VarianceTest
VarianceTest[data]
tests whether the variance of the data is one.
VarianceTest[{data1,data2}]
tests whether the variances of data1 and data2 are equal.
VarianceTest[dspec,σ02]
tests a dispersion measure against σ02.
VarianceTest[dspec,σ02,"property"]
returns the value of "property".
Details and Options




- VarianceTest tests the null hypothesis
against the alternative hypothesis
:
-
data {data1,data2} - where σi2 is the population variance for datai.
- 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 {x1,x2,…}.
- 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:
In[1]:= |
Create a HypothesisTestData object for further property extraction:
Compare the variance of a population to a particular value:
In[1]:= |
Test the ratio of the variances of two populations against a particular value:
In[1]:= |
Scope (15)
Options (10)
Applications (2)
Properties & Relations (7)
Possible Issues (2)
Neat Examples (1)
See Also
HypothesisTestData LocationTest LocationEquivalenceTest VarianceEquivalenceTest DistributionFitTest IndependenceTest LogRankTest FisherRatioTest LeveneTest BrownForsytheTest ConoverTest SiegelTukeyTest