apply the chi-square test for independence in a matrix - Maple Help

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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 or output; 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.

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.

Examples

withStatistics:

infolevel[Statistics]:=1:

Specify the matrices of categorized data values.

X:=Matrix32,12,14,22,6,9:

Y:=Matrix2,4,4,9,7,12:

Perform the independence test on the first sample.

ChiSquareIndependenceTestX,level=0.05

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:          5.99146454710798

Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false

hypothesis=false,criticalvalue=5.99146454710798,distribution=ChiSquare2,pvalue=0.00471928013704082,statistic=10.71219801

(1)

Perform the independence test on the second sample.

ChiSquareIndependenceTestY,level=0.05

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:          5.99146454710798

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

hypothesis=true,criticalvalue=5.99146454710798,distribution=ChiSquare2,pvalue=0.937575872647938,statistic=0.1289151874

(2)

See Also

Statistics, Statistics[Computation]

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.


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