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A rigorous derivation of the exact contingency formula†

Published online by Cambridge University Press:  24 October 2008

John H. Halton
John H. Halton
Affiliation:
Computer Sciences Department, The University of Wisconsin, Madison, Wisconsin 53706, U.S.A.
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Extract

The formula

gives the conditional probability of an (r1 × r2 × … × rk) k-variate contingency table (where is the entry in the cell identified by the k indices im), given all the marginal totals

and the hypothesis that the k random variables tabulated are mutually independent. This formula appears in (1) and more restricted forms can be found elsewhere in the literature. Certain criticisms have been made of the logic and clarity of the available proofs of (1); it is hoped that the alternative derivation given here will dispel any residual doubts, and will provide better insight into the nature of the problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 527 - 530
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCE

(1)Freeman, G. H. and Halton, J. H.Note on an exact treatment of contingency, goodness of fit, and other problems of significance. Biometrika 38 (1951), 141–149.CrossRefGoogle Scholar