Detection theory, or signal detection theory, is a means to quantify the ability to discern between signal and noise. It was first introduced in 1966 by John A. Swets and David M. Green and has been continuously improved since. Green and Swets criticized the traditional methods of Psychophysics for their inability to discriminate between the real sensitivity of subjects and their (potential) response biases. In information theory, a signal is the sequence of states of a communications channel that encodes a message. ... In science, and especially in physics and telecommunication, noise is fluctuations in and the addition of external factors to the stream of target information (signal) being received at a detector. ... 1966 (MCMLXVI) was a common year starting on Saturday (the link is to a full 1966 calendar). ... Psychophysics is the branch of cognitive psychology dealing with the relationship between physical stimuli and their perception. ...

Detection theory has applications in many fields such as diagnostics of any kind, quality control, telecommunications, and psychology. The concept is similar to the signal to noise ratio used in the sciences, and it is also usable in alarm management, where it is important to separate important events from background noise. ... In engineering and manufacturing, quality control and quality engineering are involved in developing systems which ensure that products or services are designed and produced to meet or exceed customer requirements and expectations. ... Telecommunication involves the transmission of signals over a distance for the purpose of communication. ... Psychology is an academic and applied field involving the study of the human mind, brain, and behavior. ... The phrase signal-to-noise ratio, often abbreviated SNR or S/N, is an engineering term for the ratio between the magnitude of a signal (meaningful information) and the magnitude of background noise. ... Alarm management is the application of human factors (or ergonomics as the field is referred to outside the U.S.) along with instrumentation engineering and systems thinking to manage the design of an alarm system to increase its usability. ... The term background can have any of the following meanings: Background (computer software) refers to software that is running, but not being displayed. ... Environmental Noise is unwanted sound, which may cause both nuisance and damage to health. ...

According to the theory, there are a number of psychological determiners of how we will detect a signal, and where our threshold levels will be. Experience, expectations, physiological state (e.g. fatigue) and other factors affect thresholds. For instance, a sentry in wartime will likely detect fainter stimuli than the same sentry in peacetime.

Psychology

Signal detection theory (SDT) is used when psychologists want to measure the way we make decisions under conditions of uncertainty, such as how we would perceive distances in foggy conditions. SDT assumes that the decision maker is not a passive receiver of information, but an active decision-maker who makes difficult perceptual judgements under conditions of uncertainty. In foggy circumstances, we are forced to decide how far an object is away from us based solely upon visual stimulus which is impaired by the fog. Since the brightness of the object, such as a traffic light, is used by the brain to discriminate the distance of an object, and the fog reduces the brightness of objects, we perceive the object to be much further away than it actually is (see also Decision theory). Decision theory is an interdisciplinary area of study, related to and of interest to practitioners in mathematics, statistics, economics, philosophy, management and psychology. ...

To apply signal detection theory to a data set where stimuli were either present or absent, and the observer categorized each trial as having the stimulus present or absent, the trials are sorted into one of four categories:

Based on the proportions of these types of trials, numerical estimates of sensitivity can be obtained with statistics like the sensitivity index d' and A', and response bias can be estimated with statistics like β. Scientists recognize two different sorts of error:[1] Statistical error: the difference between a computed, estimated, or measured value and the true, specified, or theoretically correct value that is caused by random, and inherently unpredictable fluctuations in the measurement apparatus. ... Scientists recognize two different sorts of error:[1] Statistical error: the difference between a computed, estimated, or measured value and the true, specified, or theoretically correct value that is caused by random, and inherently unpredictable fluctuations in the measurement apparatus. ... The sensitivity index or d (pronounced dee-prime) is a statistic used in signal detection theory. ...

See also

• Statistical signal processing
• Estimation theory
• Just noticeable difference
• Likelihood-ratio test
• Neyman-Pearson lemma
• Psychometric function
• Receiver operating characteristic

Statistical signal processing is an area of signal processing dealing with signals and their statistical properties (e. ... It has been suggested that this article or section be merged with estimator. ... In psychophysics, a just noticeable difference, customarily abbreviated with lowercase letters as jnd, is the smallest difference in a specified modality of sensory input that is detectable by a human being or other animal. ... A likelihood-ratio test is a statistical test relying on a test statistic computed by taking the ratio of the maximum value of the likelihood function under the constraint of the null hypothesis to the maximum with that constraint relaxed. ... In statistics, the Neyman-Pearson lemma states that when doing a hypothesis test between two point hypotheses H0: θ=θ0 and H1: θ=θ1, then the likelihood-ratio test which rejects H0 in favour of H1 when is the most powerful test of size α. ... A psychometric function describes the relationship between a parameter of a physical stimulus and the responses of a person who has to decide about a certain aspect of that stimulus. ... In signal detection theory, a receiver operating characteristic (ROC), also receiver operating curve, is a graphical plot of the sensitivity vs. ...

References

• Abdi, H. (2007). "Signal detection theory". in: Salkind, N.J. (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage.
• Coren, S., Ward, L.M., Enns, J. T. (1994) Sensation and Perception. (4th Ed.) Toronto: Harcourt Brace.
• Green, D.M., Swets J.A. (1966) Signal Detection Theory and Psychophysics. New York: Wiley. (ISBN 0471324205)
• Kay, SM. Fundamentals of Statistical Signal Processing: Detection Theory (ISBN 0-13-504135-X)
• McNichol, D. (1972) A Primer of Signal Detection Theory. London: George Allen & Unwin.
• Swets, J.A. (ed.) (1964) Signal detection and recognition by human observers. New York: Wiley
• Van Trees HL. Detection, Estimation, and Modulation Theory, Part 1 (ISBN 0-47-109517-6; website)

External links

• A Description of Signal Detection Theory
• An application of SDT to safety (pdf file)