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The Estimation of Proportions in m Groups

Published online by Cambridge University Press:  01 January 2025

Melvin R. Novick ,
Charles Lewis  and
Paul H. Jackson
Melvin R. Novick
Affiliation:
The American College Testing Program The University of Iowa
Charles Lewis
Affiliation:
The University of Illinois
Paul H. Jackson
Affiliation:
The University College of Wales, Aberystwyth
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Abstract

In many applications, it is desirable to estimate binomial proportions in m groups where it is anticipated that these proportions are similar but not identical. Following a general approach due to Lindley, a Bayesian Model II aposteriori modal estimate is derived that estimates the inverse sine transform of each proportion by a weighted average of the inverse sine transform of the observed proportion in the individual group and the average of the estimated values. Comparison with a classical method due to Jackson spotlights some desirable features of Model II analyses. The simplicity of the present formulation makes it possible to study the behavior of the Bayesian Model II approach more closely than in more complex formulations. Also, it is possible to estimate the amount of gain afforded by the Model II analyses.

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 1 , March 1973 , pp. 19 - 46
Copyright
Copyright © 1973 The Psychometric Society

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