apply Shapiro and Wilk's W-test for normality of a sample - Maple Help

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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

-

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 3 and 2000 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

withStatistics:

infolevel[Statistics]:=1:

Specify the data sample.

S:=SampleNormal5,2,10:

T:=SampleUniform4,6,10:

Calculate Shapiro and Wilk's W-test on the normally distributed sample.

ShapiroWilkWTestS,level=0.05

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]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false

hypothesis=true,pvalue=0.856735713777028,statistic=0.967478742211855

(1)

Calculate Shapiro and Wilk's W-test on the uniformly distributed sample.

ShapiroWilkWTestT,level=0.05

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]
This statistical test provides evidence that the null hypothesis is false

hypothesis=false,pvalue=0.0351513590317937,statistic=0.832591474899495

(2)

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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