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Exact Probabilities for Contingency Tables Using Binomial Coefficients

Published online by Cambridge University Press:  01 January 2025

James M. Sakoda  and
Burton H. Cohen
James M. Sakoda
Affiliation:
University of Connecticut
Burton H. Cohen
Affiliation:
University of Connecticut
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Abstract

The use of binomial coefficients in place of factorials to shorten the calculation of exact probabilities for 2 × 2 and 2 × r contingency tables is discussed. A useful set of inequalities for estimating the cumulative probabilities in the tail of the distribution from the probability of a single table is given. A table of binomial coefficients with four significant places and n through 60 is provided.

Type
Original Paper
Information
Psychometrika , Volume 22 , Issue 1 , March 1957 , pp. 83 - 86
Copyright
Copyright © 1957 The Psychometric Society

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References

Federighi, E. The use of chi square in small samples. Amer. soc. Rev., 1950, 15, 777–779CrossRefGoogle Scholar
Fisher, R. A. Statistical methods for research workers, New York: Hafner, 1954Google Scholar
Freeman, G. H. and Halton, J. H. Note of an exact treatment of contingency, goodness of fit, and other problems of significance. Biometrika, 1951, 38, 141–149CrossRefGoogle ScholarPubMed
Hald, A. Statistical tables and formulas, New York: Wiley, 1952Google Scholar
Miller, J. C. P. Tables of binomial coefficients. Royal Society mathematical tables Vol. 3, Cambridge: University Press, 1954Google Scholar