VarianceTest
VarianceTest[data]
tests whether the variance of the data is one.
VarianceTest[{data_{1},data_{2}}]
tests whether the variances of data_{1} and data_{2} are equal.
VarianceTest[dspec,σ_{0}^{2}]
tests a dispersion measure against σ_{0}^{2}.
VarianceTest[dspec,σ_{0}^{2},"property"]
returns the value of "property".
Details and Options
 VarianceTest tests the null hypothesis against the alternative hypothesis :

data {data_{1},data_{2}}  where σ_{i}^{2} is the population variance for data_{i}.
 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 {x_{1},x_{2},…}.
 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  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 "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
Examples
open allclose allBasic Examples (3)
Test variances from two populations for equality:
Create a HypothesisTestData object for further property extraction:
Compare the variance of a population to a particular value:
Test the ratio of the variances of two populations against a particular value:
Scope (15)
Testing (11)
Test whether the variance of a population is one:
The values are typically large under :
The values are typically small when is false:
Compare the variance of a population to a particular value:
Compare the variance of a quantity data to a particular value:
Compare the variances of two populations:
The values are typically large when the variances are equal:
The values are typically small when the variances are not equal:
Test whether the ratio of the variances of two populations is a particular value:
The following forms are equivalent:
The order of the datasets should be considered when determining :
Using Automatic applies the generally most powerful appropriate test:
The property "AutomaticTest" can be used to determine which test was chosen:
Perform a particular test for equal variance:
Any number of tests can be performed simultaneously:
Perform all tests appropriate to the data simultaneously:
Use the property "AllTests" to identify which tests were used:
Create a HypothesisTestData object for repeated property extraction:
The properties available for extraction:
Extract some properties from a HypothesisTestData object:
The value and test statistic from a Levene test:
Reporting (4)
Tabulate the results from a selection of tests:
A full table of all appropriate test results:
A table of selected test results:
Retrieve the entries from a test table for customized reporting:
The values are above 0.05, so there is not enough evidence to reject normality at that level:
Tabulate values for a test or group of tests:
A table of values from all appropriate tests:
A table of values from a subset of tests:
Report the test statistic from a test or group of tests:
Options (10)
AlternativeHypothesis (3)
SignificanceLevel (3)
VerifyTestAssumptions (4)
Diagnostics can be controlled as a group using All or None:
Diagnostics can be controlled independently:
Assume normality but check for symmetry:
Test assumption values can be explicitly set:
It is often useful to bypass diagnostic tests for simulation purposes:
The assumptions of the test hold by design, so a great deal of time can be saved:
Applications (2)
Test whether the variances of some populations are equivalent:
The first two populations have similar variances:
The third population differs in variance from the first:
An object with a length of 2.15 cm was measured with the same ruler by 25 gradeschool students in two different classes:
The second group is superior in their precision:
Properties & Relations (7)
The value suggests the expected proportion of false positives (Type I errors):
Setting the size of a test to 0.05 results in an erroneous rejection of about 5% of the time:
The power of each test is the probability of rejecting when it is false:
The power of the tests at six different levels. The Siegel–Tukey has the lowest power:
The power of the tests is proportional to the sample size:
The power of the tests is lower than in the previous example:
A twosided value is twice the smaller of the two onesided values:
The Brown–Forsythe and Levene tests are equivalent to the Fisher ratio test for a single sample:
The variance test works with the values only when the input is a TimeSeries:
The variance test works with all the values together when the input is a TemporalData:
Possible Issues (2)
Text
Wolfram Research (2010), VarianceTest, Wolfram Language function, https://reference.wolfram.com/language/ref/VarianceTest.html.
CMS
Wolfram Language. 2010. "VarianceTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VarianceTest.html.
APA
Wolfram Language. (2010). VarianceTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VarianceTest.html