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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-->\n\n\n<details>\n  <summary>\n    About stdlib...\n  </summary>\n  <p>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.</p>\n  <p>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.</p>\n  <p>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.</p>\n  <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href=\"https://github.com/stdlib-js/stdlib\">GitHub</a>, and please consider <a href=\"https://opencollective.com/stdlib\">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>\n</details>\n\n# Binomial Test\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->\n\n> Exact test for the success probability in a Bernoulli experiment.\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-binomial-test\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar binomialTest = require( '@stdlib/stats-binomial-test' );\n```\n\n#### binomialTest( x\\[, n]\\[, opts] )\n\nWhen supplied nonnegative integers `x` (number of successes in a Bernoulli experiment) and `n` (total number of trials), the function computes an exact test for the success probability in a Bernoulli experiment. Alternatively, `x` may be a two-element array containing the number of successes and failures, respectively.\n\n```javascript\nvar out = binomialTest( 550, 1000 );\n/* returns\n    {\n        'rejected': true,\n        'pValue': ~0.001,\n        'statistic': 0.55,\n        'ci': [ ~0.519, ~0.581 ],\n        // ...\n    }\n*/\n\nout = binomialTest( [ 550, 450 ] );\n/* returns\n    {\n        'rejected': true,\n        'pValue': ~0.001,\n        'statistic': 0.55,\n        'ci': [ ~0.519, ~0.581 ],\n        // ...\n    }\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<!-- run-disable -->\n\n```javascript\nconsole.log( out.print() );\n/* e.g., =>\n    Exact binomial test\n\n    Alternative hypothesis: True correlation coefficient is not equal to 0.5\n\n        pValue: 0.0017\n        statistic: 0.55\n        95% confidence interval: [0.5186,0.5811]\n\n    Test Decision: Reject null in favor of alternative at 5% significance level\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-   **alternative**: Either `two-sided`, `less` or `greater`. Indicates whether the alternative hypothesis is that the true ratio of variances is greater than one (`greater`), smaller than one (`less`), or that the variances are the same (`two-sided`). Default: `two-sided`.\n-   **p**: success `probability` under the null hypothesis. Default: `0.5`.\n\nBy default, the hypothesis test is carried out at a significance level of `0.05`. To choose a different significance level, set the `alpha` option.\n\n```javascript\nvar out = binomialTest( 59, 100, {\n    'alpha': 0.1\n});\n/* returns\n    {\n        'rejected': true,\n        'pValue': ~0.089,\n        'statistic': 0.59,\n        'ci': [ ~0.487, ~0.687 ],\n        // ...\n    }\n*/\n```\n\nBy default, a two-sided test is performed. To perform either of the one-sided tests, set the `alternative` option to `less` or `greater`.\n\n```javascript\nout = binomialTest( 550, 1000, {\n    'alternative': 'greater'\n});\ntable = out.print();\n/** e.g., returns\n    Exact binomial test\n\n    Alternative hypothesis: True correlation coefficient is greater than 0.5\n\n        pValue: 0.0009\n        statistic: 0.55\n        95% confidence interval: [0.5235,1]\n\n    Test Decision: Reject null in favor of alternative at 5% significance level\n*/\n\nout = binomialTest( 550, 1000, {\n    'alternative': 'less'\n});\ntable = out.print();\n/* e.g., returns\n    Exact binomial test\n\n    Alternative hypothesis: True correlation coefficient is less than 0.5\n\n        pValue: 0.9993\n        statistic: 0.55\n        95% confidence interval: [0,0.5762]\n\n    Test Decision: Fail to reject null in favor of alternative at 5% significance level\n*/\n```\n\nTo test whether the success probability in the population is equal to some other value than `0.5`, set the `p` option.\n\n```javascript\nvar out = binomialTest( 23, 100, {\n    'p': 0.2\n});\n/* returns\n    {\n        'rejected': false,\n        'pValue': ~0.453,\n        'statistic': 0.23,\n        'ci': [ ~0.152, ~0.325 ],\n        // ...\n    }\n*/\n\nvar table = out.print();\n/* e.g., returns\n    Exact binomial test\n\n    Alternative hypothesis: True correlation coefficient is not equal to 0.2\n\n        pValue: 0.4534\n        statistic: 0.23\n        95% confidence interval: [0.1517,0.3249]\n\n    Test Decision: Fail to reject null in favor of alternative at 5% significance level\n*/\n```\n\n</section>\n\n<!-- /.usage -->\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\n\n```javascript\nvar binomialTest = require( '@stdlib/stats-binomial-test' );\n\nvar out = binomialTest( 682, 925 );\n/* returns\n    {\n        'rejected': true,\n        'pValue': ~3.544e-49,\n        'statistic': 0.737,\n        'ci': [ ~0.708, ~0.765 ],\n        // ...\n    }\n*/\n\nout = binomialTest( [ 682, 925 - 682 ] );\n/* returns\n    {\n        'rejected': true,\n        'pValue': ~3.544e-49,\n        'statistic': 0.737,\n        'ci': [ ~0.708, ~0.765 ],\n        // ...\n    }\n*/\n\nout = binomialTest( 682, 925, {\n    'p': 0.75,\n    'alpha': 0.05\n});\n/* returns\n    {\n        'rejected': false,\n        'pValue': ~0.382\n        'statistic': 0.737,\n        'ci': [ ~0.708, ~0.765 ],\n        // ...\n    }\n*/\n\nout = binomialTest( 21, 40, {\n    'p': 0.4,\n    'alternative': 'greater'\n});\n/* returns\n    {\n        'rejected': false,\n        'pValue': ~0.382,\n        'statistic': 0.737,\n        'ci': [ ~0.385, 1.0 ],\n        // ...\n    }\n*/\n```\n\n</section>\n\n<!-- /.examples -->\n\n<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->\n\n<section class=\"related\">\n\n</section>\n\n<!-- /.related -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n\n<section class=\"main-repo\" >\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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n</section>\n\n<!-- /.stdlib -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"links\">\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-binomial-test.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-binomial-test\n\n[test-image]: https://github.com/stdlib-js/stats-binomial-test/actions/workflows/test.yml/badge.svg?branch=v0.2.3\n[test-url]: https://github.com/stdlib-js/stats-binomial-test/actions/workflows/test.yml?query=branch:v0.2.3\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-binomial-test/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-binomial-test?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-binomial-test.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-binomial-test/main\n\n-->\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-binomial-test/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-binomial-test/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-binomial-test/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-binomial-test/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-binomial-test/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-binomial-test/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-binomial-test/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-binomial-test/main/LICENSE\n\n</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}