@stdlib/stats-kruskal-test

Compute the Kruskal-Wallis test for equal medians.

https://github.com/stdlib-js/stats-kruskal-test

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equality hypothesis javascript math mathematics median node node-js nodejs non-parametric nonparametric statistics stats stdlib summary test

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Compute the Kruskal-Wallis test for equal medians.

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Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
Default Branch: main
Homepage: https://github.com/stdlib-js/stdlib
Size: 2.78 MB

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equality hypothesis javascript math mathematics median node node-js nodejs non-parametric nonparametric statistics stats stdlib summary test

Created over 4 years ago · Last pushed 6 months ago

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Readme Changelog Contributing License Code of conduct Citation Security

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

kruskalTest

Compute the Kruskal-Wallis test for equal medians.

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 ```math H = \frac{\tfrac{12}{N(N+1)}\sum_h\tfrac{S_h^2}{n_h}-3(N+1)}{1-\tfrac{1}{(N^3-N)} \sum t_{r(i)}^3 - t_{r(i)}} ``` where `N` denotes the total number of observations and `t_{r(i)}` are the number of tied observations with rank _i_.

## Installation ```bash npm install @stdlib/stats-kruskal-test ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships. To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage ```javascript 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. ```javascript // 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. ```javascript 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. ```javascript 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. ```javascript 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 ```javascript 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][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][stdlib], see the main project [repository][stdlib]. #### Community [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].

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Login: stdlib-js
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Twitter: stdlibjs
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Standard library for JavaScript.

Citation (CITATION.cff)

cff-version: 1.2.0
title: stdlib
message: >-
  If you use this software, please cite it using the
  metadata from this file.

type: software

authors:
  - name: The Stdlib Authors
    url: https://github.com/stdlib-js/stdlib/graphs/contributors

repository-code: https://github.com/stdlib-js/stdlib
url: https://stdlib.io

abstract: |
  Standard library for JavaScript and Node.js.

keywords:
  - JavaScript
  - Node.js
  - TypeScript
  - standard library
  - scientific computing
  - numerical computing
  - statistical computing

license: Apache-2.0 AND BSL-1.0

date-released: 2016

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npmjs.org: @stdlib/stats-kruskal-test

Compute the Kruskal-Wallis test for equal medians.

Homepage: https://stdlib.io
License: Apache-2.0
Latest release: 0.2.2
published over 1 year ago

Versions: 11
Dependent Packages: 2
Dependent Repositories: 0
Downloads: 1,504 Last month

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Downloads: 13.3%

Average: 16.5%

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Dependent repos count: 25.3%

Maintainers (4)

planeshifter rreusser stdlib-bot kgryte

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@stdlib/stats-kruskal-test

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