Psychometrika

, Volume 22, Issue 1, pp 83–86 | Cite as

Exact probabilities for contingency tables using binomial coefficients

  • James M. Sakoda
  • Burton H. Cohen
Article
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Revised:

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 andn through 60 is provided.

Keywords

Public Policy Statistical Theory Contingency Table Cumulative Probability Exact Probability 
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References

  1. [1]
    Federighi, E. The use of chi square in small samples. Amer.soc. Rev., 1950,15, 777–779.Google Scholar
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    Fisher, R. A. Statistical methods for research workers. New York: Hafner, 1954.Google Scholar
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    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, 141–149.Google Scholar
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    Hald, A. Statistical tables and formulas. New York: Wiley, 1952.Google Scholar
  5. [5]
    Miller, J. C. P., editor. Tables of binomial coefficients. Royal Society mathematical tables Vol. 3. Cambridge: University Press, 1954.Google Scholar

Copyright information

© Psychometric Society 1957

Authors and Affiliations

  • James M. Sakoda
    • 1
  • Burton H. Cohen
    • 1
  1. 1.University of ConnecticutUSA

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