Nonflavored Prescription Medicine

    @stdlib/stats-bartlett-test
    TypeScript icon, indicating that this package has built-in type declarations

    0.0.7 • Public • Published

    bartlettTest

    NPM version Build Status Coverage Status

    Compute Bartlett’s test for equal variances.

    Bartlett'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.

    For k groups each with n_i observations, the test statistic is

    Equation for Bartlett's test statistic.

    where N is the total number of observations, S_i are the biased group-level variances and S^2 is a (biased) pooled estimate for the variance. Under the null hypothesis, the test statistic follows a chi-square distribution with df = k - 1 degrees of freedom.

    Installation

    npm install @stdlib/stats-bartlett-test

    Usage

    var bartlettTest = require( '@stdlib/stats-bartlett-test' );

    bartlettTest( a[,b,...,k][, opts] )

    For input arrays a, b, ... holding numeric observations, this function calculates Bartlett’s test, which tests the null hypothesis that the variances in all k groups are the same.

    // 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 = bartlettTest( x, y, z );
    /* returns
        {
            'rejected': false,
            'alpha': 0.05,
            'df': 2,
            'pValue': ~0.573,
            'statistic': ~1.112,
            ...
        }
    */

    The function accepts the following options:

    • alpha: number in the interval [0,1] giving the significance level of the hypothesis test. Default: 0.05.
    • groups: an array of group indicators. If set, the function assumes that only a single numeric array is provided holding all observations.

    By default, the test is carried out at a significance level of 0.05. To choose a custom 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 = bartlettTest( x, y, z, {
        'alpha': 0.01
    });
    /* returns
        {
            'rejected': false,
            'alpha': 0.01,
            'df': 2,
            'pValue': ~0.573,
            'statistic': ~1.112,
            ...
        }
    */

    The function provides an alternate interface by supplying an array of group indicators to the groups option. In this case, it is assumed that only a single numeric array holding all observations is provided to the function.

    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 = bartlettTest( arr, {
        'groups': groups
    });

    The returned object comes with a .print() method which when invoked will print a formatted output of the results of the hypothesis test. print accepts a digits option that controls the number of decimal digits displayed for the outputs and a decision option, which when set to false will hide the test decision.

    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 = bartlettTest( x, y, z );
    console.log( out.print() );
    /* =>
        Bartlett's test of equal variances
    
        Null hypothesis: The variances in all groups are the same.
    
            pValue: 0.5735
            statistic: 1.1122
            df: 2
    
        Test Decision: Fail to reject null in favor of alternative at 5% significance level
    */

    Examples

    var bartlettTest = require( '@stdlib/stats-bartlett-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 = bartlettTest( x, y, z );
    /* returns
        {
            'rejected': false,
            'alpha': 0.05,
            'df': 2,
            'pValue': ~0.573,
            'statistic': ~1.112,
            ...
        }
    */
    
    var table = out.print();
    /* returns
        Bartlett's test of equal variances
    
        Null hypothesis: The variances in all groups are the same.
    
            pValue: 0.5735
            statistic: 1.1122
            df: 2
    
        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.

    Community

    Chat


    License

    See LICENSE.

    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/stats-bartlett-test

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    38

    Version

    0.0.7

    License

    Apache-2.0

    Unpacked Size

    71.8 kB

    Total Files

    13

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser