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:

Test whether two matrices are independent:

The -values are typically small for dependent matrices:

The -values are typically large when matrices are independent:

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:

Extract any number of properties simultaneously:

The -value and test statistic:

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:

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:

Set the significance level for diagnostic tests:

By default, 0.05 is used. The message shows 0.025 because two tests were performed:

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

By default, normality is tested when appropriate:

Diagnostics can be controlled as a group using All or None:

Verify all assumptions:

Check no assumptions:

Diagnostics can be controlled independently:

Check for normality:

Explicitly set the diagnostic result:

It is often useful to bypass diagnostic tests for simulation purposes:

The assumptions of the test hold by design, so a great deal of time can be saved:

The results are identical: