This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# SiegelTukeyTest

 SiegelTukeyTesttests whether the variances of and are equal. SiegelTukeyTesttests a dispersion measure against. SiegelTukeyTestreturns the value of .
• 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.
• 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 .
• 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 .
 "Symmetry" verify that all data is symmetric
Test variances from two populations for equality:
Create a HypothesisTestData object for further property extraction:
Properties of the test:
Test the ratio of the variances of two populations against a particular value:
Perform the test with alternative hypothesis :
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]=
 Scope   (7)
Compare the variances of two populations:
The -values are typically large when the variances are equal:
The -values are typically small when the variances are not equal:
Test whether the ratio of the variances of two populations is a particular value:
The following forms are equivalent:
The order of the datasets should be considered when determining :
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:
Extract any number of properties simultaneously:
The -value and test statistic:
Tabulate test results:
The values from the table can be extracted using :
Tabulate -values or test statistics:
The -value from the table:
The test statistic from the table:
 Options   (8)
By default, a two-sided test is performed:
Perform a two-sided test or one of two one-sided alternatives:
Test versus :
Test versus :
Test versus :
Perform tests with one-sided alternatives when a null value is given:
Test versus :
Test versus :
Set the significance level for diagnostic tests:
By default, is used:
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:
Check for symmetry:
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:
Under the test statistic follows a NormalDistribution:
Unlike the FisherRatioTest, the Siegel-Tukey test does not assume normality:
The FisherRatioTest results in underestimation of -values:
The Siegel-Tukey test assumes symmetry about a common median:
The distribution of the test statistic is not NormalDistribution when the data is asymmetric:
The PearsonChiSquareTest is used to test data for symmetry about a common median:
The data is found to be symmetric and no warning is issued:
The -value in the warning matches that of the PearsonChiSquareTest:
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