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Short Cut Calculation of the Fisher-Yates “Exact Test”

Published online by Cambridge University Press:  01 January 2025

Solomon E. Feldman  and
Eric Klinger
Solomon E. Feldman
Affiliation:
University of Wisconsin
Eric Klinger
Affiliation:
University of Minnesota, Morris
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Abstract

The Fisher-Yates “Exact Test” has become widely known to researchers in psychology as the significance test of choice for comparing pairs of proportions in 2 × 2 contingency tables, particularly when the expected frequency of one or more of the cells is small. Less widely recognized are some readily available tabular aids for calculating the “Exact Test” in a substantial number of the cases in which it might be applied. Thus, Finney [1] has tabled probability levels at or beyond the .05 level for those 2 × 2 tables in which neither of the two row marginals exceeds 15. Since it is a matter of arbitrary choice as to which pair of marginals of an obtained table is designated the row pair and which the column pair, Finney’s table has broad applicability. It has been incorporated into the Biometrika Tables for Statisticians [3], which also present extensive discussion of its applications and extensions. Finney’s table has been extended by Latscha [2] to accommodate those contingency tables in which neither of the two row marginals exceeds 20. The Biometrika Tables provide additional, if less direct, help in their tables of n! for values of n up to 250, and of log10n! for values of n up to 1000.

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 3 , September 1963 , pp. 289 - 291
Copyright
Copyright © 1963 The Psychometric Society

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References

Finney, D. J. The Fisher-Yates test of significance in 2 × 2 contingency tables. Biometrika, 1948, 35, 145–156.Google Scholar
Latscha, R. Tests of significance in a 2 × 2 contingency table: extension of Finney's table. Biometrika, 1953, 40, 74–86.Google Scholar
Pearson, E. S. and Hartley, H. O. Biometrika tables for statisticians. Vol. I, Cambridge: University Press, 1954.Google Scholar