Computation of Two-Tailed Fisher's Test

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Abstract
Fisher's method is frequently applied as a one-tailed test to find the exact probability that one specific proportion exceeds another due to chance. When it is necessary to find the exact probability that the absolute difference between two proportions is random, then a two-tailed test is necessary. There are similarities between one and two-tailed tests such as the requirement for constant marginal subtotals, but there are differences in the concepts of equivalent or more divergent possible occurrences between them. A computer program is given which performs these calculations, and differences in the tests are illustrated through examples.

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