Psychology Signal Detection Theory and its Applications
by
Harold Stanislaw
  • LAST MODIFIED: 28 March 2018
  • DOI: 10.1093/obo/9780199828340-0209

Introduction

Signal detection theory (SDT) was originally developed to describe the performance of radars, which must detect signals against a background of noise. As radars become more sensitive (capable of detecting weaker and weaker signals), they are increasingly able to correctly detect when signals are present; these events are called hits, and their probability of occurrence is the hit rate. However, radars may also mistake noise for signals; these events are false alarms, and the corresponding probability is the false alarm rate. A challenge similar to the detection of signals by radars arises when humans listen for weak auditory stimuli. A key notion here is that perception involves decision: Was that faint tone simply imagined, or was it actually presented? SDT addresses this problem by recognizing that hit and false alarm rates reflect two factors, sensitivity and bias. Sensitivity is the ability to distinguish the presence of a signal from its absence. For example, sensitivity to an auditory tone increases when the tone becomes louder or when the noise in which it is presented becomes quieter. Bias is the tendency to state that a signal is present, and it also affects hit and false alarm rates. A listener will more likely report hearing a faint tone when each hit earns $10 and each false alarm costs $1 (bias is set to favor hits), than when the rewards and penalties are reversed (bias is set to avoid false alarms). Early SDT publications demonstrated that common performance measures confound sensitivity and bias. For example, the percentage of correct responses is often conceptualized as reflecting sensitivity, but it changes when bias changes. These early SDT publications derived “pure” measures of sensitivity, including d’ and A’, and “pure” measures of bias, such as β and c. These measures are now routinely assessed in such diverse areas as memory, medicine and clinical diagnosis, library science, weather forecasting, and hazard detection by motor vehicle operators. Indeed, the literature is filled with publications that apply SDT to a wide range of problems. A frequent goal is to demonstrate how the understanding of a particular phenomenon changes when sensitivity is distinguished from bias. Other publications examine how closely human decision-making approaches the theoretical optimum described by SDT. A final group of publications examines models that extend SDT by relaxing the assumptions upon which it is based, considering novel and complex applications, or exploring links to other widely used models.

General Overviews

The references in this section are all books that provide solid overviews of SDT, though they vary in the degree to which they emphasize the mathematical underpinnings of SDT and extensions of the theory. None were published recently; even Macmillan and Creelman 2005 is based upon a 1991 edition. However, the references provide a wealth of useful information to contemporary readers—online reviews frequently describe them as “invaluable classics.” Green and Swets 1966 and Macmillan and Creelman 2005 are essential readings for any serious scholar of SDT. They have a broad scope, while Swets 1996, Swets and Pickett 1982, and Egan 1975 have a narrower focus that may suit the needs of readers with specific interests. Readers who find these books challenging may wish to first examine McNicol 1972 and Wickens 2002, or some of the articles listed under Sample Applications of Signal Detection Theory and Methodological Considerations.

  • Egan, J. P. 1975. Signal detection theory and ROC analysis. New York: Academic Press.

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    This book focuses on receiver operating characteristics (ROCs), which are integral to SDT and describe how changes in bias affect hit and false alarm rates. Opening chapters examine the ROCs resulting from the traditional assumption of Gaussian noise distributions; the text then considers Poisson and other distributions. This information will most interest readers who seek to understand how neural noise and other basic factors limit human perception and decision making.

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    • Green, D. M., and J. A. Swets. 1966. Signal detection theory and psychophysics. New York: Wiley.

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      This seminal book, more than any other, introduced SDT to researchers in psychology. It describes the basics of SDT and demonstrates its applicability, with examples drawn largely from auditory and speech perception. One chapter examines other applications; another explores extensions to multiple observations and multiple observers. A reprint issued in 1974 includes corrections and a bibliography organized by topic; another reprint (published by Peninsula in 1988) expands the bibliography further.

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      • Macmillan, N. A., and C. D. Creelman. 2005. Detection theory: A user’s guide. 2d ed. Mahwah, NJ: Lawrence Erlbaum.

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        The first half of this book echoes Green and Swets 1966, while the second half examines applications of SDT in a variety of experimental paradigms. The book provides extensive advice on the implications of SDT for research design. Thus, it may have greater utility than Green and Swets 1966 for readers who are more interested in practical issues than in the statistical theory behind SDT.

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        • McNicol, D. 1972. A primer of signal detection theory. London: Allen & Unwin.

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          Readers may have difficulty locating this book. However, those who are successful may find the text more accessible than the other books in this section; McNicol’s book has fewer pages, fewer words per page, and introduces key mathematical concepts more gradually than is true of other SDT books.

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          • Swets, J. A. 1996. Signal detection theory and ROC analysis in psychology and diagnostics: Collected papers. Mahwah, NJ: Lawrence Erlbaum.

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            John Swets, who passed away in 2016, was arguably the most influential proponent of SDT in psychology. This collection of twelve articles he wrote or cowrote over a period of twenty years provides an introduction to the theory that is surprisingly bereft of mathematical details. Numerous examples of SDT applications in a wide variety of fields are also included.

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            • Swets, J. A., and R. M. Pickett. 1982. Evaluation of diagnostic systems: Methods from signal detection theory. New York: Academic Press.

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              This book was written to enable comparisons of the relative accuracy of diagnostic devices, particularly those used in medical settings. Thus, it emphasizes issues that are more relevant to engineering and medicine than to psychology. However, the applicability of the material to behavioral concerns is obvious, and the practical examples used to discuss SDT may help readers who struggle with the more abstract approaches used in other general SDT books.

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              • Wickens, T. D. 2002. Elementary signal detection theory. New York: Oxford Univ. Press.

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                As the title indicates, this book explores relatively few extensions of SDT. It aims to provide an introduction to SDT that is thorough and mathematically grounded, but at the same time relatively accessible. Readers who struggle with mathematics will probably find this text easier to understand than Green and Swets 1966 and Macmillan and Creelman 2005, but more challenging than McNicol 1972.

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                Sample Applications of Signal Detection Theory

                Readers who are new to SDT may question the utility of the theory, or they be mystified by the mathematical treatments provided by the references in General Overviews. One way to address these issues is to examine applications of SDT that downplay mathematics and apply the theory in a familiar area. The articles in this section provide several such examples and serve to illustrate the value that can be gained by distinguishing sensitivity from bias. Arkes and Mellers 2002; Ventsislavova, et al. 2016; and Wiley 2006 contain abbreviated descriptions of SDT that serve as good introductions to the more extensive discussions of SDT in the books listed in General Overviews. The articles in this section also demonstrate the use of several different metrics to quantify sensitivity: d’ is used by Scoboria, et al. 2006 and Elsherif, et al. 2017; ROC analyses are used by Johnco, et al. 2015 and Sackeim, et al. 2006; and A’ is used by Meissner and Kassin 2002. Lick and Johnson 2016 focuses on bias rather than sensitivity, using the metric c for this purpose. Collectively, the articles in this section span a broad range of areas, demonstrating the wide applicability of SDT to psychology.

                • Arkes, H. R., and B. A. Mellers. 2002. Do juries meet our expectations? Law and Human Behavior 26:625–639.

                  DOI: 10.1023/A:1020929517312Save Citation »Export Citation »E-mail Citation »

                  Juries are asked to distinguish between defendants who are guilty (signals) or innocent (noise). Bias is an important element in decision making: judges who instruct juries to use the “beyond a reasonable doubt” criterion or the “preponderance of evidence” criterion are overtly attempting to manipulate bias. This article investigates whether juries adopt the bias that SDT suggests is optimal. A discussion of sensitivity in forensic settings is also included.

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                  • Elsherif, M. M., M. I. Saban, and P. Rotshtein. 2017. The perceptual saliency of fearful eyes and smiles: A signal detection study. PLoS One 12.3: e0173199.

                    DOI: 10.1371/journal.pone.0173199Save Citation »Export Citation »E-mail Citation »

                    Lick and Johnson 2016 demonstrates the importance of bias, while this article highlights the importance of sensitivity. The authors report that sensitivity is better for detecting fearful expressions in eyes than for detecting neutral or happy expressions, while sensitivity is better for detecting happy mouths (smiles) than for detecting fearful mouths. Shifts in bias are also described.

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                    • Johnco, C. J., A. Salloum, A. B. Lewin, and E. A. Storch. 2015. Refining clinical judgment of treatment response and symptom remission identification in childhood anxiety using a signal detection analysis on the Pediatric Anxiety Rating Scale. Journal of Child and Adolescent Psychopharmacology 25:674–683.

                      DOI: 10.1089/cap.2015.0102Save Citation »Export Citation »E-mail Citation »

                      One of the challenges in evaluating the impact of clinical interventions is that the criteria for assessing clients may vary across time, practitioners, and clients. Furthermore, different instruments may promote the use of different cutoff values for labeling a client symptomatic or asymptomatic. This article uses ROCs to propose a method for determining whether or not a treatment for pediatric anxiety has been successful.

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                      • Lick, D. J., and K. L. Johnson. 2016. Straight until proven gay: A systematic bias toward straight categorizations in sexual orientation judgments. Journal of Personality and Social Psychology 110:801–817.

                        DOI: 10.1037/pspa0000052Save Citation »Export Citation »E-mail Citation »

                        SDT was first applied in psychology to study audition and vision, but perception takes many forms. This article uses SDT to demonstrate that sensitivity for determining sexual orientation is better than chance, but there is a strong bias toward assuming that individuals are straight. These issues are explored in several studies that readers should find easy to understand, regardless of their area of specialization.

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                        • Meissner, C. A., and S. M. Kassin. 2002. ‘He’s guilty!’: Investigator bias in judgments of truth and deception. Law and Human Behavior 26:469–480.

                          DOI: 10.1023/A:1020278620751Save Citation »Export Citation »E-mail Citation »

                          A problem similar to the jury’s task of deciding guilt or innocence is distinguishing deception from truth. This article applies the SDT framework to analyze previously published and new data concerning the ability of humans to detect lies. The primary finding is that investigative experience and training generally shift bias, but they do not improve sensitivity.

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                          • Sackeim, H. A., S. P. Roose, and P. W. Lavori. 2006. Determining the duration of antidepressant treatment: Application of signal detection methodology and the need for duration adaptive designs (DAD). Biological Psychiatry 59:483–492.

                            DOI: 10.1016/j.biopsych.2005.08.033Save Citation »Export Citation »E-mail Citation »

                            This article shares features with Johnco, et al. 2015, in that both examine clinical applications and apply ROC analyses to distinguish successful from ineffective treatment. However, this article contains a more extensive mathematical treatment of conventional approaches and SDT. It also describes a dynamic approach for predicting treatment outcomes that can be applied earlier than the static approach described in Johnco, et al. 2015.

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                            • Scoboria, A., G. Mazzoni, and I. Kirsch. 2006. Effects of misleading questions and hypnotic memory suggestion on memory reports: A signal-detection analysis. International Journal of Clinical and Experimental Hypnosis 54:340–359.

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                              Individuals often recall more information when they are hypnotized than when they are not, which might signify improved memory under hypnosis (a change in sensitivity). However, individuals also recall more false memories under hypnosis, which suggests an increased willingness to report “hazy” memories (a change in bias). This article examines these alternative possibilities and uses SDT to examine how memory is affected by hypnosis and by the presentation of misleading questions.

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                              • Ventsislavova, P., A. Gugliotta, E. Peña-Suarez, et al. 2016. What happens when drivers face hazards on the road? Accident Analysis and Prevention 91:43–54.

                                DOI: 10.1016/j.aap.2016.02.013Save Citation »Export Citation »E-mail Citation »

                                This article applies SDT to a task that is probably familiar to all researchers: driving. The article also briefly reviews SDT and a “fuzzy” version that acknowledges the indefinite nature of some signals. The authors report that drivers who are inexperienced or have a history of violations are less sensitive to hazards than experienced drivers and those without violations.

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                                • Wiley, R. H. 2006. Signal detection and animal communication. Advances in the Study of Behavior 36:217–247.

                                  DOI: 10.1016/S0065-3454(06)36005-6Save Citation »Export Citation »E-mail Citation »

                                  This article describes the implications of SDT for studies of communication in human and nonhuman species. Readers with other interests will still find the article useful, as it provides a general overview of SDT that includes a review of psychophysical applications. A range of issues is considered, including multidimensional SDT tasks, which are described in more detail in the section on Multiple Signals and Observers.

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                                  Methodological Considerations

                                  Researchers who appreciate the value of SDT may wish to apply the theory in their own work. For example, studies that compare memory or hazard recognition in different experimental conditions typically conclude that any differences found reflect changes in sensitivity (although this terminology may not be explicitly used). A researcher familiar with SDT might realize that the different experimental conditions could also trigger differences in bias. How should a study be designed to accommodate this? More generally, what are the methodological implications when a researcher is particularly interested in studying sensitivity, or in studying bias? General methodological suggestions can be found in Stanislaw and Todorov 1999 and Thomson, et al. 2016. Corwin 1994; Kadlec 1999; and Cradit, et al. 1994 discuss the implications of presenting different numbers of signal and noise trials. Hautus 1997; Miller 1996; and Macmillan, et al. 2004 discuss the estimation of d’, which is one of the most popular measures of sensitivity. Sensitivity can also be assessed by determining the proportion of correct responses in a forced choice task; O’Mahony and Hautus 2008 and García-Pérez and Alcalá-Quintana 2011 discuss methodological issues relating to this approach.

                                  • Corwin, J. 1994. On measuring discrimination and response bias: Unequal numbers of targets and distractors and two classes of distractors. Neuropsychology 8:110–117.

                                    DOI: 10.1037/0894-4105.8.1.110Save Citation »Export Citation »E-mail Citation »

                                    Studies that utilize SDT often present equal numbers of signal and noise trials, but many do not. This article compares SDT to alternatives (called high-threshold models) and examines the performance of each when there are more noise trials than signal trials. The findings are equally applicable to studies that present more signal trials than noise trials. Implications of presenting two different types of noise trials are also explored.

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                                    • Cradit, J. D., A. Tashchian, and C. F. Hofacker. 1994. Signal detection theory and single observation designs: Methods and indices for advertising recognition testing. Journal of Marketing Research 31:117–127.

                                      DOI: 10.2307/3151951Save Citation »Export Citation »E-mail Citation »

                                      SDT typically prescribes presenting a signal multiple times in order to estimate its sensitivity. This may be problematic; for example, a marketer might wish to estimate sensitivity for an advertisement that a consumer has viewed only once. This article describes a methodology for estimating sensitivity in these conditions.

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                                      • García-Pérez, M. A., and R. Alcalá-Quintana. 2011. Improving the estimation of psychometric functions in 2AFC discrimination tasks. Frontiers in Psychology 2.96: 1–9.

                                        DOI: 10.3389/fpsyg.2011.00096Save Citation »Export Citation »E-mail Citation »

                                        In a 2-alternative forced-choice (2AFC) task, sensitivity corresponds to the percentage with which the signal’s location or interval can be correctly identified. However, this relationship holds only in the absence of response bias, such as favoring a particular location or interval when guessing. This article describes how to correct for response bias in 2AFC tasks. The information is geared toward psychophysical studies, but researchers in other areas should also find it useful.

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                                        • Hautus, M. J. 1997. Calculating estimates of sensitivity from group data: Pooled versus averaged estimators. Behavior Research Methods, Instruments & Computers 29:556–562.

                                          DOI: 10.3758/BF03210608Save Citation »Export Citation »E-mail Citation »

                                          d’ is a popular measure of sensitivity. This article compares two methods for estimating a single d’ value when sensitivity is assessed in a group of individuals, which may be of interest in settings that include marketing (as demonstrated by Cradit, et al. 1994). Monte Carlo simulations suggest that the best estimation method varies, depending upon the number of signal and noise trials presented to each participant.

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                                          • Kadlec, H. 1999. Statistical properties of d’ and β estimates of signal detection theory. Psychological Methods 4:22–43.

                                            DOI: 10.1037/1082-989X.4.1.22Save Citation »Export Citation »E-mail Citation »

                                            This article examines how the number of trials affects the accuracy of sensitivity and/or bias estimates. It is recommended that at least 100 signal and 100 noise trials be presented. (This is based purely on statistical considerations; vigilance decrements, as described in Thomson, et al. 2016, may argue for fewer trials.) Recommendations are also provided for methods to use when testing for sensitivity and bias shifts in single-subject designs.

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                                            • Macmillan, N. A., C. M. Rotello, and J. O. Miller. 2004. The sampling distributions of Gaussian ROC statistics. Perception & Psychophysics 66:406–421.

                                              DOI: 10.3758/BF03194889Save Citation »Export Citation »E-mail Citation »

                                              d’ is a good measure of sensitivity when the signal and noise events have Gaussian (normal) distributions of equal variance. This article considers alternative sensitivity measures that work better when the two variances are not equal. Recommendations are provided for both study design and data analysis.

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                                              • Miller, J. 1996. The sampling distribution of d’. Perception & Psychophysics 58:65–72.

                                                DOI: 10.3758/BF03205476Save Citation »Export Citation »E-mail Citation »

                                                Calculation of d’ is problematic when the hit rate equals 1 or the false alarm rate equals 0. This article describes several possible workarounds, and examines the performance of each approach in a series of simulation studies involving different sample sizes.

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                                                • O’Mahony, M., and M. J. Hautus. 2008. The signal detection theory ROC curve: Some applications in food sensory science. Journal of Sensory Studies 23:186–204.

                                                  DOI: 10.1111/j.1745-459X.2007.00149.xSave Citation »Export Citation »E-mail Citation »

                                                  This highly readable article discusses three methods for assessing sensitivity: yes/no tasks, which present either a signal or noise and ask which was presented; 2-alternative forced-choice (2AFC) tasks, which present a signal in one location or trial interval and noise in another, and ask where or when the signal was presented; and 3AFC tasks, which are similar to 2AFC tasks but present noise twice and the signal once.

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                                                  • Stanislaw, H., and N. Todorov. 1999. Calculation of signal detection theory measures. Behavior Research Methods, Instruments, & Computers 31:137–149.

                                                    DOI: 10.3758/BF03207704Save Citation »Export Citation »E-mail Citation »

                                                    This article is light on mathematical details, emphasizing instead methods for calculating SDT metrics using commonly available software. The article is widely cited, but SPSS and other popular software packages now have the ability to calculate SDT measures, rendering some of the material obsolete. Note also that Table 6 contains errors: the final three entries in the A’ column should be 0.77, 0.74, and 0.82.

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                                                    • Thomson, D. R., D. Besner, and D. Smilek. 2016. A critical examination of the evidence for sensitivity loss in modern vigilance tasks. Psychological Review 123:70–83.

                                                      DOI: 10.1037/rev0000021Save Citation »Export Citation »E-mail Citation »

                                                      Vigilance tasks require spending long periods of time searching for signals that rarely occur. Typically, fewer signals are detected as time passes. These vigilance decrements can result from a change in sensitivity or in bias, depending upon task conditions. The authors note that many studies are designed to detect changes in sensitivity rather than bias, and they describe alternative methods—suited to a broad range of tasks—that avoid this problem.

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                                                      Multiple Signals and Observers

                                                      The simplest example of an SDT task in psychology involves a single individual who is tasked with identifying the presence of a single stimulus with precisely specified characteristics. For example, a listener may be asked to detect a tone that has a particular pitch, loudness, and duration. However, researchers have applied SDT to tasks that are far more complex. Stanislaw 1995 and Sorkin, et al. 2001 consider tasks in which two or more individuals (generically called observers) search simultaneously for a signal. The optimal strategy for these tasks is described in Deshmukh and Rajagopalan 2006. Further complications arise when several different signals can occur, as considered by Corbett and Smith 2017 and Kingdom, et al. 2015. More complex still are tasks in which stimuli can vary along a variety of different dimensions. These are considered in the articles DeCarlo 2003 and Ashby and Soto 2015, and in the book Ashby 1992. To illustrate some of the issues that arise in all of these tasks, consider two different strategies that two observers can use when searching for a signal. Each might make a separate decision about its presence, and the two observers could agree to conclude that the signal occurred if either reaches this conclusion individually. An alternative strategy is for the two observers to combine their sensations before making a decision; for example, each could rate the likelihood of the signal on a scale of 1 to 10, with the signal being regarded as present only if the sum of the two ratings is 15 or higher. SDT can predict performance for both decision-making strategies. Making a single decision by simultaneously examining multiple sources of information generally leads to better performance than making separate decisions that are each based upon a single information source (although summing ratings is not the optimal method for combining information across observers). The multiple observer problem is analogous to statistical significance testing, when a researcher measures several dependent variables that each assess the same underlying construct. One analytic approach is to conduct separate univariate tests for each variable, but this is less powerful than conducting a single, multivariate test that examines all variables simultaneously. However, as any reader familiar with statistical testing can attest, the multivariate approach adds considerable mathematical complexity. The references in this section acknowledge this complexity and include figures and worked examples that help elucidate challenging concepts.

                                                      • Ashby, F. G., ed. 1992. Multidimensional models of perception and cognition. Hillsdale, NJ: Lawrence Erlbaum.

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                                                        This book is composed of sixteen chapters from a variety of authors, all of whom discuss some aspect of the multiple signal problem. Some of the material has since been superseded; more advanced theoretical formulations are described by Corbett and Smith 2017 and Ashby and Soto 2015. Nevertheless, this book remains a convenient starting point for readers with an interest in the processing of stimuli that can vary along several dimensions.

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                                                        • Ashby, F. G., and F. A. Soto. 2015. Multidimensional signal detection theory. In The Oxford handbook of computational and mathematical psychology. Edited by J. R. Busemeyer, Z. Wang, J. T. Townsend, and A. Eidels, 13–34. New York: Oxford Univ. Press.

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                                                          Multidimensional extensions of SDT apply when observers make decisions about stimuli that can vary along several dimensions, such as sounds that can differ in pitch and location and duration. One popular extension is general recognition theory (GRT). The authors describe GRT and its underlying assumptions, then use it to analyze data from a two-dimensional discrimination task. They close by considering implications for reaction time studies. A useful glossary is included.

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                                                          • Corbett, E. A., and P. L. Smith. 2017. The magical number one-on-square-root-two: The double-target detection deficit in brief visual displays. Journal of Experimental Psychology: Human Perception and Performance 43:1376–1396.

                                                            DOI: 10.1037/xhp0000386Save Citation »Export Citation »E-mail Citation »

                                                            This article illustrates a multiple signal task by examining how performance declines when observers search for two visual targets simultaneously, instead of focusing upon the detection of a single target. SDT can be used (in conjunction with several key assumptions) to predict the magnitude of this decline. However, the actual decline exceeds the SDT prediction, which has implications for visual processing.

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                                                            • DeCarlo, L. T. 2003. Source monitoring and multivariate signal detection theory, with a model for selection. Journal of Mathematical Psychology 47:292–303.

                                                              DOI: 10.1016/S0022-2496(03)00005-1Save Citation »Export Citation »E-mail Citation »

                                                              This article describes a task that blends simple detection (Is a signal present or not?) with a second decision: If a signal is present, which of two possible characteristics does it possess? A multivariate extension of SDT is presented to analyze the data from this task, and the author describes the advantages provided by this analytic framework over more conventional approaches that eschew SDT.

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                                                              • Deshmukh, A., and B. Rajagopalan. 2006. Performance analysis of filtering software using signal detection theory. Decision Support Systems 42:1015–1028.

                                                                DOI: 10.1016/j.dss.2005.08.002Save Citation »Export Citation »E-mail Citation »

                                                                This article for engineers introduces SDT with examples from psychology. The authors evaluate software filters, which automatically restrict access to undesirable websites. The article deals with extremely low false alarm rates, which can result in the problems examined by Miller 1996 (cited under Methodological Considerations). The article closes with a discussion of sequential software filters, which function in an analogous manner to multiple observers.

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                                                                • Kingdom, F. A., A. S. Baldwin, and G. Schmidtmann. 2015. Modeling probability and additive summation for detection across multiple mechanisms under the assumptions of signal detection theory. Journal of Vision 15.5: 1–18.

                                                                  DOI: 10.1167/15.5.1Save Citation »Export Citation »E-mail Citation »

                                                                  When observers monitor several sources, they can decide if a signal is present by making a separate judgment for each source. However, SDT predicts better performance if the sources are combined before a judgment is made. This article describes these two strategies, along with methods for testing which strategy observers actually appear to use.

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                                                                  • Sorkin, R. D., C. J. Hays, and R. West. 2001. Signal-detection analysis of group decision making. Psychological Review 108:183–203.

                                                                    DOI: 10.1037/0033-295X.108.1.183Save Citation »Export Citation »E-mail Citation »

                                                                    Stanislaw 1995 considers two observers. This article considers tasks that require larger groups of observers to make collective decisions. This increase in the number of observers markedly increases the mathematical complexity required to apply SDT. Readers who are challenged by this complexity will find the included figures helpful. The theoretical discussion is accompanied by descriptions of two studies, which demonstrate how the theoretical material can be applied.

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                                                                    • Stanislaw, H. 1995. Effect of type of task and number of inspectors on performance of an industrial inspection-type task. Human Factors 37:182–192.

                                                                      DOI: 10.1518/001872095779049552Save Citation »Export Citation »E-mail Citation »

                                                                      Industrial inspectors examine goods on a production line or in a quality control lab, seeking defective items. Two inspectors working in tandem or sequentially should identify defects more often than inspectors who work alone, but does the performance improvement match the SDT prediction, and how do inspectors combine their judgments to reach a single decision? A simulated industrial inspection task is used to answer these questions.

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                                                                      Attention Operating Characteristics

                                                                      The ROC (receiver operating characteristic) is a concept central to SDT. Traditional ROCs are two-dimensional figures that plot the hit rate on the y-axis and the false alarm rate on the x-axis. A range of points can be generated to describe the shape of the ROC by asking observers to adopt different biases; rating tasks are frequently used for this purpose. The shape of the ROC provides insight into the noise processes that limit human decision-making. This basic logic can also be applied to situations in which humans must decide how to perform multiple tasks simultaneously; central issues here are how performance is affected by the availability or processing efficiency of the resources needed to perform the tasks (analogous to sensitivity), and the strategy used to allocate those resources to the tasks being performed (analogous to bias). To study these issues, performance on one task can be plotted as a function of performance on the other, creating what are typically called attention operating characteristics (AOCs) or performance operating characteristics (POCs). Their shape provides insight into whether and how the two tasks compete with each other. Norman and Bobrow 1975 is essential reading on this topic, while Sperling and Melchner 1978 is an early implementation of the ideas proposed by Norman and Bobrow. More recent examples are provided by Granholm, et al. 1996; Tsujimoto and Tayama 2004; and Alvarez, et al. 2005. Researchers who study ROCs often have different interests than researchers who study AOCs, but an understanding of SDT is extremely useful when implementing studies of AOCs, and researchers who are familiar with the logic and implementation of AOCs can greatly benefit from this in designing and interpreting SDT studies.

                                                                      • Alvarez, G. A., T. S. Horowitz, H. C. Arsenio, J. S. DiMase, and J. M. Wolfe. 2005. Do multielement visual tracking and visual search draw continuously on the same visual attention resources? Journal of Experimental Psychology: Human Perception and Performance 31:643–667.

                                                                        DOI: 10.1037/0096-1523.31.4.643Save Citation »Export Citation »E-mail Citation »

                                                                        This article begins with a general overview of AOC methodology. This includes a brief description of the AOCs generated by various performance-resource functions, which are fundamental in studies of attention and described in more detail by Norman and Bobrow 1975. The theoretical discussion of AOCs is followed by a series of experiments demonstrating that the resources required to perform visual search partially overlap with those used for visual tracking.

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                                                                        • Granholm, E., R. F. Asarnow, and S. R. Marder. 1996. Dual-task performance operating characteristics, resource limitations, and automatic processing in schizophrenia. Neuropsychology 10:11–21.

                                                                          DOI: 10.1037/0894-4105.10.1.11Save Citation »Export Citation »E-mail Citation »

                                                                          This article compares the performance of schizophrenic patients with that of controls. The former perform worse than the latter in dual-task conditions. AOC analysis suggests this is due to reduced resource availability in the schizophrenic patients, rather than problems with resource allocation. The ability to make this distinction demonstrates the power of AOC analyses, and is similar to the ability of SDT to distinguish sensitivity effects from bias effects.

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                                                                          • Norman, D. A., and D. G. Bobrow. 1975. On data-limited and resource-limited processes. Cognitive Psychology 7:44–64.

                                                                            DOI: 10.1016/0010-0285(75)90004-3Save Citation »Export Citation »E-mail Citation »

                                                                            Green and Swets 1966 (cited under General Overviews) is the seminal reference for SDT; this is the seminal article for AOCs. It provides a thorough introduction to the logic underlying AOCs, and interprets several previously published studies from the AOC perspective. Suggestions for implementing AOC methodology are provided, but readers hoping to find a worked example of AOC data analysis will need to turn instead to one of the other articles in this section.

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                                                                            • Sperling, G., and M. J. Melchner. 1978. The attention operating characteristic: Examples from visual search. Science 202:315–318.

                                                                              DOI: 10.1126/science.694536Save Citation »Export Citation »E-mail Citation »

                                                                              This article describes one of the earliest implementations of AOC methodology. The treatment is almost entirely lacking in mathematical details, and numerous figures depicting a variety of AOCs present the study findings. Readers who are new to the concept of AOCs will find this a highly accessible introduction.

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                                                                              • Tsujimoto, S., and T. Tayama. 2004. Independent mechanisms for dividing attention between the motion and the color of dynamic random dot patterns. Psychological Research 68:237–244.

                                                                                DOI: 10.1007/s00426-003-0137-6Save Citation »Export Citation »E-mail Citation »

                                                                                Alvarez, et al. 2005 uses AOCs to demonstrate that visual search and visual tracking may compete for resources, while this article uses a similar AOC-based approach to demonstrate that motion and color perception do not compete for attentional resources. An analysis of correlations between motion and color responses across trials leads to a similar conclusion, demonstrating the link between AOCs and alternative methods of testing for resource competition.

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                                                                                Extensions and Relationships to Other Models

                                                                                When SDT was first applied in psychology, researchers were not particularly concerned with identifying where noise is introduced in the chain of events leading from stimulus presentation to overt response; it was sufficient to simply recognize that noise is present when observers search for signals, and that observers respond to this problem by adopting a particular bias. More recently, research such as Cabrera, et al. 2015 has noted that bias itself may vary, thereby generating noise. Similarly, DeCarlo 2011 notes that signals may vary, and this variability—another source of noise—may be of interest. To investigate these and related issues, researchers have extended SDT well beyond the parameters specified by Green and Swets 1966 (cited under General Overviews). Further extensions have resulted from attempts to integrate or compare and contrast SDT with other major theories in psychology. Williams and Zumbo 2003 notes similarities between SDT and item response theory; DeCarlo 1998 notes that SDT is an example of a generalized linear model; and Luan, et al. 2011 explores links between SDT and fast-and-frugal trees. Massoni, et al. 2014 and Kellen and Klauer 2015 examine the implications of SDT for understanding confidence ratings, as well as the implications of confidence rating data for SDT. A final group of articles proposes novel methods that supplement traditional SDT approaches with other methodologies. Koop and Criss 2016 and Pleskac and Busemeyer 2010 suggest dynamic data collection approaches that can provide far more information than the static approaches commonly used in SDT. These proposals require more refinement before they can be widely implemented, but they are intriguing and point toward the development of a general theory of perception, cognition, and decision-making in which SDT will play a central role.

                                                                                • Cabrera, C. A., Z. Lu, and B. A. Dosher. 2015. Separating decision and encoding noise in signal detection tasks. Psychological Review 122:429–460.

                                                                                  DOI: 10.1037/a0039348Save Citation »Export Citation »E-mail Citation »

                                                                                  SDT assumes that bias remains constant across trials within a given experimental condition. However, bias may vary when the number of response options is large or data are obtained across multiple days. This variation results in decision noise. The authors describe a method for distinguishing it from the representational noise that traditional SDT acknowledges. The method is tested using simulated data, and demonstrated using data from a visual detection task.

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                                                                                  • DeCarlo, L. T. 1998. Signal detection theory and generalized linear models. Psychologiocal Methods 3:186–205.

                                                                                    DOI: 10.1037/1082-989X.3.2.186Save Citation »Export Citation »E-mail Citation »

                                                                                    Generalized linear models (GLMs) are ubiquitous in statistics and underlie popular statistical tools such as multiple regression and analysis of variance. This article demonstrates that SDT is a subset of GLMs, and that an extension of logistic regression can be useful for modeling and analyzing SDT parameters. The utility of this approach is demonstrated by reexamining the data from classic studies, resulting in alternative interpretations of those data.

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                                                                                    • DeCarlo, L. T. 2011. Signal detection theory with item effects. Journal of Mathematical Psychology 55:229–239.

                                                                                      DOI: 10.1016/j.jmp.2011.01.002Save Citation »Export Citation »E-mail Citation »

                                                                                      Variability may be introduced by decision noise, as Cabrera, et al. 2015 notes; however, signals themselves may vary. For example, recognition memory studies present several different “old” items, some of which may be more familiar than others. DeCarlo describes a method for estimating these item effects. The method is demonstrated using data from a recognition memory task, and from a task in which X-rays are examined for bone fractures.

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                                                                                      • Kellen, D., and K. C. Klauer. 2015. Signal detection and threshold modeling of confidence-rating ROCs: A critical test with minimal assumptions. Psychological Review 122:542–557.

                                                                                        DOI: 10.1037/a0039251Save Citation »Export Citation »E-mail Citation »

                                                                                        SDT assumes that the evidence upon which decisions are based has a continuous distribution. The authors here question this assumption in the context of recognition memory studies, and suggest that familiarity (the cognitive dimension upon which recognition decisions are based) may instead have a finite number of discrete states. Data from several previously published studies are used to support this interpretation, which has implications that extend well beyond the memory domain.

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                                                                                        • Koop, G. J., and A. H. Criss. 2016. The response dynamics of recognition memory: Sensitivity and bias. Journal of Experimental Psychology: Learning, Memory, and Cognition 42:671–685.

                                                                                          DOI: 10.1037/xlm0000202Save Citation »Export Citation »E-mail Citation »

                                                                                          This article discusses baseball before turning to the limits of SDT in quantifying performance on memory tasks. The authors then describe response dynamics, which complements the examination of traditional SDT parameters and differs from the analysis of response times, which is considered in Pleskac and Busemeyer 2010. Response dynamics involves mapping and examining fine-grained responses (such as pixel-level computer mouse movements) that take place between the presentation of a stimulus and the response to that stimulus.

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                                                                                          • Luan, S., L. J. Schooler, and A. Gigerenzer. 2011. A signal-detection analysis of fast-and-frugal trees. Psychological Review 118:316–338.

                                                                                            DOI: 10.1037/a0022684Save Citation »Export Citation »E-mail Citation »

                                                                                            Fast-and-frugal trees (FFTs) are tools used in medical triage applications and for other tasks that require decisions to be made extremely quickly. Each FFT consists of a series of questions that are asked in a fixed order. Depending upon the answer, a decision is made or another question is asked. This article describes the links between SDT and FFT theory, and demonstrates how each informs the other.

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                                                                                            • Massoni, S., T. Gajdos, and J. Vergnaud. 2014. Confidence measurement in the light of signal detection theory. Frontiers in Psychology 5.1455: 1–13.

                                                                                              DOI: 10.3389/fpsyg.2014.01455Save Citation »Export Citation »E-mail Citation »

                                                                                              Under the SDT framework, confidence ratings—as elicited by rating tasks—can be used to generate ROCs and estimate sensitivity. However, studies can also examine how confidence ratings are generated. This article compares three different methods for doing so, and interprets the results in terms of SDT.

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                                                                                              • Pleskac, T. J., and J. R. Busemeyer. 2010. Two-stage dynamic signal detection: A theory of choice, decision time, and confidence. Psychological Review 117:864–901.

                                                                                                DOI: 10.1037/a0019737Save Citation »Export Citation »E-mail Citation »

                                                                                                The authors of this article note that choice, confidence, and reaction time are commonly studied in cognition and other areas of psychology; however, the three measures are usually studied individually or in pairs. For example, SDT links choice to confidence, but it ignores reaction time. To remedy this, the authors propose a dynamic model that links SDT with random walk models, which are frequently used to analyze reaction time data.

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                                                                                                • Williams, K. M., and B. D. Zumbo. 2003. Item characteristic curve estimation of signal detection theory-based personality data: A two-stage approach to item response modeling. International Journal of Testing 3:189–213.

                                                                                                  DOI: 10.1207/S15327574IJT0302_7Save Citation »Export Citation »E-mail Citation »

                                                                                                  Item effects, as described by DeCarlo 2011, are related to the item parameters that are of paramount interest in item response theory (IRT). This article is one of several that identifies links between SDT, which prescribes metrics that can be used to describe how well individuals can distinguish items, and IRT, which prescribes metrics that can be used to describe how well items can distinguish individuals.

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