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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 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 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 
-valuesSignificanceLevel 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 
.
Examplesopen all
Basic Examples (2)
Test whether the medians of two independent populations differ:
| In[1]:= |
| In[2]:= |
| Out[2]= |  |
| In[3]:= |
| Out[3]= |  |
At the 
level the medians are significantly different:
| In[4]:= |
| Out[4]= |  |
Compare the locations of multivariate populations:
| In[1]:= |
The median difference vector 
:
| In[2]:= |
| Out[2]= |  |
| In[3]:= |
| Out[3]= |  |
At the 
level 
is not significantly different from 
:
| In[4]:= |
| Out[4]= |  |
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