tests whether the matrices m1 and m2 are independent.
returns the value of "property".
Details 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:
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 "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
Examplesopen allclose all
Basic Examples (2)
Test whether two vectors are independent:
The -values are typically large when the vectors are independent:
The -values are typically small when there are dependencies:
Test whether two matrices are independent:
The -values are typically small for dependent matrices:
The -values are typically large when matrices are independent:
Create a HypothesisTestData object for repeated property extraction:
The properties available for extraction:
Extract some properties from the HypothesisTestData object:
The -value and test statistic:
Extract any number of properties simultaneously:
By default, normality is tested when appropriate:
Diagnostics can be controlled as a group using All or None:
Diagnostics can be controlled independently:
Explicitly set the diagnostic result:
It is often useful to bypass diagnostic tests for simulation purposes:
The assumptions of the test hold by design, so a great deal of time can be saved:
Properties & Relations (4)
PillaiTraceTest uses the PillaiTrace measure as a test statistic:
The -value is computed using a ChiSquareDistribution[r*s]:
PillaiTraceTest is one of the tests available to IndependenceTest:
IndependenceTest automates the choice of test:
The Pillai trace test works with the values only when the input is a TimeSeries:
The Pillai trace test works with all the values together when the input is a TemporalData:
Test selected components of the temporal data explicitly:
Wolfram Research (2012), PillaiTraceTest, Wolfram Language function, https://reference.wolfram.com/language/ref/PillaiTraceTest.html.
Wolfram Language. 2012. "PillaiTraceTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PillaiTraceTest.html.
Wolfram Language. (2012). PillaiTraceTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PillaiTraceTest.html