apply the chi-square test for goodness-of-fit - Maple Help

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Statistics[ChiSquareGoodnessOfFitTest] - apply the chi-square test for goodness-of-fit

Calling Sequence

ChiSquareGoodnessOfFitTest(Ob, Ex, options)




data sample of categorized observed data



data sample of categorized expected data



(optional) equation(s) of the form option=value where option is one of fitparameters, level, or output; specify options for the ChiSquareGoodnessOfFitTest function



The ChiSquareGoodnessOfFitTest function computes the chi-square test for goodness-of-fit.  This test attempts to determine if an observed sample can be considered to match an expected sample.


The first parameter Ob is a data sample of categorized observed data.  This parameter must have the same length as Ex.


The second parameter Ex is a data sample of categorized expected data.  This parameter must have the same length as Ob.



The options argument can contain one or more of the options shown below.




This option is used to specify if this goodness-of-fit test is used to indicate the number of categories used when fitting this data to a distribution. A positive value for this parameter negatively affects the number of degrees of freedom used in the calculation, and so should be no greater than rtable_num_elems(Ex)-1.




This option is used to specify the level of the analysis (minimum criteria for the observed data to be considered well-fit to the expected data).  By default, this value is 0.05.


output='report', 'statistic', 'pvalue', 'criticalvalue', 'distribution', 'hypothesis', or list('statistic', 'pvalue', 'criticalvalue', 'distribution', '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.



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.


To compare observed samples against a distribution rather than a categorized data set, the chi-square suitable model test should be applied instead.




Specify the matrices of categorized data values.



Perform the goodness-of-fit test on this sample.


Chi-Square Test for Goodness-of-Fit
Null Hypothesis:
Observed sample does not differ from expected sample
Alt. Hypothesis:
Observed sample differs from expected sample

Categories:              6
Distribution:            ChiSquare(5)
Computed statistic:      5
Computed pvalue:         0.41588
Critical value:          11.0704974062099

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



See Also

Statistics, Statistics[Computation]



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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