{"id":50166346,"url":"https://github.com/stdlib-js/stats-bartlett-test","last_synced_at":"2026-05-24T21:04:40.949Z","repository":{"id":41404798,"uuid":"377245729","full_name":"stdlib-js/stats-bartlett-test","owner":"stdlib-js","description":"Compute Bartlett’s test for equal variances.","archived":false,"fork":false,"pushed_at":"2026-05-10T03:57:18.000Z","size":3792,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"main","last_synced_at":"2026-05-10T05:33:05.663Z","etag":null,"topics":["bartlett","equal","hypothesis","javascript","math","mathematics","node","node-js","nodejs","statistics","stats","stdlib","summary","test","variance"],"latest_commit_sha":null,"homepage":"","language":"JavaScript","has_issues":false,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/stdlib-js.png","metadata":{"files":{"readme":"README.md","changelog":"CHANGELOG.md","contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE","code_of_conduct":"CODE_OF_CONDUCT.md","threat_model":null,"audit":null,"citation":"CITATION.cff","codeowners":null,"security":"SECURITY.md","support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":"NOTICE","maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null},"funding":{"github":["stdlib-js"],"open_collective":"stdlib","tidelift":"npm/@stdlib/stdlib"}},"created_at":"2021-06-15T17:36:41.000Z","updated_at":"2026-05-10T03:32:23.000Z","dependencies_parsed_at":"2023-09-24T08:58:11.536Z","dependency_job_id":"9b06afe8-878d-434f-99b9-71026d694b38","html_url":"https://github.com/stdlib-js/stats-bartlett-test","commit_stats":{"total_commits":50,"total_committers":1,"mean_commits":50.0,"dds":0.0,"last_synced_commit":"354bfa4b83ca09babb014409148b0a088b16cf2a"},"previous_names":[],"tags_count":27,"template":false,"template_full_name":null,"purl":"pkg:github/stdlib-js/stats-bartlett-test","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-bartlett-test","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-bartlett-test/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-bartlett-test/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-bartlett-test/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/stdlib-js","download_url":"https://codeload.github.com/stdlib-js/stats-bartlett-test/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-bartlett-test/sbom","scorecard":{"id":848787,"data":{"date":"2025-08-11","repo":{"name":"github.com/stdlib-js/stats-bartlett-test","commit":"1dde9af84a27a833af921e79268daabc0c72e3eb"},"scorecard":{"version":"v5.2.1-40-gf6ed084d","commit":"f6ed084d17c9236477efd66e5b258b9d4cc7b389"},"score":4.4,"checks":[{"name":"Security-Policy","score":9,"reason":"security policy file detected","details":["Info: security policy file detected: SECURITY.md:1","Info: Found linked content: SECURITY.md:1","Warn: One or no descriptive hints of disclosure, vulnerability, and/or timelines in security policy","Info: Found text in security policy: SECURITY.md:1"],"documentation":{"short":"Determines if the project has published a security policy.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#security-policy"}},{"name":"Maintained","score":2,"reason":"3 commit(s) and 0 issue activity found in the last 90 days -- score normalized to 2","details":null,"documentation":{"short":"Determines if the project is \"actively maintained\".","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#maintained"}},{"name":"Code-Review","score":0,"reason":"Found 0/30 approved changesets -- score normalized to 0","details":null,"documentation":{"short":"Determines if the project requires human code review before pull requests (aka merge requests) are merged.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#code-review"}},{"name":"CII-Best-Practices","score":0,"reason":"no effort to earn an OpenSSF best practices badge detected","details":null,"documentation":{"short":"Determines if the project has an OpenSSF (formerly CII) Best Practices Badge.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#cii-best-practices"}},{"name":"Binary-Artifacts","score":10,"reason":"no binaries found in the repo","details":null,"documentation":{"short":"Determines if the project has generated executable (binary) artifacts in the source repository.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#binary-artifacts"}},{"name":"Dangerous-Workflow","score":10,"reason":"no dangerous workflow patterns detected","details":null,"documentation":{"short":"Determines if the project's GitHub Action workflows avoid dangerous patterns.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#dangerous-workflow"}},{"name":"Packaging","score":-1,"reason":"packaging workflow not detected","details":["Warn: no GitHub/GitLab publishing workflow detected."],"documentation":{"short":"Determines if the project is published as a package that others can easily download, install, easily update, and uninstall.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#packaging"}},{"name":"Token-Permissions","score":0,"reason":"detected GitHub workflow tokens with excessive permissions","details":["Warn: no topLevel permission defined: .github/workflows/benchmark.yml:1","Warn: no topLevel permission defined: .github/workflows/cancel.yml:1","Warn: no topLevel permission defined: .github/workflows/close_pull_requests.yml:1","Warn: no topLevel permission defined: .github/workflows/examples.yml:1","Warn: no topLevel permission defined: .github/workflows/npm_downloads.yml:1","Warn: no topLevel permission defined: .github/workflows/productionize.yml:1","Warn: no topLevel permission defined: .github/workflows/publish.yml:1","Warn: no topLevel permission defined: .github/workflows/test.yml:1","Warn: no topLevel permission defined: .github/workflows/test_bundles.yml:1","Warn: no topLevel permission defined: .github/workflows/test_coverage.yml:1","Warn: no topLevel permission defined: .github/workflows/test_install.yml:1","Warn: no topLevel permission defined: .github/workflows/test_published_package.yml:1","Info: no jobLevel write permissions found"],"documentation":{"short":"Determines if the project's workflows follow the principle of least privilege.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#token-permissions"}},{"name":"Fuzzing","score":0,"reason":"project is not fuzzed","details":["Warn: no fuzzer integrations found"],"documentation":{"short":"Determines if the project uses fuzzing.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#fuzzing"}},{"name":"Vulnerabilities","score":10,"reason":"0 existing vulnerabilities detected","details":null,"documentation":{"short":"Determines if the project has open, known unfixed vulnerabilities.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#vulnerabilities"}},{"name":"Pinned-Dependencies","score":3,"reason":"dependency not pinned by hash detected -- score normalized to 3","details":["Warn: third-party GitHubAction not pinned by hash: .github/workflows/productionize.yml:85: update your workflow using https://app.stepsecurity.io/secureworkflow/stdlib-js/stats-bartlett-test/productionize.yml/main?enable=pin","Warn: third-party GitHubAction not pinned by hash: .github/workflows/productionize.yml:275: update your workflow using https://app.stepsecurity.io/secureworkflow/stdlib-js/stats-bartlett-test/productionize.yml/main?enable=pin","Warn: third-party GitHubAction not pinned by hash: .github/workflows/productionize.yml:449: update your workflow using https://app.stepsecurity.io/secureworkflow/stdlib-js/stats-bartlett-test/productionize.yml/main?enable=pin","Warn: third-party GitHubAction not pinned by hash: .github/workflows/productionize.yml:457: update your workflow using https://app.stepsecurity.io/secureworkflow/stdlib-js/stats-bartlett-test/productionize.yml/main?enable=pin","Warn: third-party GitHubAction not pinned by hash: .github/workflows/productionize.yml:623: update your workflow using https://app.stepsecurity.io/secureworkflow/stdlib-js/stats-bartlett-test/productionize.yml/main?enable=pin","Warn: npmCommand not pinned by hash: .github/workflows/benchmark.yml:58","Warn: npmCommand not pinned by hash: .github/workflows/benchmark.yml:58","Warn: npmCommand not pinned by hash: .github/workflows/benchmark.yml:58","Warn: npmCommand not pinned by hash: .github/workflows/examples.yml:58","Warn: npmCommand not pinned by hash: .github/workflows/examples.yml:58","Warn: npmCommand not pinned by hash: .github/workflows/examples.yml:58","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:436","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:436","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:436","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:617","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:617","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:617","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:157","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:157","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:157","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:165","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:269","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:269","Warn: npmCommand not pinned by hash: .github/workflows/productionize.yml:269","Warn: npmCommand not pinned by hash: .github/workflows/test.yml:76","Warn: npmCommand not pinned by hash: .github/workflows/test.yml:76","Warn: npmCommand not pinned by hash: .github/workflows/test.yml:76","Warn: npmCommand not pinned by hash: .github/workflows/test.yml:83","Warn: npmCommand not pinned by hash: .github/workflows/test_bundles.yml:72","Warn: npmCommand not pinned by hash: .github/workflows/test_coverage.yml:67","Warn: npmCommand not pinned by hash: .github/workflows/test_coverage.yml:67","Warn: npmCommand not pinned by hash: .github/workflows/test_coverage.yml:67","Warn: npmCommand not pinned by hash: .github/workflows/test_coverage.yml:74","Warn: npmCommand not pinned by hash: .github/workflows/test_install.yml:75","Warn: npmCommand not pinned by hash: .github/workflows/test_install.yml:75","Warn: npmCommand not pinned by hash: .github/workflows/test_install.yml:75","Warn: npmCommand not pinned by hash: .github/workflows/test_published_package.yml:93","Info:  33 out of  33 GitHub-owned GitHubAction dependencies pinned","Info:  19 out of  24 third-party GitHubAction dependencies pinned","Info:   0 out of  32 npmCommand dependencies pinned"],"documentation":{"short":"Determines if the project has declared and pinned the dependencies of its build process.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#pinned-dependencies"}},{"name":"License","score":10,"reason":"license file detected","details":["Info: project has a license file: LICENSE:0","Info: FSF or OSI recognized license: Apache License 2.0: LICENSE:0"],"documentation":{"short":"Determines if the project has defined a license.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#license"}},{"name":"SAST","score":0,"reason":"no SAST tool detected","details":["Warn: no pull requests merged into dev branch"],"documentation":{"short":"Determines if the project uses static code analysis.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#sast"}},{"name":"Signed-Releases","score":-1,"reason":"no releases found","details":null,"documentation":{"short":"Determines if the project cryptographically signs release artifacts.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#signed-releases"}},{"name":"Branch-Protection","score":0,"reason":"branch protection not enabled on development/release branches","details":["Warn: branch protection not enabled for branch 'main'"],"documentation":{"short":"Determines if the default and release branches are protected with GitHub's branch protection settings.","url":"https://github.com/ossf/scorecard/blob/f6ed084d17c9236477efd66e5b258b9d4cc7b389/docs/checks.md#branch-protection"}}]},"last_synced_at":"2025-08-23T21:58:28.735Z","repository_id":41404798,"created_at":"2025-08-23T21:58:28.735Z","updated_at":"2025-08-23T21:58:28.735Z"},"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":33450408,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-24T19:21:36.376Z","status":"ssl_error","status_checked_at":"2026-05-24T19:21:10.562Z","response_time":57,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.5:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["bartlett","equal","hypothesis","javascript","math","mathematics","node","node-js","nodejs","statistics","stats","stdlib","summary","test","variance"],"created_at":"2026-05-24T21:04:39.981Z","updated_at":"2026-05-24T21:04:40.941Z","avatar_url":"https://github.com/stdlib-js.png","language":"JavaScript","funding_links":["https://github.com/sponsors/stdlib-js","https://opencollective.com/stdlib","https://tidelift.com/funding/github/npm/@stdlib/stdlib"],"categories":[],"sub_categories":[],"readme":"\u003c!--\n\n@license Apache-2.0\n\nCopyright (c) 2018 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n--\u003e\n\n\n\u003cdetails\u003e\n  \u003csummary\u003e\n    About stdlib...\n  \u003c/summary\u003e\n  \u003cp\u003eWe 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.\u003c/p\u003e\n  \u003cp\u003eThe 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.\u003c/p\u003e\n  \u003cp\u003eWhen 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.\u003c/p\u003e\n  \u003cp\u003eTo join us in bringing numerical computing to the web, get started by checking us out on \u003ca href=\"https://github.com/stdlib-js/stdlib\"\u003eGitHub\u003c/a\u003e, and please consider \u003ca href=\"https://opencollective.com/stdlib\"\u003efinancially supporting stdlib\u003c/a\u003e. We greatly appreciate your continued support!\u003c/p\u003e\n\u003c/details\u003e\n\n# bartlettTest\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \u003c!-- [![dependencies][dependencies-image]][dependencies-url] --\u003e\n\n\u003e Compute Bartlett’s test for equal variances.\n\n\u003csection class=\"intro\"\u003e\n\nBartlett'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.\n\nFor `k` groups each with `n_i` observations, the test statistic is\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:bartlett-test-statistic\" align=\"center\" raw=\"\\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)}\" alt=\"Equation for Bartlett's test statistic.\"\u003e --\u003e\n\n```math\n\\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)}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"\\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)}\" data-equation=\"eq:bartlett-test-statistic\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@4b1db4ebd815eb54bf53a3fa132b992604743d9c/lib/node_modules/@stdlib/stats/bartlett-test/docs/img/equation_bartlett-test-statistic.svg\" alt=\"Equation for Bartlett's test statistic.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere `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.\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003csection class=\"installation\"\u003e\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-bartlett-test\n```\n\nAlternatively,\n\n-   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]).\n-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).\n-   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]).\n\nThe [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.\n\nTo 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.\n\n\u003c/section\u003e\n\n\u003csection class=\"usage\"\u003e\n\n## Usage\n\n```javascript\nvar bartlettTest = require( '@stdlib/stats-bartlett-test' );\n```\n\n#### bartlettTest( a\\[,b,...,k]\\[, opts] )\n\nFor 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.\n\n```javascript\n// Data from Hollander \u0026 Wolfe (1973), p. 116:\nvar x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];\nvar y = [ 3.8, 2.7, 4.0, 2.4 ];\nvar z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];\n\nvar out = bartlettTest( x, y, z );\n/* returns\n    {\n        'rejected': false,\n        'alpha': 0.05,\n        'df': 2,\n        'pValue': ~0.573,\n        'statistic': ~1.112,\n        ...\n    }\n*/\n```\n\nThe function accepts the following `options`:\n\n-   **alpha**: `number` in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`.\n-   **groups**: an `array` of group indicators. If set, the function assumes that only a single numeric array is provided holding all observations.\n\nBy default, the test is carried out at a significance level of `0.05`. To choose a custom significance level, set the `alpha` option.\n\n```javascript\nvar x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];\nvar y = [ 3.8, 2.7, 4.0, 2.4 ];\nvar z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];\n\nvar out = bartlettTest( x, y, z, {\n    'alpha': 0.01\n});\n/* returns\n    {\n        'rejected': false,\n        'alpha': 0.01,\n        'df': 2,\n        'pValue': ~0.573,\n        'statistic': ~1.112,\n        ...\n    }\n*/\n```\n\nThe 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.\n\n\u003c!-- eslint-disable array-element-newline --\u003e\n\n```javascript\nvar arr = [\n    2.9, 3.0, 2.5, 2.6, 3.2,\n    3.8, 2.7, 4.0, 2.4,\n    2.8, 3.4, 3.7, 2.2, 2.0\n];\nvar groups = [\n    'a', 'a', 'a', 'a', 'a',\n    'b', 'b', 'b', 'b',\n    'c', 'c', 'c', 'c', 'c'\n];\nvar out = bartlettTest( arr, {\n    'groups': groups\n});\n```\n\nThe 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.\n\n```javascript\nvar x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];\nvar y = [ 3.8, 2.7, 4.0, 2.4 ];\nvar z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];\n\nvar out = bartlettTest( x, y, z );\nconsole.log( out.print() );\n/* =\u003e\n    Bartlett's test of equal variances\n\n    Null hypothesis: The variances in all groups are the same.\n\n        pValue: 0.5735\n        statistic: 1.1122\n        df: 2\n\n    Test Decision: Fail to reject null in favor of alternative at 5% significance level\n*/\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar bartlettTest = require( '@stdlib/stats-bartlett-test' );\n\n// Data from Hollander \u0026 Wolfe (1973), p. 116:\nvar x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];\nvar y = [ 3.8, 2.7, 4.0, 2.4 ];\nvar z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];\n\nvar out = bartlettTest( x, y, z );\n/* returns\n    {\n        'rejected': false,\n        'alpha': 0.05,\n        'df': 2,\n        'pValue': ~0.573,\n        'statistic': ~1.112,\n        ...\n    }\n*/\n\nvar table = out.print();\n/* returns\n    Bartlett's test of equal variances\n\n    Null hypothesis: The variances in all groups are the same.\n\n        pValue: 0.5735\n        statistic: 1.1122\n        df: 2\n\n    Test Decision: Fail to reject null in favor of alternative at 5% significance level\n*/\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003csection class=\"references\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.references --\u003e\n\n\u003c!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --\u003e\n\n\u003csection class=\"related\"\u003e\n\n* * *\n\n## See Also\n\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-vartest`][@stdlib/stats/vartest]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003etwo-sample F-test for equal variances.\u003c/span\u003e\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/stats-levene-test`][@stdlib/stats/levene-test]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003eLevene's test for equal variances.\u003c/span\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.related --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\n\u003csection class=\"main-repo\" \u003e\n\n* * *\n\n## Notice\n\nThis 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.\n\nFor 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].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright \u0026copy; 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n\u003c/section\u003e\n\n\u003c!-- /.stdlib --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"links\"\u003e\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-bartlett-test.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-bartlett-test\n\n[test-image]: https://github.com/stdlib-js/stats-bartlett-test/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/stats-bartlett-test/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-bartlett-test/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-bartlett-test?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-bartlett-test.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-bartlett-test/main\n\n--\u003e\n\n[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-url]: https://stdlib.zulipchat.com\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/stats-bartlett-test/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-bartlett-test/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-bartlett-test/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-bartlett-test/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-bartlett-test/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-bartlett-test/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-bartlett-test/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-bartlett-test/main/LICENSE\n\n\u003c!-- \u003crelated-links\u003e --\u003e\n\n[@stdlib/stats/vartest]: https://github.com/stdlib-js/stats-vartest\n\n[@stdlib/stats/levene-test]: https://github.com/stdlib-js/stats-levene-test\n\n\u003c!-- \u003c/related-links\u003e --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.links --\u003e\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-bartlett-test","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fstats-bartlett-test","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-bartlett-test/lists"}