MannWhitneyTest

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

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

MannWhitneyTest[dspec,μ0,"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,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 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 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:

In[1]:=
Click for copyable input

The median difference :

In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

At the level the medians are significantly different:

In[4]:=
Click for copyable input
Out[4]=

Compare the locations of multivariate populations:

In[1]:=
Click for copyable input

The median difference vector :

In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

At the level is not significantly different from :

In[4]:=
Click for copyable input
Out[4]=
Introduced in 2010
(8.0)