Fisher's exact test (FET) is a nonparametric version of the chi-square test. The most common use of FET is with small data sets, in particular when at least one cell in a cross-tabulation table has an expected frequency of less than 5. Small data sets and sparse cells may render the results reached by a chi-square test invalid, because it is based on asymptotic normality. Because the FET is a nonparametric test, this assumption does not apply to it. The FET calculates the exact probability (p value) of observing the table containing the data or more extreme distribution of the data. This probability is calculated by looking at all possible rearrangements of the table (in the direction of the alternative). The row and column totals ...

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