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Statistics[ShapiroWilkWTest] - apply Shapiro and Wilk's W-test for normality of a sample
Calling Sequence
ShapiroWilkWTest(X, options)
Parameters
X
-
rtable; data sample
options
(optional) equation(s) of the form option=value where option is one of level or output; specify options for the ShapiroWilkWTest function
Description
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.
Options
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.
Notes
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.
Examples
Specify the data sample.
Calculate Shapiro and Wilk's W-test on the normally distributed sample.
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: 0.967479 Computed pvalue: 0.856736 Result: [Accepted] There is no statistical evidence against the null hypothesis
Calculate Shapiro and Wilk's W-test on the uniformly distributed sample.
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
See Also
Statistics, Statistics[Computation]
References
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.
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