BUILT-IN MATHEMATICA SYMBOL

# VarianceTest

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

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

VarianceTest[dspec, 02]
tests a dispersion measure against .

VarianceTest[dspec, 02, "property"]
returns the value of .

## Details and OptionsDetails and Options

• performs a hypothesis test on data with null hypothesis that the true population dispersion parameter , and alternative hypothesis that .
• Given and , 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 .
• 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 .
• 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 .
• 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:
•  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 and 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 .
• Named settings for VerifyTestAssumptions in VarianceTest include:
•  "Normality" verify that all data is normally distributed "Symmetry" verify symmetry about a common median

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Test variances from two populations for equality:

 Out[2]=

Create a HypothesisTestData object for further property extraction:

 Out[3]=

The full test table:

 Out[4]=

Compare the variance of a population to a particular value:

 Out[2]=
 Out[3]=

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]=

## See AlsoSee Also

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