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Simultaneous Testing of McNemar’s Problem for Several Populations

Published online by Cambridge University Press:  01 January 2025

M. A. Hamdan ,
W. R. Pirie  and
J. C. Arnold
M. A. Hamdan
Affiliation:
Virginia Polytechnic Institute and State University
W. R. Pirie
Affiliation:
Virginia Polytechnic Institute and State University
J. C. Arnold
Affiliation:
Virginia Polytechnic Institute and State University
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Abstract

McNemar’s problem concerns the hypothesis of equal probabilities for the unlike pairs of correlated binary variables.

We consider four different extensions to this problem, each for testing simultaneous equality of proportions of unlike pairs in c independent populations of correlated binary variables, but each under different assumptions and/or additional hypotheses. For each extension both the likelihood ratio test and the goodness-of-fit chi-square test are given. When c = 1, all cases reduce to McNemar’s problem. Forc ≥ 2, however, the tests are quite different, depending on exactly how the hypothesis and alternatives of McNemar are extended.

An example illustrates how widely the results may differ, depending on which extended framework is appropriate.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 2 , June 1975 , pp. 153 - 161
Copyright
Copyright © 1975 The Psychometric Society

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Footnotes

*

On leave from the American University of Beirut, Beirut, Lebanon.

References

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