Statistics[ShapiroWilkWTest] - apply Shapiro and Wilk's W-test for normality of a sample
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Calling Sequence
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ShapiroWilkWTest(X, options)
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Parameters
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X
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rtable; data sample
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options
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(optional) equation(s) of the form option=value where option is one of level or output; specify options for the ShapiroWilkWTest function
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Description
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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.
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The first parameter X is the data sample to use in the analysis. It should contain between and data points.
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Options
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The options argument can contain one or more of the options shown below.
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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.
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output='report', 'statistic', 'pvalue', 'hypothesis', or list('statistic', 'pvalue', 'hypothesis')
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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.
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Notes
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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.
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Examples
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Specify the data sample.
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Calculate Shapiro and Wilk's W-test on the normally distributed sample.
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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
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Calculate Shapiro and Wilk's W-test on the uniformly distributed sample.
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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: 0.832591
Computed pvalue: 0.0351514
Result: [Rejected]
There exists statistical evidence against the null hypothesis
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References
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Kanji, Gopal K. 100 Statistical Tests. London: SAGE Publications Ltd., 1994.
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Sheskin, David J. Handbook of Parametric and Nonparametric Statistical Procedures. London: CRC Press, 1997.
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Download Help Document
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