The Kruskal-Wallis rank sum test evaluates for multiple samples the null hypothesis that their medians are identical. The Kruskal-Wallis test is a nonparametric test which does not require the data to be normally distributed.

To carry out the test, the rank sums S_h of the individual groups are calculated. The test statistic is then calculated as

where N denotes the total number of observations and t_{r(i)} are the number of tied observations with rank i.

Installation

npm install @stdlib/stats-kruskal-test

Usage

var kruskalTest = require( '@stdlib/stats-kruskal-test' );

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

For input arrays a, b, ... holding numeric observations, this function calculates the Kruskal-Wallis rank sums test, which tests the null hypothesis that the medians 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 = kruskalTest( x, y, z );
/* returns
    {
        'rejected': false,
        'alpha': 0.05,
        'df': 2,
        'pValue': ~0.68,
        'statistic': ~0.771,
        ...
    }
*/

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 = kruskalTest( x, y, z, {
    'alpha': 0.01
});
/* returns
    {
        'rejected': false,
        'alpha': 0.01,
        'df': 2,
        'pValue': ~0.68,
        'statistic': ~0.771,
        ...
    }
*/

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 = kruskalTest( 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 = kruskalTest( x, y, z );
console.log( out.print() );
/* =>
    Kruskal-Wallis Test

    Null hypothesis: the medians of all groups are the same

        pValue: 0.68
        statistic: 0.7714    df: 2

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

Examples

var kruskalTest = require( '@stdlib/stats-kruskal-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 = kruskalTest( x, y, z );
/* returns
    {
        'rejected': false,
        'alpha': 0.05,
        'df': 2,
        'pValue': ~0.68,
        'statistic': ~0.771,
        ...
    }
*/

var table = out.print();
/* returns
    Kruskal-Wallis Test

    Null hypothesis: the medians of all groups are the same

        pValue: 0.68
        statistic: 0.7714    df: 2

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

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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.