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

Calling Sequence

ChiSquareGoodnessOfFitTest(Ob, Ex, options)

Parameters

Ob

-

data sample of categorized observed data

Ex

-

data sample of categorized expected data

options

-

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

Description

• 

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.

Options

  

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.

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.

• 

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

Examples

withStatistics:

infolevel[Statistics]:=1:

Specify the matrices of categorized data values.

Ob:=Array25,17,15,23,24,16:

Ex:=Array20,20,20,20,20,20:

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

ChiSquareGoodnessOfFitTestOb,Ex,level=0.05

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

hypothesis=true,criticalvalue=11.0704974062099,distribution=ChiSquare5,pvalue=0.415879723998286,statistic=5.000000000

(1)

See Also

Statistics, Statistics[Computation]

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.


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