MannWhitneyTest

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

MannWhitneyTest[dspec,μ0]
tests the median difference against μ0.

MannWhitneyTest[dspec,μ0,"property"]
returns the value of "property".

Details and OptionsDetails and Options

  • MannWhitneyTest performs a hypothesis test on data1 and data2 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 {x1,x2,} or multivariate {{x1,y1,},{x2,y2,},}.
  • The argument μ0 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 "property".
  • 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 MannWhitney -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 MannWhitney -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
    MaxIterationsAutomaticmax iterations for multivariate median tests
    MethodAutomaticthe method to use for computing -values
    SignificanceLevel0.05cutoff for diagnostics and reporting
  • For the MannWhitneyTest, a cutoff is chosen such that is rejected only if . The value of used for the "TestConclusion" and "ShortTestConclusion" properties is controlled by the SignificanceLevel option. By default, is set to 0.05.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Test whether the medians of two independent populations differ:

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The median difference :

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At the 0.05 level, the medians are significantly different:

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Compare the locations of multivariate populations:

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The median difference vector :

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At the 0.05 level, is not significantly different from {1,2}:

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Introduced in 2010
(8.0)