tests whether the matrices and are independent.

returns the value of .

Details and OptionsDetails and Options

  • PillaiTraceTest performs a hypothesis test on and with null hypothesis that the matrices are linearly 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 and can be any real-valued vectors or matrices of equal length.
  • PillaiTraceTest is based on Pillai's trace statistic computed by PillaiTrace[m1,m2].
  • PillaiTraceTest[m1,m2,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • PillaiTraceTest[m1,m2,"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 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:
  • MethodAutomaticthe method to use for computing -values
    SignificanceLevel0.05cutoff for diagnostics and reporting
    VerifyTestAssumptionsAutomaticwhat assumptions to verify
  • For tests of independence, 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 normality. By default, is set to .
  • Named settings for VerifyTestAssumptions in IndependenceTest include:
  • "Normality"verify that all data is normally distributed

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Test whether two vectors are independent:

Click for copyable input
Click for copyable input
Click for copyable input

Test whether two matrices are independent:

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

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Introduced in 2012
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