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

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Student[Statistics][ShapiroWilkWTest] - apply Shapiro and Wilk's W-test for normality of a sample

Calling Sequence

ShapiroWilkWTest(X, level_option, output_option)

Parameters

X

-

data sample

level_option

-

(optional) equation of the form level=float.

output_option

-

(optional) equation of the form output=x where x is report, plot, or both

Description

• 

The ShapiroWilkWTest function computes Shapiro and Wilk's W-test applied to a data sample X.  This tests whether X comes from a normally distributed population.

• 

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

• 

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.

• 

If the option output is not included or is specified to be output=report, then the function will return a report. If output=plot is specified, then the function will return a plot of the sample test. If output=both is specified, then both the report and the plot will be returned.

Examples

withStudent[Statistics]:

Specify the data sample.

S:=SampleNormalRandomVariable5,2,10:

T:=SampleUniformRandomVariable4,6,10:

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)

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)

If the output=plot option is included, then a plot will be returned.

ShapiroWilkWTestS,level=0.05,output=plot

If the output=both option is included, then both a report and a plot will be returned.

report,graph:=ShapiroWilkWTestT,level=0.05,output=both:

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
Histogram Type:  default
Data Range:      4.0095669690037 .. 5.99292266316546
Bin Width:       .0661118564720588
Number of Bins:  30
Frequency Scale: relative

report

hypothesis=false,pvalue=0.0351513590317937,statistic=0.832591474899495

(3)

graph

See Also

Statistics[ShapiroWilkWTest], Student, Student/Statistics/ShapiroWilkWTest/overview, Student[Statistics], Student[Statistics][HypothesisTest]

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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