@stdlib/stats-wilcoxon

Wilcoxon signed rank test.

https://github.com/stdlib-js/stats-wilcoxon

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Keywords

difference distribution hypothesis javascript math mathematics median node node-js nodejs nonparametric paired signed statistics stats stdlib summary symmetric test

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Repository

Wilcoxon signed rank test.

Basic Info

Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
Default Branch: main
Homepage: https://github.com/stdlib-js/stdlib
Size: 1.93 MB

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difference distribution hypothesis javascript math mathematics median node node-js nodejs nonparametric paired signed statistics stats stdlib summary symmetric test

Created over 4 years ago · Last pushed 7 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!

Wilcoxon Signed Rank Test

One-sample and paired Wilcoxon signed rank test.

## Installation ```bash npm install @stdlib/stats-wilcoxon ``` 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 wilcoxon = require( '@stdlib/stats-wilcoxon' ); ``` #### wilcoxon( x\[, y]\[, opts] ) Performs a one-sample t-test for the null hypothesis that the data in [array][mdn-array] or [typed array][mdn-typed-array] `x` is drawn from a distribution that is symmetric around zero (i.e., with median zero). ```javascript // Differences in plant heights, see Cureton (1967) var x = [ 6, 8, 14, 16, 23, 24, 28, 29, 41, -48, 49, 56, 60, -67, 75 ]; var out = wilcoxon( x ); /* e.g., returns { 'rejected': true, 'alpha': 0.05, 'pValue': 0.04125976562499978, 'statistic': 96, // ... } */ ``` When [array][mdn-array] or [typed array][mdn-typed-array] `y` is supplied, the function tests whether the paired differences `x - y` come from a distribution that is symmetric around zero (i.e., with median zero). ```javascript // Patient measurements at first (x) and second (y) visit, see Hollander & Wolfe (1973) var x = [ 1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30 ]; var y = [ 0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29 ]; var out = wilcoxon( x, y ); /* e.g., returns { 'rejected': true, 'alpha': 0.05, 'pValue': 0.0390625, 'statistic': 40, // ... } */ ``` The returned object comes with a `.print()` method which when invoked will print a formatted output of the hypothesis test results. `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 console.log( out.print() ); /* e.g., => Paired Wilcoxon signed rank test Alternative hypothesis: Median of the difference `x - y` is not equal to 0 pValue: 0.0391 statistic: 40 Test Decision: Reject null in favor of alternative at 5% significance level */ ``` The `wilcoxon` function accepts the following `options`: - **alpha**: `number` in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`. - **alternative**: Either `two-sided`, `less` or `greater`. Indicates whether the alternative hypothesis is that the mean of `x` is larger than `mu` (`greater`), smaller than `mu` (`less`), or equal to `mu` (`two-sided`). Default: `two-sided`. - **correction**: continuity correction adjusting the Wilcoxon rank statistic by 0.5 towards the mean when using the normal approximation. Default: `true`. - **exact**: Determines whether to force use of the exact distribution instead of a normal approximation when there are more than fifty data points. Default: `false`. - **mu**: `number` denoting the hypothesized median under the null hypothesis. Default: `0`. - **zeroMethod**: Method governing how zero-differences are handled (`pratt`, `wilcox`, or `zsplit`). Default: `'wilcox'`. By default, the hypothesis test is carried out at a significance level of `0.05`. To choose a different significance level, set the `alpha` option. ```javascript var table; var out; var arr; arr = [ 2, 4, 3, 1, 0 ]; out = wilcoxon( arr, { 'alpha': 0.01 }); table = out.print(); /* e.g., returns One-Sample Wilcoxon signed rank test Alternative hypothesis: Median of `x` is not equal to 0 pValue: 0.035 statistic: 21 Test Decision: Reject null in favor of alternative at 5% significance level */ out = wilcoxon( arr, { 'alpha': 0.1 }); table = out.print(); /* e.g., returns One-Sample Wilcoxon signed rank test Alternative hypothesis: Median of `x` is not equal to 0 pValue: 0.035 statistic: 21 Test Decision: Fail to reject null in favor of alternative at 1% significance level */ ``` To test whether the data comes from a distribution with a median different than zero, set the `mu` option. ```javascript var arr = [ 4, 4, 6, 6, 5 ]; var out = wilcoxon( arr, { 'mu': 5 }); /* e.g., returns { 'rejected': false, 'pValue': 1, 'statistic': 0, // ... } */ ``` By default, a two-sided test is performed. To perform either of the one-sided tests, set the `alternative` option to `less` or `greater`. ```javascript var arr = [ 4, 4, 6, 6, 5 ]; var out = wilcoxon( arr, { 'alternative': 'less' }); var table = out.print(); /* e.g., returns One-Sample Wilcoxon signed rank test Alternative hypothesis: Median of `x` is less than 0 pValue: 0.9853 statistic: 15 Test Decision: Fail to reject null in favor of alternative at 5% significance level */ out = wilcoxon( arr, { 'alternative': 'greater' }); table = out.print(); /* e.g., returns One-Sample Wilcoxon signed rank test Alternative hypothesis: Median of `x` is greater than 0 pValue: 0.0284 statistic: 15 Test Decision: Reject null in favor of alternative at 5% significance level */ ``` By default, all zero-differences are discarded before calculating the ranks. Set `zeroMethod` to `pratt` when you wish differences of zero to be used in the rank calculation but then drop them or to `zsplit` when differences of zero are shall be used in the ranking procedure and the ranks then split between positive and negative ones. ```javascript var arr = [ 0, 2, 3, -1, -4, 0, 0, 8, 9 ]; var out = wilcoxon( arr, { 'zeroMethod': 'pratt' }); /* e.g., returns { 'rejected': false, 'alpha': 0.05, 'pValue': ~0.331, 'statistic': 28, // ... } */ out = wilcoxon( arr, { 'zeroMethod': 'zsplit' }); /* e.g., returns { 'rejected': false, 'alpha': 0.05, 'pValue': ~0.342, 'statistic': 31, // ... } */ ``` By default, the test uses the exact distribution of the rank statistic to calculate the critical values for the test in case of no ties and no zero-differences. Since it is more computationally efficient, starting with fifty observations a normal approximation is employed. If you would like the test to use the correct distribution even for larger samples, set the `exact` option to `true`. ```javascript var normal = require( '@stdlib/random-array-normal' ); var rnorm = normal.factory( 0.0, 4.0, { 'seed': 100 }); var arr = rnorm( 100 ); var out = wilcoxon( arr, { 'exact': false }); /* e.g., returns { 'rejected': false, 'alpha': 0.05, 'pValue': ~0.422, 'statistic': 2291, // ... } */ out = wilcoxon( arr, { 'exact': true }); /* e.g., returns { 'rejected': false, 'alpha': 0.05, 'pValue': ~0.424, 'statistic': 2291, // ... } */ ``` By default, when using the normal approximation, the test uses a continuity correction, which adjusts the Wilcoxon rank statistic by `0.5` towards the mean. To disable this correction, set `correction` to `false`. ```javascript var normal = require( '@stdlib/random-array-normal' ); var rnorm = normal.factory( 0.0, 4.0, { 'seed': 100 }); var arr = rnorm( 100 ); var out = wilcoxon( arr, { 'correction': false }); /* e.g., returns { 'rejected': false, 'alpha': 0.05, 'pValue': ~0.421, 'statistic': 2291, // ... } */ out = wilcoxon( arr, { 'correction': true }); /* e.g., returns { 'rejected': false, 'alpha': 0.05, 'pValue': ~0.422, 'statistic': 2291, // ... } */ ```

## Examples ```javascript var uniform = require( '@stdlib/random-array-discrete-uniform' ); var wilcoxon = require( '@stdlib/stats-wilcoxon' ); var runif = uniform.factory( -50.0, 50.0, { 'seed': 37827 }); var arr = runif( 100 ); // Test whether distribution is symmetric around zero: var out = wilcoxon( arr ); var table = out.print(); /* e.g., returns One-Sample Wilcoxon signed rank test Alternative hypothesis: Median of `x` is not equal to 0 pValue: 0.7714 statistic: 2438.5 Test Decision: Fail to reject null in favor of alternative at 5% significance level */ // Test whether distribution has median of five: out = wilcoxon( arr, { 'mu': 5.0 }); table = out.print(); /* e.g, returns One-Sample Wilcoxon signed rank test Alternative hypothesis: Median of `x` is not equal to 5 pValue: 0.0529 statistic: 1961.5 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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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-wilcoxon

Wilcoxon signed rank test.

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

Versions: 11
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@stdlib/string-format ^0.0.x
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@stdlib/stats-wilcoxon

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Wilcoxon Signed Rank Test

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