tests whether the medians of and are equal.
tests the median difference against .
returns the value of .
- MannWhitneyTest performs a hypothesis test on and with null hypothesis that the true median difference against that .
- By default, a probability value or -value is returned.
- A small -value suggests that it is unlikely that is true.
- The data in dspec can be univariate or multivariate .
- The argument can be a real number or a real vector with length equal to the dimension of the data.
- MannWhitneyTest assumes that the data is elliptically symmetric about a common spatial median in the multivariate case.
- MannWhitneyTest[dspec,μ0,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
- MannWhitneyTest[dspec,μ0,"property"] can be used to directly give the value of .
- Properties related to the reporting of test results include:
"DegreesOfFreedom" the degrees of freedom used in a test "PValue" list of -values "PValueTable" formatted table of -values "ShortTestConclusion" a short description of the conclusion of a test "TestConclusion" a description of the conclusion of a test "TestData" list of pairs of test statistics and -values "TestDataTable" formatted table of -values and test statistics "TestStatistic" list of test statistics "TestStatisticTable" formatted table of test statistics
- For univariate samples MannWhitneyTest performs the Mann–Whitney -test for median differences of independent samples. A correction for ties is applied for both asymptotic and permutation-based -values. By default, the test statistic is corrected for continuity and is assumed to follow a NormalDistribution.
- For multivariate samples, MannWhitneyTest performs an extension of the Mann–Whitney -test using spatial ranks. The test statistic is assumed to follow a ChiSquareDistribution[dim] where dim is the dimension of dspec.
- The following options can be used:
AlternativeHypothesis "Unequal" the inequality for the alternative hypothesis MaxIterations Automatic max iterations for multivariate median tests Method Automatic the method to use for computing -values SignificanceLevel 0.05 cutoff for diagnostics and reporting
- For the MannWhitneyTest, a cutoff is chosen such that is rejected only if . The value of used for the and properties is controlled by the SignificanceLevel option. By default, is set to .
Introduced in 2010