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Levene's Test

Compute Levene's test for equal variances.

Levene's test is used to test the null hypothesis that the variances of k groups are equal against the alternative that at least two of them are different.

Installation

npm install @stdlib/stats-levene-test

Usage

var leveneTest = require( '@stdlib/stats-levene-test' );

leveneTest( x[, y, ..., z][, opts] )

Calculates Levene's test for input arrays x, y, ..., z holding numeric observations.

// Data from Hollander & Wolfe (1973), p. 116:
var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
var y = [ 3.8, 2.7, 4.0, 2.4 ];
var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];

var out = leveneTest( x, y, z );
/* returns
    {
        'rejected': false,
        'alpha': 0.05,
        'df': [ 2, 11 ],
        'pValue': ~0.1733,
        'statistic': ~2.0638,
        ...
    }
*/

The function accepts the following options:

• alpha: number on the interval [0,1] giving the significance level of the hypothesis test. Default: 0.05.
• groups: an array of group indicators. Only applicable when providing a single numeric array holding all observations.

By default, the test is carried out at a significance level of 0.05. To test at a different significance level, set the alpha option.

var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
var y = [ 3.8, 2.7, 4.0, 2.4 ];
var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];

var out = leveneTest( x, y, z, {
    'alpha': 0.01
});
/* returns
    {
        'rejected': false,
        'alpha': 0.01,
        'df': [ 2, 11 ],
        'pValue': ~0.1733,
        'statistic': ~2.0638,
        ...
    }
*/

In addition to providing multiple arrays, the function supports providing a single numeric array holding all observations along with an array of group indicators.

var arr = [
    2.9, 3.0, 2.5, 2.6, 3.2,
    3.8, 2.7, 4.0, 2.4,
    2.8, 3.4, 3.7, 2.2, 2.0
];
var groups = [
    'a', 'a', 'a', 'a', 'a',
    'b', 'b', 'b', 'b',
    'c', 'c', 'c', 'c', 'c'
];
var out = leveneTest( arr, {
    'groups': groups
});

The returned object comes with a .print() method which, when invoked, prints a formatted output of test results. The method accepts the following options:

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

var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
var y = [ 3.8, 2.7, 4.0, 2.4 ];
var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];

var out = leveneTest( x, y, z );
console.log( out.print() );
/* =>
    Levene's test for Homogeneity of Variance

    Null hypothesis: The variances in all groups are the same.

        df 1: 2
        df 2: 11
        F score: 2.0638
        P Value: 0.1733

    Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/

Examples

var leveneTest = require( '@stdlib/stats-levene-test' );

// Data from Hollander & Wolfe (1973), p. 116:
var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
var y = [ 3.8, 2.7, 4.0, 2.4 ];
var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];

var out = leveneTest( x, y, z );
/* returns
    {
        'rejected': false,
        'alpha': 0.05,
        'df': [ 2, 11 ],
        'pValue': ~0.1733,
        'statistic': ~2.0638,
        ...
    }
*/

var table = out.print();
/* returns
    Levene's test for Homogeneity of Variance

    Null hypothesis: The variances in all groups are the same.

        df 1: 2
        df 2: 11
        F score: 2.0638
        P Value: 0.1733

    Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/

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See Also

• @stdlib/stats-vartest: two-sample F-test for equal variances
• @stdlib/stats-bartlett-test: Bartlett’s test for equal variances.

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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.