PillaiTraceTest

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

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

Details and OptionsDetails and Options

  • PillaiTraceTest performs a hypothesis test on m1 and m2 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 m1 and m2 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 "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:
  • 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 "TestConclusion" and "ShortTestConclusion" properties is controlled by the SignificanceLevel option. This value is also used in diagnostic tests of normality. By default, is set to 0.05.
  • 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:

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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)