The ShapiroWilkWTest function computes Shapiro and Wilk's W-test applied to a data set X.  This test attempts to determine how closely a given sample matches a normal distribution.

The first parameter X is the data sample to use in the analysis. It should contain between $3$ and $2000$ data points.

The options argument can contain one or more of the options shown below.

level=float

This option is used to specify the level of the analysis (minimum criteria for a data set to be considered roughly normal).  By default this value is 0.05.

output='report', 'statistic', 'pvalue', 'hypothesis', or list('statistic', 'pvalue', 'hypothesis')

This option is used to specify the desired format of the output from the function.  If 'report' is specified then a module containing all output from this test is returned.  If a single parameter name is specified other than 'report' then that quantity alone is returned.  If a list of parameter names is specified then a list containing those quantities in the specified order will be returned.

summarize= 'true', 'false', 'embed'

This option controls the display of a printed or embedded summary for the hypothesis test. Unlike the output option, the displayed summary is not assignable output.

This test generates a complete report of all calculations in the form of a userinfo message.  In order to access this report, specify infolevel[Statistics] := 1 or use the summarize option.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$S≔\mathrm{Sample}\left(\mathrm{Normal}\left(5\,2\right)\,10\right)\:$

$T≔\mathrm{Sample}\left(\mathrm{Uniform}\left(4\,6\right)\,10\right)\:$

$\mathrm{ShapiroWilkWTest}\left(S\,\mathrm{level}=0.05\,\mathrm{summarize}=\mathrm{embed}\right)\:$

$\mathrm{ShapiroWilkWTest}\left(T\,\mathrm{level}=0.05\,\mathrm{summarize}=\mathrm{true}\right)\:$

Shapiro and Wilk's W-Test for Normality

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Null Hypothesis:
Sample drawn from a population that follows a normal distribution

Alt. Hypothesis:
Sample drawn from population that does not follow a normal distribution

Sample Size:             10

Computed Statistic:      .832591474899495

Computed p-value:        .0351513590317937

Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false.

Kanji, Gopal K. 100 Statistical Tests. London: SAGE Publications Ltd., 1994.

Sheskin, David J. Handbook of Parametric and Nonparametric Statistical Procedures. London: CRC Press, 1997.

The Statistics[ShapiroWilkWTest] command was updated in Maple 2016.

The summarize option was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.