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Statistics

 ChiSquareIndependenceTest
 apply the chi-square test for independence in a matrix

 Calling Sequence ChiSquareIndependenceTest(X, options)

Parameters

 X - Matrix of categorized data options - (optional) equation(s) of the form option=value where option is one of level, output, or summarize; specify options for the ChiSquareIndependenceTest function

Description

 • 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.

Options

 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.

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 or use the summarize option.

Examples

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

Specify the matrices of categorized data values.

 > $X≔\mathrm{Matrix}\left(\left[\left[32,12\right],\left[14,22\right],\left[6,9\right]\right]\right):$
 > $Y≔\mathrm{Matrix}\left(\left[\left[2,4\right],\left[4,9\right],\left[7,12\right]\right]\right):$

Perform the independence test on the first sample.

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

Null Hypothesis:

Two attributes within a population are independent of one another

Alternative Hypothesis:

Two attributes within a population are not independent of one another

 Dimensions Total Elements Distribution Computed Statistic Computed p-value Critical Value ${3.}$ ${95.}$ ${\mathrm{ChiSquare}}{}\left({2}\right)$ ${10.7122}$ ${0.00471928}$ ${5.99146}$

Result:

Rejected: This statistical test provides evidence that the null hypothesis is false.

Perform the independence test on the second sample.

 > $\mathrm{ChiSquareIndependenceTest}\left(Y,\mathrm{level}=0.05,\mathrm{summarize}=\mathrm{true}\right)$
 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.
 ${\mathrm{hypothesis}}{=}{\mathrm{true}}{,}{\mathrm{criticalvalue}}{=}{5.99146454710798}{,}{\mathrm{distribution}}{=}{\mathrm{ChiSquare}}{}\left({2}\right){,}{\mathrm{pvalue}}{=}{0.937575872647938}{,}{\mathrm{statistic}}{=}{0.1289151874}$ (1)
 > 

References

 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.

Compatibility

 • The Statistics[ChiSquareIndependenceTest] command was updated in Maple 2016.
 • The summarize option was introduced in Maple 2016.