Exact Tests for Two-Way Contingency Tables with Structural Zeros

Abstract

Fisher's exact test, named for Sir Ronald Aylmer Fisher, tests contingency tables for homogeneity of proportion. This paper discusses a generalization of Fisher's exact test for the case where some of the table entries are constrained to be zero. The resulting test is useful for assessing cases where the null hypothesis of conditional multinomial distribution is suspected to be false. The test is implemented in the form of a new R package, aylmer.

Keywords

• Fisher's exact test
• computational combinatorics
• R
• multinomial distribution
• rock-paper-scissors
• transitivity
• pairwise comparison
• odds ratio
• one-sided tests
• structural zeros