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)
Create a HypothesisTestData object for repeated property extraction:
Extract some properties from the HypothesisTestData object:
Properties & Relations (4)
For vector-to-vector comparisons, the test statistic is computed as BlomqvistBeta:
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: