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SiegelTukeyTest

SiegelTukeyTest[{data₁,data₂}]

tests whether the variances of data₁ and data₂ are equal.

SiegelTukeyTest[dspec,]

tests a dispersion measure against .

SiegelTukeyTest[dspec,,"property"]

returns the value of "property".

Details and Options

SiegelTukeyTest performs a hypothesis test on data₁ and data₂ 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 {x₁,x₂,…}.
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 "property".
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 data₁ 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 data_i 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 "TestConclusion" and "ShortTestConclusion" 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 0.05.
Named settings for VerifyTestAssumptions in SiegelTukeyTest include:
"Symmetry" verify that all data is symmetric

Examples

open allclose all

Basic Examples (2)

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 :

Scope (7)

Testing (5)

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:

Reporting (2)

Tabulate test results:

The values from the table can be extracted using "TestData":

Tabulate -values or test statistics:

The -value from the table:

The test statistic from the table:

Options (7)

AlternativeHypothesis (3)

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 :

SignificanceLevel (2)

Set the significance level for diagnostic tests:

By default, 0.05 is used:

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

VerifyTestAssumptions (2)

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:

Set the symmetry assumption to True:

Properties & Relations (6)

Under the test statistic follows a NormalDistribution[0,1]:

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[0,1] 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:

The Siegel-Tukey test ignores the time stamps when the input is a TimeSeries:

The Siegel–Tukey test recognizes the path structure of a TemporalData with exactly two paths:

Use the values directly:

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:

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