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.
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:
-
- 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 |
New in 8
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