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Biometrika 1974 61(1):91-100; doi:10.1093/biomet/61.1.91
© 1974 by Biometrika Trust
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Value systems for comparing two independent multinomial trials

MITCHELL GAIL

National Cancer Institute Bethesda, Maryland

A value system is any real function on the outcome space of a multinomial random variable. The mean value of this function can be regarded as a figure of merit useful for comparing two multinomial populations. For a given value system, we test the null hypothesis that two multinomial populations have the same figure of merit. We also find that value system which maximizes the difference in figure of merit between trials. These results are extended to cross-classified contingency array multinomials, and the concept of the lower-order value system, based on the factorial structure of the outcome space, is developed.

Key Words: Categorical data • Comparative multinomial trials • Contingency tables • Utility • Value system


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