BUILTIN MATHEMATICA SYMBOL
SignedRankTest
SignedRankTest[{data_{1}, data_{2}}]
tests whether the median of is zero.
 SignedRankTest performs a hypothesis test on data with null hypothesis that the true population median is some value , and alternative hypothesis that .
 Given and , SignedRankTest performs a test on the paired differences of the two datasets.
 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 .
 If two samples are given, they must be of equal length.
 The argument can be a real number or a real vector with length equal to the dimension of the data.
 SignedRankTest assumes that the data is symmetric about the median in the univariate case and elliptically symmetric in the multivariate case. For this reason, SignedRankTest is also a test of means.
 SignedRankTest[dspec, _{0}, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
 SignedRankTest[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 
 The SignedRankTest is a more powerful alternative to the SignTest.
 For univariate samples SignedRankTest performs the Wilcoxon signed rank test for medians of paired samples. A correction for ties is applied for permutationbased values. By default, the test statistic is corrected for continuity and an asymptotic result is returned.
 For multivariate samples, SignedRankTest performs an affine invariant test for paired samples using standardized spatial signed ranks. The test statistic is assumed to follow a ChiSquareDistribution[dim] where dim is the dimension of the data.
 The following options can be used:

 For the SignedRankTest, a cutoff is chosen such that is rejected only if . The value of used for the and properties is controlled by the SignificanceLevel option. This value is also used in diagnostic tests of assumptions including a test for symmetry. By default is set to .
 Named settings for VerifyTestAssumptions in SignedRankTest include:

 "Symmetry"  verify that all data is symmetric 
Test whether the median of a population is zero:
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Compare the median difference for paired data to a particular value:
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Report the test results in a table:
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Test whether the spatial median of a multivariate population is some value:
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Compute the test statistic:
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Create a HypothesisTestData object for repeated property extraction:
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A list of available properties:
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Extract a single property or a list of properties:
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