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### Exact Test for Three-way Contingency Tables

*Josef Bukac*

#### Abstract

The method by Gross is applied to calculate the minimum product of factorials in a 2 by n table or a lower bound for 3 by n tables. The list of vertices of polytopes is used to calculate the maximum product of factorials in a table. Symmetries among such verticies enable us to reduce the size of the list. A method to generate three-way tables is presented. Lower and upper bounds and a simple summation formula are a basis for a branch and bound method. Such methods are described in the case of two-way tables but they can be readily generalized to the test of independence in a three-way table. The method by Gross is applied to calculate the minimum product of factorials in a 2 by n table or a lower bound for 3 by n tables. The list of vertices of polytopes is used to calculate the maximum product of factorials in a table. Symmetries among such verticies enable us to reduce the size of the list.

#### Keywords

Maximal table; Minimal table; Summation; Symmetry Three-way table.

#### Full Text:

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