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Chi-square independence test

Perform a chi-square independence test.

Installation

npm install @stdlib/stats-chi2test

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var chi2test = require( '@stdlib/stats-chi2test' );

chi2test( x[, options] )

Computes a chi-square independence test for the null hypothesis that the joint distribution of the observed frequencies is the product of the row and column marginals (i.e., that the row and column variables are independent).

// 2x2 contigency table:
var x = [
    [ 20, 30 ],
    [ 30, 20 ]
];

var res = chi2test( x );

var o = res.toJSON();
/* returns
    {
        'rejected': false,
        'alpha': 0.05,
        'pValue': ~0.072,
        'df': 1,
        'statistic': 3.24,
        ...
    }
*/

The function accepts the following options:

• alpha: significance level of the hypothesis test. Must be on the interval [0,1]. Default: 0.05.
• correct: boolean indicating whether to use Yates' continuity correction when provided a 2x2 contingency table. Default: true.

By default, the test is performed at a significance level of 0.05. To adjust the significance level, set the alpha option.

var x = [
    [ 20, 30 ],
    [ 30, 20 ]
];
var opts = {
    'alpha': 0.1
};
var res = chi2test( x, opts );

var o = res.toJSON();
/* returns
    {
        'rejected': true,
        'alpha': 0.1,
        'pValue': ~0.072,
        'df': 1,
        'statistic': 3.24,
        ...
    }
*/

By default, the function applies Yates' continuity correction for 2x2 contingency tables. To disable the continuity correction, set correct to false.

var x = [
    [ 20, 30 ],
    [ 30, 20 ]
];
var opts = {
    'correct': false
};
var res = chi2test( x, opts );

var o = res.toJSON();
/* returns
    {
        'rejected': true,
        'alpha': 0.05,
        'pValue': ~0.046,
        'df': 1,
        'statistic': 4,
        ...
    }
*/

The function returns a results object having the following properties:

• alpha: significance level.
• rejected: boolean indicating the test decision.
• pValue: test p-value.
• statistic: test statistic.
• df: degrees of freedom.
• expected: expected observation frequencies.
• method: test name.
• toString: serializes results as formatted test output.
• toJSON: serializes results as a JSON object.

To print formatted test output, invoke the toString method. The method accepts the following options:

• digits: number of displayed decimal digits. Default: 4.
• decision: boolean indicating whether to show the test decision. Default: true.

var x = [
    [ 20, 30 ],
    [ 30, 20 ]
];
var res = chi2test( x );

var table = res.toString({
    'decision': false
});
/* e.g., returns

    Chi-square independence test

    Null hypothesis: the two variables are independent

       pValue: 0.0719
       statistic: 3.24
       degrees of freedom: 1

*/

Notes

• The chi-square approximation may be incorrect if the observed or expected frequencies in each category are too small. Common practice is to require frequencies greater than five. The Yates' continuity correction is enabled by default for 2x2 tables to account for this, although it tends to over-correct.

Examples

var array = require( '@stdlib/ndarray-array' );
var chi2test = require( '@stdlib/stats-chi2test' );

/*
* Data from students in grades 4-6 on whether good grades, athletic ability, or popularity are most important to them:
*
* Source: Chase, M.A and Dummer, G.M. (1992), "The Role of Sports as a Social Determinant for Children"
*/
var table = array([
    /* Grades Popularity Sports */
    [    63,      31,      25   ], // 4th
    [    88,      55,      33   ], // 5th
    [    96,      55,      32   ]  // 6th
]);

// Assess whether the grade level and the students' goals are independent of each other:
var out = chi2test( table );
// returns {...}

console.log( out.toString() );

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.