KendallTauTest

KendallTauTest[v1,v2]
tests whether the vectors v1 and v2 are independent.

KendallTauTest[m1,m2]
tests whether the matrices m1 and m2 are independent.

KendallTauTest[,"property"]
returns the value of "property".

Details and OptionsDetails and Options

  • KendallTauTest performs a hypothesis test on v1 and v2 with null hypothesis that the vectors are independent, and alternative hypothesis that they are not.
  • By default, a probability value or -value is returned.
  • A small -value suggests that it is unlikely that is true.
  • The arguments v1 and v2 can be any real-valued vectors or matrices of equal length.
  • KendallTauTest is based on Kendall's rank correlation computed by KendallTau[v1,v2].
  • For testing matrices, the test statistic is based on the ratio inner standardized spatial signs and ranks and asymptotically follows a ChiSquareDistribution[r*s] where r and s are the dimension of m1 and m2, respectively.
  • KendallTauTest[v1,v2,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • KendallTauTest[v1,v2,"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 the test
    "PValue"the -value of the test
    "PValueTable"formatted table containing the -value
    "ShortTestConclusion"a short description of the conclusion of the test
    "TestConclusion"a description of the conclusion of the test
    "TestData"a list containing the test statistic and -value
    "TestDataTable"formatted table of the -value and test statistic
    "TestStatistic"the test statistic
    "TestStatisticTable"formatted table containing the test statistic
  • The following options can be used:
  • AlternativeHypothesis"Unequal"the inequality for the alternative hypothesis
    MaxIterationsAutomaticmax iterations for multivariate test
    MethodAutomaticthe method to use for computing -values
    SignificanceLevel0.05cutoff for diagnostics and reporting
  • For tests of independence, 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 two vectors are independent:

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Test whether two matrices are independent:

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At the 0.05 level, there is insufficient evidence to reject independence:

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Introduced in 2012
(9.0)