BUILT-IN MATHEMATICA SYMBOL

# MannWhitneyTest

MannWhitneyTest[{data1, data2}]
tests whether the medians of and are equal.

MannWhitneyTest[dspec, 0]
tests the median difference against .

MannWhitneyTest[dspec, 0, "property"]
returns the value of .

## Details and OptionsDetails and Options

• 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, 0, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• MannWhitneyTest[dspec, 0, "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 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 .

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Test whether the medians of two independent populations differ:

The median difference :

 Out[2]=
 Out[3]=

At the level the medians are significantly different:

 Out[4]=

Compare the locations of multivariate populations:

The median difference vector :

 Out[2]=
 Out[3]=

At the level is not significantly different from :

 Out[4]=

## See AlsoSee Also

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