@stdlib/stats-bartlett-test

Compute Bartlett’s test for equal variances.

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

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bartlett equal hypothesis javascript math mathematics node node-js nodejs statistics stats stdlib summary test variance

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Compute Bartlett’s test for equal variances.

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Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
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bartlett equal hypothesis javascript math mathematics node node-js nodejs statistics stats stdlib summary test variance

Created over 4 years ago · Last pushed 6 months ago

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bartlettTest

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 ```math \chi^2 = \frac{\displaystyle N\ln(S^2) - \sum_{i=0}^{k-1} n_i \ln(S_i^2)}{\displaystyle 1 + \frac{1}{3(k-1)}\left(\sum_{i=0}^{k-1} \frac{1}{n_i} - \frac{1}{N}\right)} ``` 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 ```bash npm install @stdlib/stats-bartlett-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 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. ```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 = 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. ```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 = 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. ```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 = 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. ```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 = 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 ```javascript 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 */ ```

* * * ## 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 and Node.js.

keywords:
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license: Apache-2.0 AND BSL-1.0

date-released: 2016

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

Bartlett’s test for equal variances.

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

Versions: 11
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Downloads: 43 Last month

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@stdlib/stats-bartlett-test

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