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HoeffdingDTest

HoeffdingDTest[v₁,v₂]

tests whether the vectors v₁ and v₂ are independent.

HoeffdingDTest[…,"property"]

returns the value of "property".

Details and Options

HoeffdingDTest 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.
HoeffdingDTest is based on Hoeffding's  statistic computed by HoeffdingD[v₁,v₂].
HoeffdingDTest[v₁,v₂,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
HoeffdingDTest[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:
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.

Examples

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Basic Examples (1)

Test whether two vectors are independent:

Scope (7)

Testing (4)

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:

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:

The -value and test statistic from the test:

Reporting (3)

Tabulate the results from the test:

A table of the test results:

Retrieve the entries from a test table for customized reporting:

Tabulate the -value or test statistic:

The -value from the table:

The test statistic from the table:

Options (5)

Method (4)

By default, -values are computed using asymptotic test statistic distributions:

The -value can be obtained using permutation methods:

Set the number of permutations to use:

By default, random permutations are used:

Set the seed used for generating random permutations:

SignificanceLevel (1)

The significance level is used for "TestConclusion" and "ShortTestConclusion":

Properties & Relations (3)

The test statistic is computed as HoeffdingD:

IndependenceTest can be used to select an appropriate test of independence:

HoeffdingDTest is one of the available tests:

HoeffdingDTest can detect a wide variety of dependence structures:

Tests such as SpearmanRankTest can only detect monotonic structures:

Neat Examples (1)

Compute the statistic when the null hypothesis is true:

The test statistic given a particular alternative:

Compare the distributions of the test statistics:

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