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.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Statistics}\right]\right)\:$

$S≔\mathrm{Sample}\left(\mathrm{NormalRandomVariable}\left(5\,2\right)\,10\right)\:$

$T≔\mathrm{Sample}\left(\mathrm{UniformRandomVariable}\left(4\,6\right)\,10\right)\:$

$\mathrm{ShapiroWilkWTest}\left(S\,\mathrm{level}=0.05\right)$

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:      .967478742211855
Computed p-value:        .856735713777028
 
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false.

$\left[\mathrm{hypothesis}=\mathrm{true}\,\mathrm{pvalue}=0.856735713777028\,\mathrm{statistic}=0.967478742211855\right]$

$\mathrm{ShapiroWilkWTest}\left(T\,\mathrm{level}=0.05\right)$

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:      .832591474899495
Computed p-value:        .0351513590317937
 
Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false.

$\left[\mathrm{hypothesis}=\mathrm{false}\,\mathrm{pvalue}=0.0351513590317937\,\mathrm{statistic}=0.832591474899495\right]$

$\mathrm{ShapiroWilkWTest}\left(S\,\mathrm{level}=0.05\,\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{report},\mathrm{graph}≔\mathrm{ShapiroWilkWTest}\left(T\,\mathrm{level}=0.05\,\mathrm{output}=\mathrm{both}\right)\:$

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:      .832591474899495
Computed p-value:        .0351513590317937
 
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

$\mathrm{report}$

$\left[\mathrm{hypothesis}=\mathrm{false}\,\mathrm{pvalue}=0.0351513590317937\,\mathrm{statistic}=0.832591474899495\right]$

$\mathrm{graph}$

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.

The Student[Statistics][ShapiroWilkWTest] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.