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A Generalization of the Bush-Mosteller Model with Some Significance Tests

Published online by Cambridge University Press:  01 January 2025

Mary I. Hanania
Mary I. Hanania*
Affiliation:
University of California, Berkeley
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Abstract

A generalization of the Bush-Mosteller learning model is proposed in connection with two-alternative learning situations with continuous reinforcement. The problem is to test the hypothesis that reward and non-reward are equally effective in promoting learning. Statistically this reduces to testing a hypothesis about the value of a single parameter θ, while a set of other parameters remains unspecified. The test presented has the property of being asymptotically locally most powerful among all tests of the same size and asymptotically similar. The application of the test is illustrated.

Type
Original Paper
Information
Psychometrika , Volume 24 , Issue 1 , March 1959 , pp. 53 - 68
Copyright
Copyright © 1959 The Psychometric Society

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Footnotes

*

I would like to express my gratitude to Professors J. Neyman and E. L. Scott, Department of Statistics, University of California, for their constant assistance and encouragement throughout the research that led to this paper and during its preparation, and to Professor F. W. Irwin, Department of Psychology, University of Pennsylvania, for his many helpful suggestions and comments.

References

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Hanania, M. Some statistical tests of hypotheses on the effect of reward in learning, Berkeley: Univ. California, 1957.Google Scholar
Lehmann, E. L. and Stein, C. Most powerful tests of composite hypotheses: I. Normal distributions. Ann. math. Statist., 1948, 19, 495–516.CrossRefGoogle Scholar
Neyman, J. and Pearson, E. S. On the problem of the most efficient tests of statistical hypotheses. Phil. Trans., Ser. A, 1933, 231, 289–337.Google Scholar
Neyman, J.Sur une famille de tests asymptotiques des hypothèses statistiques composées. Trabajos de Estadística, 1954, 5, 161–168.CrossRefGoogle Scholar