BUILT-IN MATHEMATICA SYMBOL

# ShapiroWilkTest

ShapiroWilkTest[data]
tests whether data is normally distributed using the Shapiro-Wilk test.

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

## Details and OptionsDetails and Options

• ShapiroWilkTest performs the Shapiro-Wilk 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 or multivariate .
• The Shapiro-Wilk 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 .
• Properties related to the reporting of test results include:
•  "PValue" -value "PValueTable" formatted version of "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 "TestStatistic" test statistic "TestStatisticTable" formatted
• 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:
•  Method Automatic the method to use for computing -values SignificanceLevel 0.05 cutoff 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 and properties is controlled by the SignificanceLevel option. By default is set to .
• 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 Shapiro-Wilk test for normality:

 Out[2]=
 Out[3]=

Perform a test for multivariate normality:

The full test table:

 Out[2]=

The test statistic and -value:

 Out[3]=