tests whether the vectors v1 and v2 are independent.
tests whether the matrices m1 and m2 are independent.
returns the value of "property".
Details and Options
- BlomqvistBetaTest 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.
- BlomqvistBetaTest is based on Blomqvist's medial correlation coefficient β computed by BlomqvistBeta[v1,v2].
- For testing matrices, the test statistic is based on inner standardized spatial signs and asymptotically follows a ChiSquareDistribution[r*s] where r and s are the dimensions of m1 and m2, respectively. The test statistic is invariant under affine transformations.
- BlomqvistBetaTest[v1,v2,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
- BlomqvistBetaTest[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 MaxIterations Automatic max iterations for multivariate test Method Automatic the method to use for computing -values SignificanceLevel 0.05 cutoff 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.
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 from the test:
Extract any number of properties simultaneously:
Properties & Relations (4)
For vector-to-vector comparisons, the test statistic is computed as BlomqvistBeta:
For matrix comparisons, the test statistic is invariant under affine transformations:
IndependenceTest can be used to select an appropriate test of independence:
BlomqvistBetaTest is one of the available tests:
BlomqvistBetaTest only detects monotonic dependence:
HoeffdingDTest can be used to detect a wider variety of dependence structures:
Wolfram Research (2012), BlomqvistBetaTest, Wolfram Language function, https://reference.wolfram.com/language/ref/BlomqvistBetaTest.html.
Wolfram Language. 2012. "BlomqvistBetaTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BlomqvistBetaTest.html.
Wolfram Language. (2012). BlomqvistBetaTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BlomqvistBetaTest.html