LocationEquivalenceTest

Perform a particular test for equal locations:

Any number of tests can be performed simultaneously:

Perform all tests appropriate to the data simultaneously:

Use the property to identify which tests were used:

Create a HypothesisTestData object for repeated property extraction:

The properties available for extraction:

Extract some properties from a HypothesisTestData object:

The -value and test statistic from a -sample -test:

Extract any number of properties simultaneously:

The -value and test statistic from a Kruskal-Wallis test:

Tabulate the results from a selection of tests:

A full table of all appropriate test results:

A table of selected test results:

Retrieve the entries from a test table for customized reporting:

The -values are above so there is not enough evidence to reject at that level:

Tabulate -values for a test or group of tests:

The -value from the table:

A table of -values from all appropriate tests:

A table of -values from a subset of tests:

Report the test statistic from a test or group of tests:

The test statistic from the table:

A table of test statistics from all appropriate tests:

Compute the Kruskal-Wallis test for a group of datasets:

The rescaled test statistic follows an FRatioDistribution:

Use the asymptotic chi-square approximation:

Use the asymptotic chi-square distribution for the Friedman rank test:

By default Conover's -distribution approximation is used:

Set the significance level for diagnostic tests:

The default level is :

Setting the significance level may alter which test is automatically chosen:

A median-based test would have been chosen by default:

The significance level is also used for and :

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

Verify all assumptions:

Check no assumptions:

Diagnostics can be controlled independently:

Assume normality but check for symmetry:

Only check for normality:

Test whether a group of populations shares a common location:

The first group of datasets was drawn from populations with very different locations:

Populations represented by the second group all have similar locations:

Morphological measures of two crab varieties were taken for each of the two sexes. Determine whether the measures differ across the various groups:

The rear width is the only measure that differs by gender when variety is ignored:

All measures are significantly different when gender and variety are considered simultaneously:

A pilot study was conducted for 75 patients with type II diabetes who had failed to achieve target weight loss with a particular medication. The patients were randomly assigned to three groups: a control group continuing the original medication, and two treatment groups that received 50 and 100 mg of a new medication, respectively. Weight loss in pounds over a 12-week period was recorded:

There is a significant difference in the means of the groups:

Using a Bonferroni correction in a test of each pairwise difference shows that both treatment levels perform better than the control but that they are not significantly different from one another:

A group of six food critics rated four restaurants for quality on a 100-point scale. Determine whether there is a significant difference in the quality of the restaurants according to critics:

Bar charts of the median score by critic:

Bar charts of the median score for each restaurant:

Accounting for the blocked structure, a significant difference in quality can be detected:

The -value returned by a -sample -test is equivalent to that of TTest for two samples:

The Kruskal-Wallis test is a -sample extension of the two-sample Mann-Whitney test:

The Mann-Whitney -value is corrected for continuity and ties:

Under the -sample -test statistic follows an FRatioDistribution where g is the number of datasets and n is the total number of observations:

Under the complete block and Friedman rank test statistics with t treatments and g blocks follows an FRatioDistribution:

The Friedman statistic can be transformed to follow a ChiSquareDistribution:

Compute a -value using ChiSquareDistribution:

This transformation is done automatically with Method set to :

Under the Kruskal-Wallis test statistic asymptotically follows a ChiSquareDistribution where g is the number of datasets:

By default the test statistic is rescaled to follow an FRatioDistribution:

Conceptually, a comparison is made between the pooled and average individual variances:

Larger pooled variances indicate different means:

The ratio of pooled to individual variances:

LocationEquivalenceTest effectively detects how far this ratio is from 1:

The and test statistics are used in LocationEquivalenceTest:

The Kruskal-Wallis statistic is rank based:

For -sample and Kruskal-Wallis tests, the statistic can be computed using LinearModelFit:

A design matrix:

The -sample -test:

The Kruskal-Wallis test is identical but uses ranks:

Use LocationTest for two datasets:

The results are equivalent:

LocationTest can also test more complicated hypotheses:

All of the tests require that the data has equal variances:

The -sample -test and complete block -test require that the data is normally distributed:

The Kruskal-Wallis test or Friedman rank test should be used if the data is not normally distributed:

The Friedman rank and complete block tests require equal sample sizes: