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A Note on the Sequential Probability Ratio Test

Published online by Cambridge University Press:  01 January 2025

Ewart A. C. Thomas
Ewart A. C. Thomas*
Affiliation:
Stanford University
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Abstract

Link and Heath [1975] have analysed a random walk model for two-choice reaction time on the assumption that the two probability density functions (p.d.f.s) of the step-size, each p.d.f. corresponding to one stimulus, are mirror reflections of each other; and they have demonstrated the critical role played by the symmetry of the moment generating function (m.g.f.) of the step size in the determination of whether or not error and correct reaction times are equal. It is shown here that, given reflection symmetry, m.g.f. symmetry is necessary and sufficient for the random walk model to be equivalent to a sequential probability ratio test.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 1 , March 1975 , pp. 107 - 111
Copyright
Copyright © 1975 Psychometric Society

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Footnotes

*

I am very grateful to Stephen W. Link for lengthy discussions of the ideas contained in the paper by Link and Heath, and to D. R. J. Laming and the referees for their comments.

References

Bartlett, M. S. Introduction to Stochastic Processes. Cambridge University Press, 1962.Google Scholar
Laming, D. R. J.. Information Theory of Choice-Reaction Times, 1968, New York: Academic Press.Google Scholar
Link, S. W. and Heath, R. A.. A theory of sequential comparative judgement. Psychometrika, 1975, 40, 77–106.CrossRefGoogle Scholar
Stone, M.. Models for Choice-Reaction Time. Psychometrika, 1960, 25, 251–260.CrossRefGoogle Scholar
Widder, D. V. The Laplace Transform. Princeton University Press, 1946.Google Scholar