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:
  • MethodAutomaticthe method to use for computing -values
    SignificanceLevel0.05cutoff 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

open allclose all

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:

Introduced in 2012
 (9.0)