@stdlib/stats-levene-test
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    0.0.2 • Public • Published

    Levene's Test

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    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
    */

    See Also


    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.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/stats-levene-test

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