tests whether the vectors and are independent.
tests whether the matrices and are independent.
returns the value of .
- BlomqvistBetaTest performs a hypothesis test on and 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 and 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 dimension of and , 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 .
- 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 and properties is controlled by the SignificanceLevel option. By default is set to .
Introduced in 2012