Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T10:21:40.138Z Has data issue: false hasContentIssue false

Simple Reaction Time with Markovian Evolution of Gaussian Discriminal Processes

Published online by Cambridge University Press:  01 January 2025

Phillip L. Emerson*
Affiliation:
Cleveland State University

Abstract

If the discriminal distributions of signal-detectability theory evolve in time according to a normal Markov process, they can be characterized by Brownian motion generalized with a constant bias determined by signal strength. If the process is stopped at the first occurrence of a preset criterion displacement, the resulting latency distribution provides a model for the central component of simple reaction time. Discussed are properties of the distribution which should be useful in obtaining experimental predictions from neural-counting assumptions, and in relating reaction times to basic variables of the theory of signal-detectability.

Type
Original Paper
Copyright
Copyright © 1970 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

This paper was written while the author was on a post-doctoral fellowship at the Mental Health Research Institute, University of Michigan, supported by U.S.P.H.S. Training grant T01-MH-7417-07.

References

Christie, L. S., & Luce, R. D. Decision structure and time relations in simple choice behavior. Bulletin of Mathematical Biophysics, 1956, 18, 89112.CrossRefGoogle Scholar
Cox, D. R., & Miller, H. D. The theory of stochastic processes, 1965, New York: Wiley.Google Scholar
Creelman, C. D. Human discrimination of auditory duration. Journal of the Acoustical Society of America, 1961, 34, 582593.Google Scholar
Falmagne, J. C. Stochastic models of choice reaction time with applications to experimental results. Journal of Mathematical Psychology, 1965, 2, 77124.Google Scholar
Feller, W. An introduction to probability theory and its applications, Vol. I, 1950, New York: Wiley.Google Scholar
Feller, W. An introduction to probability theory and its applications, Vol. II, 1966, New York: Wiley.Google Scholar
Granit, R. Receptors and sensory perception, 1955, New Haven: Yale University Press.Google Scholar
Green, D. M., Birdsall, T. G., & Tanner, W. P. Jr. Signal detection as a function of signal intensity and duration. Journal of the Acoustical Society of America, 1957, 29, 523531.CrossRefGoogle Scholar
Hohle, R. H. Inferred components of reaction times as functions of fore-period duration. Journal of Experimental Psychology, 1965, 69, 382386.CrossRefGoogle Scholar
Lit, A. The magnitude of the Pulfrich stereophenomenon as a function of binocular differences of intensity at various levels of illumination. American Journal of Psychology, 1949, 62, 159181.CrossRefGoogle ScholarPubMed
McGill, W. J. Stochastic latency mechanisms. In Luce, R. D., Bush, R. R., and Galanter, E. (Eds.), Handbook of mathematical psychology, Vol. I. New York: Wiley. 1963, 309360.Google Scholar
McGill, W. J. Neural counting mechanisms and energy detection in audition. Journal of Mathematical Psychology, 1967, 4, 351376.Google Scholar
Pieron, H. Nouvelles recherches sur l'analyse du temps de latence sensorielle et sur la loi qui relie ce temps à l'intensitē de l'excitation. Année Psychologie, 1920, 22, 58142.CrossRefGoogle Scholar
Selin, I. The sequential estimation and detection of signals in normal noise II. Information and Control, 1965, 8, 135.CrossRefGoogle Scholar
Stone, M. Models of choice reaction time. Psychometrika, 1960, 25, 251260.CrossRefGoogle Scholar
Swets, J. A., Tanner, W. P., & Birdsall, T. G. Decision processes in perception. Psychological Review, 1961, 68, 301340.Google ScholarPubMed
Takacs, L. Combinatorial methods in the theory of stochastic processes, 1967, New York: Wiley.Google Scholar
Taylor, D. H. Latency models for reaction time distributions. Psychometrika, 1965, 30, 157163.Google ScholarPubMed
Viterbi, A. J. The effect of sequential decision feedback on communication over the Gaussian channel. Information and Control, 1965, 8, 8092.CrossRefGoogle Scholar
Wald, A. Sequential analysis, 1947, New York: Wiley.Google Scholar
Welford, A. T. The measurement of sensory-motor performance: Survey and reappraisal of twelve years' progress. Ergonomics, 1960, 3, 189230.CrossRefGoogle Scholar

A correction has been issued for this article: