tests whether the matrices and are independent.
returns the value of .
- 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:
Method Automatic the method to use for computing -values SignificanceLevel 0.05 cutoff for diagnostics and reporting VerifyTestAssumptions Automatic what 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
Introduced in 2012