A survey of algorithms for exact distributions of test statistics in r × c contingency tables with fixed margins

Authors:
Albert Verbeek;Pieter M. Kroonenberg
Affiliations:
Department of Sociology, University of Utrecht and Netherlands Central Bureau of Statistics, Voorburg, The Netherlands;Department of Education, University of Leiden, Leiden, The Netherlands
Venue:
Computational Statistics & Data Analysis
Year:
1985

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Abstract

Testing of independence in an r x c tables is generally carried out by using a continuous limiting distribution of the test statistic, rather than the discrete distribution itself. This paper surveys algorithms for the computation of the latter. The central idea is the efficient enumeration of all tables with the same margins, or of a suitable subset thereof. The simplest case is Fisher's exact test for a 2 x 2 table and a one-side alternative hypothesis. Fisher's method is easily extended to r x c tables and to arbitrary statistics.