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The American Statistician Volume 49, 1995 - Issue 4
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General

Exact Tests of Significance in Higher Dimensional Tables

Daniel Zelterman The Division of Biostatistics, University of Minnesota, Minneapolis, MN, 55455, USA; The Division of Biostatistics, Yale University, New Haven, CT, 06520, USA
,
Ivan Siu-Fung Chan The Division of Biostatistics, University of Minnesota, Minneapolis, MN, 55455, USA; Merck Research Laboratories, Clinical Biostatistics, West Point, PA, 19486, USA
&
Paul W. Mielke Jr. Department of Statistics, Colorado State University, Fort Collins, CO, 80523, USA
Pages 357-361 | Received 01 May 1993, Published online: 27 Feb 2012
 
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Abstract

We describe methods used to provide an exact test of significance of the hypothesis that all factors are mutually independent of each other in 23 and 24 contingency tables. Several numerical examples demonstrate the advantages of exact tests over approximate significance levels. We give bounds on the number of tables needed to perform this exact significance test. In four or more dimensions the number of tables in this enumeration becomes astronomical with even modest sample sizes. Inverting the characteristic function of the exact distribution has proved useful in these situations.

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