Signal Detection Theory and its Applications

by

Harold Stanislaw

• LAST REVIEWED: 28 March 2018
• 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.

  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.

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

  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.

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

  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.

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

  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.

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

  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.

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

  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.

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

  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.