Chi-square independence test

Perform a chi-square independence test.

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() );