BUILT-IN WOLFRAM LANGUAGE SYMBOL

VarianceTest

VarianceTest[data]
tests whether the variance of the data is one.

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

VarianceTest[dspec,σ₀²]
tests a dispersion measure against σ₀².

VarianceTest[dspec,σ₀²,"property"]
returns the value of "property".

Details and Options Details and Options

VarianceTest performs a hypothesis test on data with null hypothesis that the true population dispersion parameter , and alternative hypothesis that .
Given data₁ and data₂, VarianceTest tests against .
By default, a probability value or -value is returned.
A small -value suggests that it is unlikely that is true.
The data in dspec must be univariate {x₁,x₂,…}.
The argument can be any positive real number.
VarianceTest[dspec,] will choose the most powerful test that applies to dspec.
VarianceTest[dspec,,All] will choose all tests that apply to dspec.
VarianceTest[dspec,,"test"] reports the -value according to "test".
Most tests require normally distributed data. If a test is less sensitive to a normality assumption, it is called robust. Some tests assume that data is symmetric around its medians.
The following tests can be used:

"BrownForsythe"	robust	robust Levene test
"Conover"	symmetry	based on squared ranks of data
"FisherRatio"	normality	based on
"Levene"	robust,symmetry	compare individual and group variances
"SiegelTukey"	symmetry	based on ranks of pooled data

VarianceTest[data,,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
VarianceTest[data,,"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

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 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 VarianceTest include:
"Normality" verify that all data is normally distributed

"Symmetry" verify symmetry about a common median