The ChiSquareIndependenceTest function computes the chi-square 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.

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.

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

$X≔\mathrm{Matrix}\left(\left[\left[32\,12\right]\,\left[14\,22\right]\,\left[6\,9\right]\right]\right)\:$

$Y≔\mathrm{Matrix}\left(\left[\left[2\,4\right]\,\left[4\,9\right]\,\left[7\,12\right]\right]\right)\:$

$\mathrm{ChiSquareIndependenceTest}\left(X\,\mathrm{level}=0.05\,\mathrm{summarize}=\mathrm{embed}\right)\:$

$\mathrm{ChiSquareIndependenceTest}\left(Y\,\mathrm{level}=0.05\,\mathrm{summarize}=\mathrm{true}\right)$

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:      .1289151874

Computed p-value:        .937575872647938

Critical Values:         5.99146454710798

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

$\mathrm{hypothesis}=\mathrm{true},\mathrm{criticalvalue}=5.99146454710798,\mathrm{distribution}=\mathrm{ChiSquare}\left(2\right),\mathrm{pvalue}=0.937575872647938,\mathrm{statistic}=0.1289151874$

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.

The Statistics[ChiSquareIndependenceTest] 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.