Statistics

Calling Sequence Parameters Description Options Notes Examples References Compatibility

Calling Sequence ShapiroWilkWTest(X, options) Parameters X - data sample options - (optional) equation(s) of the form option=value where option is one of level, output, or summarize; 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. •  summarize= 'true', 'false', 'embed'    This option controls the display of a printed or embedded summary for the hypothesis test. Unlike the output option, the displayed summary is not assignable output. 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 or use the summarize option. Examples >  $\mathrm{with}\left(\mathrm{Statistics}\right)\:$ Specify the data sample. >  $S≔\mathrm{Sample}\left(\mathrm{Normal}\left(5\,2\right)\,10\right)\:$ >  $T≔\mathrm{Sample}\left(\mathrm{Uniform}\left(4\,6\right)\,10\right)\:$ Calculate Shapiro and Wilk's W-test on the normally distributed sample. >  $\mathrm{ShapiroWilkWTest}\left(S\,\mathrm{level}\=0.05\,\mathrm{summarize}\=\mathrm{embed}\right)\:$ Null Hypothesis: Sample drawn from a population that follows a normal distribution Alternative Hypothesis: Sample drawn from population that does not follow a normal distribution Sample Size Computed Statistic Computed p-value $10.$ $0.967479$ $0.856736$ Result: Accepted: This statistical test does not provide enough evidence to conclude that the null hypothesis is false. Calculate Shapiro and Wilk's W-test on the uniformly distributed sample. >  $\mathrm{ShapiroWilkWTest}\left(T\,\mathrm{level}\=0.05\,\mathrm{summarize}\=\mathrm{true}\right)\:$ 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. 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. Compatibility •  The Statistics[ShapiroWilkWTest] command was updated in Maple 2016. •  The summarize option was introduced in Maple 2016. •  For more information on Maple 2016 changes, see Updates in Maple 2016. See Also Statistics Statistics[Computation]