The ChiSquareIndependenceTest function computes the chi-square test for independence in a Matrix. This tests whether two factors in a population are independent of one another. The rows represent the levels of one factor; the columns represent the levels of another. The entries in the Matrix are interpreted as counts of observations with the given combination of levels.

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

level=float

This option is used to specify the level of analysis (minimum criteria for the observed data to be considered well-fit to the expected data). By default, this value is 0.05.

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

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

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

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

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:          95
Distribution:            ChiSquare(2)
Computed Statistic:      10.71219801
Computed p-value:        .00471928013704082
Critical Values:         5.99146454710798
 
Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false.

$\mathrm{hypothesis}=\mathrm{false},\mathrm{criticalvalue}=5.99146454710798,\mathrm{distribution}=\mathrm{ChiSquare}\left(2\right),\mathrm{pvalue}=0.00471928013704082,\mathrm{statistic}=10.71219801$

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

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 Student[Statistics][ChiSquareIndependenceTest] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.