BUILT-IN MATHEMATICA SYMBOL

# BrownForsytheTest

BrownForsytheTest[data]
tests whether the variance of data is 1.

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

BrownForsytheTest[dspec, ]
tests a dispersion measure against .

BrownForsytheTest[dspec, , "property"]
returns the value of .

## Details and OptionsDetails and Options

• BrownForsytheTest performs a hypothesis test on data with null hypothesis that the true population variance , and alternative hypothesis that .
• Given and , BrownForsytheTest 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.
• The BrownForsytheTest assumes that the data is normally distributed.
• The BrownForsytheTest is less sensitive to the assumption of normality than the LeveneTest.
• BrownForsytheTest[data, , "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• BrownForsytheTest[data, , "property"] can be used to directly give the value of .
• Properties related to the reporting of test results include:
•  "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
• When one sample of size is given, the BrownForsytheTest is equivalent to the FisherRatioTest.
• For two samples, the BrownForsytheTest is a modification of the LeveneTest that replaces the mean in Abs[dataij-Mean[datai]] with a function . The function fn is generally chosen to be Median[datai] but the TrimmedMean[datai, 1/10] is used if the data is heavy-tailed.
• 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 BrownForsytheTest, 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 BrownForsytheTest include:
•  "Normality" verify that all data is normally distributed

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Test variances from two populations for equality:

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Create a HypothesisTestData object for further property extraction:

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Properties of the test:

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Test the ratio of the variances of two populations against a particular value:

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Perform the test with alternative hypothesis :

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