BUILT-IN MATHEMATICA SYMBOL
BrownForsytheTest
- 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:
-
- 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 |
Test variances from two populations for equality:
| Out[2]= |  |
Create a HypothesisTestData object for further property extraction:
| Out[3]= |  |
Properties of the test:
| Out[4]= |  |
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]= |  |
New in 8
and 
are equal.
]
.
, "property"]
.
