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A generalization of Fisher's exact test: rock-paper-scissors and friendly ghosts

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Abstract: Fisher’s exact test, named for Sir Ronald Aylmer Fisher, tests contingency tables for homogeneity of proportion. Here I discuss 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. If the (unconditional) proportions are indeed identical amongst rows, they may be estimated using likelihood techniques. The test and estimators are implemented in the R programming language in the form of two packages.

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