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.

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.

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.

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.

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

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

$\mathrm{Ob}≔\mathrm{Array}\left(\left[25\,17\,15\,23\,24\,16\right]\right)\:$

$\mathrm{Ex}≔\mathrm{Array}\left(\left[20\,20\,20\,20\,20\,20\right]\right)\:$

$\mathrm{ChiSquareGoodnessOfFitTest}\left(\mathrm{Ob}\,\mathrm{Ex}\,\mathrm{level}=0.05\,\mathrm{summarize}=\mathrm{true}\right)$

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:      5.000000000
Computed p-value:        .415879723998286
Critical Values:         11.0704974062099
 
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false.

$\mathrm{hypothesis}=\mathrm{true},\mathrm{criticalvalue}=11.0704974062099,\mathrm{distribution}=\mathrm{ChiSquare}\left(5\right),\mathrm{pvalue}=0.415879723998286,\mathrm{statistic}=5.000000000$

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 Statistics[ChiSquareGoodnessOfFitTest] 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.