tests whether the vectors v1 and v2 are independent.
returns the value of "property".
Details and Options
- GoodmanKruskalGammaTest 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 of equal length.
- GoodmanKruskalGammaTest is based on the Goodman–Kruskal gamma coefficient γ, which is computed by GoodmanKruskalGamma[v1,v2].
- GoodmanKruskalGammaTest[v1,v2,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
- GoodmanKruskalGammaTest[v1,v2,"property"] can be used to directly give the value of "property".
- Properties related to the reporting of test results include:
"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 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
Create a HypothesisTestData object for repeated property extraction:
Extract some properties from the HypothesisTestData object:
Properties & Relations (3)
For vector to vector comparisons, the test statistic is computed as GoodmanKruskalGamma:
IndependenceTest can be used to select an appropriate test of independence:
GoodmanKruskalGammaTest is one of the available tests:
GoodmanKruskalGammaTest only detects monotonic dependence:
HoeffdingDTest can be used to detect a wider variety of dependence structures:
Wolfram Research (2012), GoodmanKruskalGammaTest, Wolfram Language function, https://reference.wolfram.com/language/ref/GoodmanKruskalGammaTest.html.
Wolfram Language. 2012. "GoodmanKruskalGammaTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GoodmanKruskalGammaTest.html.
Wolfram Language. (2012). GoodmanKruskalGammaTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GoodmanKruskalGammaTest.html