces. In that case, the decision would be correct for all 25 old faces and incorrect for all 25 new faces (50% correct). Thus, testing items from both states of the world can take the response bias problem out of the picture. It is important to do so because if a researcher is studying memory, then they want to measure recognition memory, per se—that is, the ability to discriminate old from new faces―separate from response bias.

Separating discriminability and response bias

Under more realistic conditions, a participant’s performance will not fall at either extreme (i.e., 100% or 50% correct), in which case, removing the effects of response bias to measure memory performance becomes tricky. To illustrate, imagine two other participants, one who achieves a score of 84% correct (Participant A) while the other achieves a score of 74% correct (Participant B). It may seem obvious that the first participant has better memory than the second participant, but this is not necessarily correct. The percent correct measure does not disentangle memory-based performance from response bias.

Consider Participant A’s performance in a bit more detail. Suppose that this participant achieved an overall score of 84% correct by symmetrically achieving 84% correct for old items (21 of those 25 faces correctly called “old”) and 84% correct for new items (21 of those 25 faces correctly called “new”). These scores can be shown in a 2 x 2 table (Table 1) in which the rows correspond to the two objective states (old and new), and the columns refer to the participant’s decisions (“old” and “new”). The four cells show the names of each possible response (hit, miss, correct rejection, or false alarm). Balanced performance like this indicates the absence of response bias (i.e., no strong bias to respond “old” to most items or “new” to most items).

Table 1

Hits, Misses, False Alarms, and Correct Rejections

Converting these frequency counts into rates yields Table 2:

Table 2

Hit Rates, Miss Rates, False Alarm Rates, and Correct Rejection Rates

After simplifying, this leads to Table 3:

Table 3

Basic Performance Measures on a Signal Detection Task

Notice that although there are four different scores shown in Table 3, there are only two pieces of information, one in each row. If the hit rate (HR) is .84 in the upper left cell, then the miss rate in the upper right cell must be $1 - .84 = .16$. Similarly, if the correct rejection rate in the lower right cell is .84, the false alarm rate (FAR) in the lower left cell must be $1 - .84 = .16$.

These two pieces of information can be put together to produce an overall memory-based accuracy score. The intuitive approach is to average the two “proportion correct” scores in the upper left and lower right cells—the HR and the correct rejection rate: $(.84 + .84) / 2 = .84$. This is a surprisingly common approach in the scientific literature, but it is not a good idea. Intuition suggests that a person either recognizes an item (extremely strong memory signal) or does not (no memory signal at all). However, it is the decision (“old” or “new”) that is binary, not the underlying memory signal. Memory signals associated with the 50 test faces vary continuously in strength ranging from very weak to very strong. New faces should generate relatively weak memory signals, on average, because they were not seen on a recent list. Even so, some new faces will generate a randomly strong memory signal. Analogously, old faces should generate relatively strong memory signals, on average, because they were seen on the list. Even so, some old faces will generate a randomly weak memory signal (e.g., perhaps the participant did not pay much attention to the face when it was presented).

There is no right answer to how strong a memory signal should be before a participant decides to declare it “old.” Thus, the participant has to select a criterion—the minimum level of memory strength that a test face must generate before calling it “old.” There is no law stipulating whether that criterion level of strength must be weak or strong or something in between; although its placement can be influenced by task instructions, incentives, and speed–accuracy tradeoffs, the criterion is ultimately set by the participant. Wherever the criterion is placed, if the memory strength of a test item falls below that criterion, the face is called “new.”

Figure 2A illustrates the hypothetical distributions of memory signals generated by the old and new items as well as the hypothetical decision criterion set by Participant A. The x-axis represents the strength of the memory signals generated by test items, ranging from very weak (left end) to very strong (right end). The old-item distribution has a higher mean than the new-item distribution, just as the mean heaviness of a 20-gram weight is higher than the mean heaviness of an 18-gram weight. The distributions are assumed to be Gaussian (see the section “History”).

In Figure 2A, the old-item distribution is placed such that 84% of the old items generate a memory signal strong enough to exceed the decision criterion. This is the signal detection interpretation of the participant’s .84 HR. In addition, the new-item distribution is placed such that 16% of the new items also generate a memory signal strong enough to exceed the decision criterion. This is the signal detection interpretation of the participant’s .16 FAR. For two Gaussian distributions that have the same standard deviation (the simplest version of SDT), there is no other way to draw the figure so that it corresponds to Participant A’s pattern of results. It is, therefore, the signal detection interpretation of what is theoretically happening in the unobservable memory of the participant.

The distributions in Figure 2A are two standard deviation units apart. This is theoretically how well Participant A’s brain separates the memory signals of old items and new items. In terms of performance, Participant A is characterized as having achieved a $d'$ of 2.0. $d'$ is a measure of discriminability. Alternatively, a researcher can try to remain purely objective, not adopting any theory, and say Participant A achieved an overall accuracy score of 84% correct. However, in truth, both measures are based on theory, but SDT makes its theoretical assumptions explicit. The implicit theoretical assumptions associated with percent correct are usually hidden from view. The reason is that the scientist who uses percent correct to quantify performance is usually unaware that it implies a theory and is probably using this measure in an understandable but futile effort to be “theory free.” If it is a signal detection task, every measure of performance based on a single pair of HR and FAR implies a theory, including any measure advertised as being theory free.

To see the problem with the use of percent correct from the perspective of SDT, consider the hypothetical performance of Participant B:

Table 4

Basic Performance Measures for Hypothetical Participant B, Who Exhibits a Liberal Response Bias

Unlike Participant A, whose performance across old and new items was balanced (84% correct for both), Participant B has a response bias to say “old” whenever the item is old or new. This is why almost all of the old items are correctly called “old” (98% correct), but half the new items are incorrectly called “old” as well (50% correct). As before, a natural approach is to average the two “proportion correct” scores: $(.98 + .50) / 2 = .74$. Clearly, Participant B achieved a percent correct score of 74%, lower than the 84% correct achieved by Participant A. A scientist might therefore conclude that Participant B has worse memory. However, that would not be a safe conclusion.

Figure 2B illustrates the performance of Participant B in terms of SDT. That is, it depicts the signal detection interpretation of the participant’s .98 HR and .50 FAR. Once again, for two Gaussian distributions that have the same standard deviation (i.e., equal variance), there is no other way to draw the figure such that it corresponds to Participant B’s pattern of results. Note that the decision criterion no longer falls midway between the two distributions but is instead shifted to the left. This leftward shift reflects a liberal response bias—that is, the criterion is placed such that Participant B does not require that a test item generate a very strong memory signal to declare it “old.”

Note that the distributions in Figure 2B are also two standard deviation units apart, just as in Figure 2A. In other words, like Participant A, Participant B achieved a $d'$ of 2.0. Thus, analyzed in terms of SDT, the two participants are equated at the level of underlying memory signals. They differ only in terms of response bias.

There are various ways to quantify response bias, but a common way is to compute how far the decision criterion is placed from the unbiased placement midway between the two distributions. This measure is usually represented as follows: Participant A has a response bias of $c=0$ (exactly at the midpoint), whereas Participant B has a response bias of $c=-1$ (one standard deviation to the left of the midpoint).

Critically, each participant’s performance is characterized by two measures; one measure reflects the participant’s ability to distinguish between old and new items based on their observable memory signals ($d'$), and the other measure reflects the participant’s response bias ($c$). If percent correct is used to measure performance in an effort to be theory free and if the assumptions of SDT are accurate, then the preferred measure of performance mixes together these two separable aspects of performance. A measure like percent correct cannot be theory free if it rejects SDT, as it implicitly does. This is true whether percent correct is used or if instead $\mathit{HR} – \mathit{FAR}$ is used, often referred to as “corrected recognition”; $(\mathit{HR} – \mathit{FAR}) / (1 – \mathit{FAR})$ is used, often referred to as “recognition corrected for guessing”; or $\mathit{HR}/\mathit{FAR}$ is used, referred to as the diagnosticity ratio. Each of these measures has its own corresponding theory, one that usually involves the strong assumption that memory signals are not continuous. 

Computing $d'$

The computational formula for $d'$ is just like $\mathit{HR} – \mathit{FAR}$ except that the researcher must first convert both measures to z-scores (which express a value in standard deviation units relative to the mean of a normal distribution): $d'=z(\mathit{HR})-z(\mathit{FAR})$. For probability $p$ (i.e., the HR or the FAR), it can be converted into its corresponding z-score using NORM.S.INV($p$) in Excel, qnorm($p$) in R, or norminv($p$) in MATLAB. Table 5 shows hypothetical performance scores for five participants.

Table 5

Data From Five Hypothetical Participants

Note. Signal detection metrics cannot be computed for Participant 3 (FAR = 0) or Participant 4 (HR = 1.0).

The $d'$ column was created using the standard formula $z(\mathit{HR})-z(\mathit{FAR})$, and the $c$ column was created using the standard formula for computing response bias: $c=[z(\mathit{HR})+z(\mathit{FAR})]/2$. Clearly, the measures do not work for two of the participants. They do not work because Participant 3 has a FAR of 0, and Participant 4 has a HR of 1.0, values that cannot be converted into z-scores. Anyone who collects data using a yes/no signal detection task is likely to run into this problem. More than anything else, this may explain why researchers often use one of the other available measures such as $\mathit{HR}–\mathit{FAR}$. These measures have no problem with HRs of 1.0 or FARs of 0, but they should. For example, if a task is much too easy, if it induces an extreme response bias, or if there are too few test trials, many participants will have HRs or FARs that fall at the extremes. In such cases, the problem is not $d'$ but is instead the experimental procedure itself. Correcting the procedure would be much better than switching to a dependent measure that may not make theoretical sense.

That said, a few participants are likely to have extreme HRs or FARs even after steps have been taken to improve the procedure. The best approach for dealing with those cases is to use a standard correction formula. The idea behind these formulas is that the HR is not truly 1.0, for example, but more trials would be needed to discover its true value. For example, assume that a researcher tests 25 old items, and the participant got all 25 correct (HR = 1.0). Although the HR is probably less than 1.0 (e.g., at least one error would likely occur if many more old items were tested), it is probably greater than $24/25=.96$ given that no error occurred for the 25 items that were tested. If $N$ represents the number of old items, an adjusted HR ($\mathit{HR}{adj}$) splits the difference using this formula: $HR_{adj}=(N-.50)/N=1-.50/N=.98$. A similar formula can be used to adjust FARs of 0: $FAR_{adj}=.50/N$ (other standard adjustment formulas have been proposed, but the choice among them rarely matters for the conceptual points illustrated). With these adjustments, $d'$ can now be computed, as in Table 6.

Table 6

Data From Five Hypothetical Participants

Note. Included in this table are an adjusted FAR for Participant 3 and an adjusted HR for Participant 4.

This allows the computation of the mean value of all four of these measures (HR, FAR, $d'$, and $c$) and the ability to statistically compare those values to the corresponding values of the participants in a different experimental condition. If a researcher is interested in the effect of an experimental manipulation on memory, the HR, FAR, and response bias ($c$) are not very relevant. The effect of the experimental manipulation on discriminability ($d'$) will facilitate the further theoretical understanding of how memory works.

Questions, controversies, and new developments

SDT has often been the focus of debate, in part because scientists often propose theories in which the underlying signals (e.g., memory signals) are in fact binary, not continuous. These theories often include provisions for randomly guessing “yes” on trials in which a memory signal (or other signal) failed to occur. One challenge for threshold theories is that confidence judgments are naturally graded; participants can report not only whether evidence exceeds a decision threshold but also how strongly the evidence supports their decision. On some trials, the participant will say, “I am 100% sure that this face was on the list.” On other trials, the participant might be 90% confident, or 80% confident, and so on. SDT offers a natural interpretation of these confidence ratings, which simply reflect the continuous nature of the strength of the underlying signal itself (Figure 3).

Many debates about SDT surround a method of analysis based on a plot known as the receiver operating characteristic (ROC). As indicated in Figure 2A (neutral response bias) and Figure 2B (liberal response bias), HRs and FARs change as response bias changes, even though $d'$ remains the same. Figure 4 shows those two cases and a third one in which the criterion is placed farther to the right (conservative response bias). Now there are three pairs of HRs and FARs, all associated with the same $d'$. These data could have come from one participant (with one $d'$) tested three times for three different lists, once with instructions to be liberal (“Only say ‘new’ if you are sure it is new”), once with neutral instructions (“Half the test items will be old and half new, so divide your ‘old/new’ decisions accordingly”), and once again with conservative instructions (“Only say ‘old’ if you are sure it is old”). The three pairs of HRs and FARs can be plotted as shown in Figure 4, which depicts the curvilinear shape of the ROC predicted by SDT. Other theories predict different (sometimes linear) shapes, and many debates have focused on that issue (e.g., Blackwell, 1953; Swets, 1961; Yonelinas, 1994).

If a researcher’s goal is to simply measure performance without worrying too much about a quantitative theory, an easy way to avoid contentious measurement issues is to simply use the two-alternative forced-choice task (Fechner, 1860/1966; Thurstone, 1927). In a two-alternative forced-choice task, there is no decision criterion to worry about because on every trial the participant simply selects the item that generates the stronger signal. In that case, even percent correct is a fine measure because, for main effects (condition A vs. condition B), it will always directionally agree with $d'$ (Brady et al., 2023).

Broader connections

The modern version of SDT emerged essentially simultaneously from the fields of statistics and psychophysics, which converged in the early 1950s with the realization that ROC analysis offers a powerful way to measure discriminability. The measure is “area under the ROC” curve. The larger that area, the better discriminability is. For applied purposes, in which theoretical assumptions are less central, it is often a more robust measure than $d'$. The reason is that $d'$ is based on a parametric model that assumes equal-variance Gaussian signal and noise distributions, which implies a symmetric ROC in z-space. In practice, empirical ROCs often deviate from this assumption. One approach is to use measures such as $d_a$ that allow the two distributions to differ in variance (Hautus et al., 2022). Alternatively, area under the ROC provides a largely model-free measure of discriminability (i.e., it does not depend on specific distributional assumptions) while remaining fully compatible with the signal-detection framework.

Beyond its role as a measurement tool, however, SDT provides a general framework for modeling decision-making under uncertainty. In this framework, behavior reflects the joint influence of underlying evidence strength and decision criteria, allowing theoretically meaningful dissociations between sensitivity (e.g., $d'$) and bias (e.g., $c$). This logic has been applied across core domains of cognitive science. In perception, SDT is used to quantify sensory sensitivity independently of response tendencies. In attention, it is used to assess how attentional manipulations alter the quality of perceptual evidence versus the placement of decision criteria. In memory, SDT provides a formal account of recognition decisions, enabling researchers to distinguish memory strength from response bias and to characterize the structure of mnemonic evidence distributions. In metacognition, extensions of SDT are used to model confidence judgments and to quantify metacognitive sensitivity (i.e., the relationship between confidence and accuracy). In each case, the goal is not simply to evaluate performance but to infer the latent processes that give rise to observable decisions.

These theoretical commitments extend naturally to neuroscience. Neural activity in sensory and associative cortices is often interpreted as reflecting the momentary strength of evidence, linking neural discriminability to behavioral sensitivity (Britten et al., 1992). Decision-related activity in frontal and parietal regions has likewise been linked to the accumulation of evidence toward a response and to criterion-like decision processes (Gold & Shadlen, 2007; Shadlen & Newsome, 2001). Trial-by-trial variability in neural firing can account for psychophysical sensitivity, providing a bridge between SDT measures such as $d'$ and underlying neural coding and decision processes (Britten et al., 1992).

In the 1970s and 1980s, and continuing to this day, the field of diagnostic medicine adopted ROC analysis as the gold standard for assessing the efficacy of diagnostic tests (e.g., Metz, 1978). This is an example of a domain in which the emphasis is on decision performance—such as how well a test discriminates individuals with and without a disease—rather than on specifying the underlying generative model. Today, the same framework underlies analyses in psychology, neuroscience, engineering, and machine learning (Swets et al., 2000), particularly for evaluating classification performance and threshold trade-offs [see AI Model Evaluation]. In modern machine learning, ROC curves and area under the curve are standard tools for assessing classifier performance across decision thresholds, reflecting the same sensitivity bias trade-off formalized by SDT. Applied domains such as eyewitness identification similarly rely on ROC analysis to assess discriminability independent of response bias (Mickes et al., 2012).

Finally, ongoing extensions of SDT, including unequal-variance models, hierarchical formulations, and models that incorporate confidence and response time, underscore its continued development as a flexible framework for linking observable behavior to underlying cognitive and neural processes.

Further reading

• Hautus, M. J., Macmillan, N. A., & Creelman, C. D. (2022). Detection theory: A user’s guide (3rd ed.). Routledge.

• Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. Wiley.

• Wixted, J. T. (2020). The forgotten history of signal detection theory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 46(2), 201–233. https://doi.org/10.1037/xlm0000732