BUILT-IN MATHEMATICA SYMBOL

# SiegelTukeyTest

SiegelTukeyTest[{data1, data2}]
tests whether the variances of and are equal.

SiegelTukeyTest[dspec, ]
tests a dispersion measure against.

SiegelTukeyTest[dspec, , "property"]
returns the value of .

## Details and OptionsDetails and Options

• SiegelTukeyTest performs a hypothesis test on and with null hypothesis that the ratio of the true population variances against .
• By default a probability value or -value is returned.
• A small -value suggests that it is unlikely that is true.
• The argument can be any positive real number.
• The data in dspec must be univariate .
• SiegelTukeyTest assumes the data is symmetric about a common median.
• SiegelTukeyTest[data, , "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• SiegelTukeyTest[data, , "property"] can be used to directly give the value of .
• Properties related to the reporting of test results include:
•  "PValue" list of -values "PValueTable" formatted table of -values "ShortTestConclusion" a short description of the conclusion of a test "TestConclusion" a description of the conclusion of a test "TestData" list of pairs of test statistics and -values "TestDataTable" formatted table of -values and test statistics "TestStatistic" list of test statistics "TestStatisticTable" formatted table of test statistics
• The test statistic is computed for the pooled sample as where if is from and zero otherwise, and are ranks associated with each . The statistic is assumed to follow a NormalDistribution under .
• SiegelTukeyTest is a less powerful ranks-based test than ConoverTest and is an alternative to the FisherRatioTest when the is not normally distributed.
• The following options can be used:
•  AlternativeHypothesis "Unequal" the inequality for the alternative hypothesis SignificanceLevel 0.05 cutoff for diagnostics and reporting VerifyTestAssumptions Automatic set which diagnostic tests to run
• For the SiegelTukeyTest, a cutoff is chosen such that is rejected only if . The value of used for the and properties is controlled by the SignificanceLevel option. This value is also used in diagnostic tests of assumptions including tests for symmetry. By default is set to .
• Named settings for VerifyTestAssumptions in SiegelTukeyTest include:
•  "Symmetry" verify that all data is symmetric

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Test variances from two populations for equality:

 Out[2]=

Create a HypothesisTestData object for further property extraction:

 Out[3]=

Properties of the test:

 Out[4]=

Test the ratio of the variances of two populations against a particular value:

 Out[2]=
 Out[3]=

Perform the test with alternative hypothesis :

 Out[4]=

### Properties & Relations (4)Properties & Relations (4)

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