Psychometrika

, Volume 40, Issue 1, pp 77–105 | Cite as

A sequential theory of psychological discrimination

  • S. W. Link
  • R. A. Heath
Article

Abstract

A theory of discrimination which assumes that subjects compare psychological values evoked by a stimulus to a subjective referent is proposed. Momentary differences between psychological values for the stimulus and the referent are accumulated over time until one or the other of two response thresholds is first exceeded. The theory is analyzed as a random walk bounded between two absorbing barriers. A general solution to response conditioned expected response times is computed and the important role played by the moment generating function (mgf) for increments to the random walk is examined. From considerations of the mgf it is shown that unlike other random walk models [Stone, 1960; Laming, 1968] the present theory does not imply that response conditioned mean correct and error times must be equal. For two fixed stimuli and a fixed referent it is shown that by controlling values of response thresholds, subjects can produce Receiver Operating Characteristics similar or identical to those predicted by Signal Detection Theory, High Threshold Theory, or Low Threshold Theory.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Audley, R. J. Some observations on theories of choice reaction time: Tutorial review. In S. Kornblum (Ed.)Attention and Performance IV. New York: Academic Press, 1973, 509–545.Google Scholar
  2. Audley, R. J. and Pike, A. R. Some alternative stochastic models of choice.British Journal of Mathematical and Statistical Psychology, 1965,18, (2), 207–225.Google Scholar
  3. Blackwell, H. R. Neural theories of simple visual discriminations.Journal of the Optical Society of America, 1963,53, 129–160.Google Scholar
  4. Cox, D. R. and Miller, H. D.The theory of stochastic processes. London: Methuen, 1965.Google Scholar
  5. Estes, W. K. and Wessel, D. L. Reaction time in relation to display size and correctness of response in forced-choice visual signal detection.Perception and Psychophysics, 1966,1, 369–373.Google Scholar
  6. Feller, W.An introduction to probability theory and its applications. Vol. 2. New York: Wiley, 1966.Google Scholar
  7. Green, D. M. and Swets, J. A.Signal detection theory and psychophysics. New York: Wiley, 1966.Google Scholar
  8. Hall, W. J. Embedding submartingales in Wiener processes with drift, with applications to sequential analysis.Journal of Applied Probability, 1969,6, 612–632.Google Scholar
  9. Helson, H. Adaptation level theory. In S. Koch (Ed.)Psychology: A Study of a Science. New York: McGraw-Hill, 1959, 565–621.Google Scholar
  10. Kinchla, R. A. and Allan, L. G. A theory of visual movement perception.Psychological Review, 1969,76, 537–558.Google Scholar
  11. Kullback, S.Information theory and statistics. New York: Wiley, 1959.Google Scholar
  12. Laming, D. R. Information theory of choice reaction time. New York: Wiley, 1968.Google Scholar
  13. Lappin, J. S. and Disch, K. The latency operating characteristic: I. The effects of stimulus probability on choice reaction time.Journal of Experimental Psychology, 1972,92, 419–427.Google Scholar
  14. Link, S. W. The relative judgment theory of two choice response time.Journal of Mathematical Psychology, 1975,12, (In press).Google Scholar
  15. Luce, R. D. A threshold theory for simple detection experiments.Psychological Review, 1963,70, 61–79.Google Scholar
  16. Miller, H. D. A generalization of Wald's identity with applications to random walks.Annals of Mathematical Statistics, 1961,32, 549–560.Google Scholar
  17. Pike, A. R. Latency and relative frequency of response in psychological discrimination.British Journal of Mathematical and Statistical Psychology, 1968,21, 161–182.Google Scholar
  18. Swets, J. A., Tanner, W. P., and Birdsall, T. G. Decision processes in perception.Psychological Review, 1961,68, 301–340.Google Scholar
  19. Stone, M. Models for choice reaction time.Psychometrika, 1960,25, 251–260.Google Scholar
  20. Thomas, E. A. C. and Myers, J. L. Implications of latency data for threshold and nonthreshold models of signal detection.Journal of Mathematical Psychology, 1972,9, 253–285.Google Scholar
  21. Thurstone, L. L. A law of comparative judgment.Psychological Review, 1927,34, 273–286.Google Scholar
  22. Wald, A.Sequential analysis. New York: Wiley, 1947.Google Scholar

Copyright information

© Psychometric Society 1975

Authors and Affiliations

  • S. W. Link
    • 1
  • R. A. Heath
    • 1
  1. 1.McMaster UniversityHamiltonCanada

Personalised recommendations