The ChiSquareIndependenceTest function computes the chisquare test for independence in a matrix.  This test attempts to determine if two factors can be considered to be independent of one another for purposes of analysis.

The first parameter X is a matrix of categorized data samples.

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 independent).  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.

Chi-Square Test for Independence
--------------------------------
Null Hypothesis:
Two attributes within a population are independent of one another
Alt. Hypothesis:
Two attributes within a population are not independent of one another

Dimensions:              3
Total Elements:          95
Distribution:            ChiSquare(2)
Computed statistic:      10.7122
Computed pvalue:         0.00471928
Critical value:          criticalvalue

Result: [Rejected]
There exists statistical evidence against the null hypothesis

Chi-Square Test for Independence
--------------------------------
Null Hypothesis:
Two attributes within a population are independent of one another
Alt. Hypothesis:
Two attributes within a population are not independent of one another

Dimensions:              3
Total Elements:          38
Distribution:            ChiSquare(2)
Computed statistic:      0.128915
Computed pvalue:         0.937576
Critical value:          criticalvalue

Result: [Accepted]
There is no statistical evidence against the null hypothesis

Kanju, Gopal K. 100 Statistical Tests. London: SAGE Publications Ltd., 1994.

Sheskin, David J. Handbook of Parametric and Nonparametric Statistical Procedures. London: CRC Press, 1997.