# VarianceEquivalenceTest

VarianceEquivalenceTest[{data1,data2,}]

tests whether the variances of the datai are equal.

VarianceEquivalenceTest[{data1,},"property"]

returns the value of "property".

# Details and Options   • VarianceEquivalenceTest performs a hypothesis test on the datai with null hypothesis that the true population variances are identical to , and alternative hypothesis that at least one is different.
• By default, a probability value or -value is returned.
• A small -value suggests that it is unlikely that .
• The datai must be univariate {x1,x2,}.
• VarianceEquivalenceTest[{data1,}] will choose the most powerful test that applies to the data.
• VarianceEquivalenceTest[{data1,},All] will choose all tests that apply to the data.
• VarianceEquivalenceTest[{data1,},"test"] reports the -value according to "test".
• Most tests require normally distributed datai. If a test is less sensitive to a normality assumption, it is called robust. Some tests assume that datai is symmetric around its medians.
• The following tests can be used:
•  "Bartlett" normality modified likelihood ratio test "BrownForsythe" robust robust Levene test "Conover" symmetry Conover's squared ranks test "FisherRatio" normality based on "Levene" robust,symmetry compares individual and group variances
• VarianceEquivalenceTest[{data1,},"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• VarianceEquivalenceTest[{data1,},"property"] can be used to directly give the value of "property".
• Properties related to the reporting of test results include:
•  "AllTests" list of all applicable tests "AutomaticTest" test chosen if Automatic is used "DegreesOfFreedom" the degrees of freedom used in a test "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 following options can be given:
•  SignificanceLevel 0.05 cutoff for diagnostics and reporting VerifyTestAssumptions Automatic set which diagnostic tests to run
• For tests of variance, 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 normality and symmetry. By default, is set to 0.05.
• Named settings for VerifyTestAssumptions in VarianceEquivalenceTest include:
•  "Normality" verify that all data is normally distributed "Symmetry" verify that all data is symmetric

# Examples

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## Basic Examples(2)

Test variances from two datasets for equivalence:

 In:= In:= Out= Create a HypothesisTestData object for further property extraction:

 In:= Out= The full test table:

 In:= Out= Compare the variances of multiple datasets simultaneously:

 In:= In:= Out= The variances of the datasets:

 In:= Out= ## Neat Examples(1)

Introduced in 2010
(8.0)