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  and  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.

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.

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:      0.967479
Computed pvalue:         0.856736

Result: [Accepted]
There is no statistical evidence against the null hypothesis

Shapiro and Wilk's W-Test for Normality
---------------------------------------
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:      0.832591
Computed pvalue:         0.0351514

Result: [Rejected]
There exists statistical evidence against the null hypothesis

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.