ShapiroWilkTest

ShapiroWilkTest[data]
tests whether data is normally distributed using the ShapiroWilk test.

ShapiroWilkTest[data,"property"]
returns the value of "property".

Details and OptionsDetails and Options

  • ShapiroWilkTest performs the ShapiroWilk goodness-of-fit test with null hypothesis that data was drawn from a NormalDistribution and alternative hypothesis that it was not.
  • By default, a probability value or -value is returned.
  • A small -value suggests that it is unlikely that the data came from dist.
  • The dist can be any symbolic distribution with numeric and symbolic parameters or a dataset.
  • The data can be univariate {x1,x2,} or multivariate {{x1,y1,},{x2,y2,},}.
  • The ShapiroWilk test effectively compares the order statistics of data to the theoretical order statistics of a NormalDistribution.
  • ShapiroWilkTest[data,dist,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • ShapiroWilkTest[data,dist,"property"] can be used to directly give the value of "property".
  • Properties related to the reporting of test results include:
  • "PValue"-value
    "PValueTable"formatted version of "PValue"
    "ShortTestConclusion"a short description of the conclusion of a test
    "TestConclusion"a description of the conclusion of a test
    "TestData"test statistic and -value
    "TestDataTable"formatted version of "TestData"
    "TestStatistic"test statistic
    "TestStatisticTable"formatted "TestStatistic"
  • The following properties are independent of which test is being performed.
  • Properties related to the data distribution include:
  • "FittedDistribution"fitted distribution of data
    "FittedDistributionParameters"distribution parameters of data
  • The following options can be given:
  • MethodAutomaticthe method to use for computing -values
    SignificanceLevel0.05cutoff for diagnostics and reporting
  • For a test for goodness of fit, 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. By default is set to 0.05.
  • With the setting Method->"MonteCarlo", datasets of the same length as the input are generated under using the fitted distribution. The EmpiricalDistribution from ShapiroWilkTest[si,"TestStatistic"] is then used to estimate the -value.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Perform a ShapiroWilk test for normality:

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Perform a test for multivariate normality:

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The full test table:

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The test statistic and -value:

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Introduced in 2010
(8.0)