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Comparisons of Power for Some Exact Multinomial Significance Tests

Published online by Cambridge University Press:  01 January 2025

Joan M. Gurian ,
Jerome Cornfield  and
James E. Mosimann
Joan M. Gurian
Affiliation:
National Heart Institute
Jerome Cornfield
Affiliation:
National Heart Institute
James E. Mosimann
Affiliation:
National Institute of Neurological Diseases and Blindness National Institutes of Health
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Abstract

Two small-sample tests (proposed by Tate and Clelland and by Chapanis respectively) of hypotheses about the parameters of the multinomial distribution, where

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f(x|p) = n!\prod\limits_{i = 1}^k {\frac{{p_i^{x_i } }}{{x_i !}}} $$\end{document}
are described. A proof is given that a test of the form
\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R = \frac{{\smallint f(x|p)g(p)dp}}{{f(x|p_0 )}}$$\end{document}
, where g(p) ≥ 0 and p0 is the vector of p's specified by the hypothesis, is admissible. It is shown that the Tate and Clelland test is obtained by setting g(p) equal to a constant for all p and is therefore admissible. The Chapanis test is shown to have power less than or equal to the power of the Tate and Clelland test for (k = n = 3) and (k = 3, n = 4).

Type
Original Paper
Information
Psychometrika , Volume 29 , Issue 4 , December 1964 , pp. 409 - 419
Copyright
Copyright © 1964 Psychometric Society

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References

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