The ChiSquareGoodnessOfFitTest function computes the chisquare 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 one-dimensional rtable of categorized observed data.  This parameter must have the same length as Ex.

The second parameter Ex is a one-dimensional rtable 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.

fitparameters=posint

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.

level=float

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 chisquare suitable model test should be applied instead.

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]
There is no statistical evidence against the null hypothesis

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.