ConoverTest

ConoverTest[{data1,data2,}]

tests whether the variances of data1, data2, are equal.

ConoverTest[dspec,]

tests a dispersion measure against .

ConoverTest[dspec,,"property"]

returns the value of "property".

Details and Options

  • ConoverTest tests the null hypothesis against the alternative hypothesis :
  • {data1,data2}
    {data1,data2,}not all equal
  • 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. The default value of is 1 if not specified, and ignored if the number of groups in dspec is more than 2.
  • ConoverTest assumes the data is symmetric about a common median.
  • ConoverTest[data,,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • ConoverTest[data,,"property"] can be used to directly give the value of "property".
  • Properties related to the reporting of test results include:
  • "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 test statistic is based on the squared ranks of the absolute deviations from the sample medians.
  • For the -sample case, with datai={xi,1,xi,2,,xi,ni}, the rank ri,j of the value xi,j is the rank of zi,j among all the elements {zi,j}1ik,1jni, where zi,j=Abs[xi,j-Median[datai]]. The test statistic is given by for equal to 2 and for greater than 2, where , , and .
  • Under , the test statistic of ConoverTest is assumed to follow NormalDistribution[0,1] for equal to 2 and ChiSquareDistribution[k-1] for greater than 2.
  • ConoverTest is sometimes called the squared ranks test and is an alternative to the FisherRatioTest when the datai is not normally distributed.
  • The following options can be used:
  • AlternativeHypothesis"Unequal"the inequality for the alternative hypothesis
    SignificanceLevel0.05cutoff for diagnostics and reporting
    VerifyTestAssumptionsAutomaticset which diagnostic tests to run
  • For the ConoverTest, 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 symmetry. By default, is set to 0.05.
  • Named settings for VerifyTestAssumptions in ConoverTest include:
  • "Symmetry"verify that all data is symmetric

Examples

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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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Scope  (8)

Options  (6)

Applications  (1)

Properties & Relations  (8)

Possible Issues  (3)

Neat Examples  (1)

See Also

HypothesisTestData  LocationTest  LocationEquivalenceTest  VarianceTest  VarianceEquivalenceTest  DistributionFitTest  BrownForsytheTest  FisherRatioTest  LeveneTest  SiegelTukeyTest

Introduced in 2010
(8.0)
| Updated in 2017
(11.1)