SignedRankTest

SignedRankTest[data]
tests whether the median of data is zero.

SignedRankTest[{data1,data2}]
tests whether the median of is zero.

SignedRankTest[dspec,μ0]
tests a location measure against .

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

Details and OptionsDetails and Options

  • 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,μ0,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • SignedRankTest[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
  • 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 permutation-based -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:
  • 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
    VerifyTestAssumptionsAutomaticwhat assumptions to verify
  • 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

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

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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Introduced in 2010
(8.0)