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BinaryContingencyTableFisherExactTest Method
Performs a Fisher exact test.

Namespace:  Meta.Numerics.Statistics
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 3.1.0.0 (3.1.0.0)
Syntax
public TestResult FisherExactTest()

Return Value

Type: TestResult
The results of the test. The test statistic is the summed probability of all tables exhibiting equal or stronger correlations, and its likelyhood under the null hypothesis is the (left) probability to obtain a smaller value. Note that, in this case, the test statistic itself is the likelyhood.
Remarks

The Fisher exact test tests for correlations between row and column entries. It is a robust, non-parametric test, which, unlike the χ2 test (see PearsonChiSquaredTest), can safely be used for tables with small, even zero-valued, entries.

The Fisher test computes, under the null hypothesis of no correlation, the exact probability of all 2 X 2 tables with the same row and column totals as the given table. It then sums the probabilities of all tables that are as or less probable than the given table. In this way it determines the total probability of obtaining a 2 X 2 table which is at least as improbable as the given one.

The test is two-sided, i.e. when considering less probable tables it does not distinguish between tables exhibiting the same and the opposite correlation as the given one.

See Also