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https://github.com/stdlib-js/stats-ztest2
Two-sample z-Test.
https://github.com/stdlib-js/stats-ztest2
hypothesis javascript math mathematics mean node node-js nodejs normal statistics stats stdlib summary test two-sample
Last synced: 27 days ago
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Two-sample z-Test.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-ztest2
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:33:32.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-11-01T10:50:42.000Z (about 2 months ago)
- Last Synced: 2024-11-03T13:05:36.786Z (about 2 months ago)
- Topics: hypothesis, javascript, math, mathematics, mean, node, node-js, nodejs, normal, statistics, stats, stdlib, summary, test, two-sample
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 1.93 MB
- Stars: 3
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
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README
About stdlib...
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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!
# z-Test
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Two-sample z-Test.
## Installation
```bash
npm install @stdlib/stats-ztest2
```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 ztest2 = require( '@stdlib/stats-ztest2' );
```#### ztest2( x, y, sigmax, sigmay\[, opts] )
By default, the function performs a two-sample z-test for the null hypothesis that the data in [arrays][mdn-array] or [typed arrays][mdn-typed-array] `x` and `y` is independently drawn from normal distributions with _equal_ means and known standard deviations `sigmax` and `sigmay`.
```javascript
var x = [ 2.66, 1.5, 3.25, 0.993, 2.31, 2.41, 1.76, 2.57, 2.62, 1.23 ]; // Drawn from N(2,1)
var y = [ 4.88, 2.93, 2.96, 4.5, -0.0603, 4.62, 3.35, 2.98 ]; // Drawn from N(3,2)var out = ztest2( x, y, 1.0, 2.0 );
/* e.g., returns
{
'rejected': false,
'pValue': ~0.141,
'statistic': ~-1.471,
'ci': [ ~-2.658, ~0.379 ],
// ...
}
*/
```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
console.log( out.print() );
/* e.g., =>
Two-sample z-testAlternative hypothesis: True difference in means is not equal to 0
pValue: 0.1412
statistic: -1.4713
95% confidence interval: [-2.6578,0.3785]Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
```The 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 `x` has a larger mean than `y` (`greater`), `x` has a smaller mean than `y` (`less`) or the means are the same (`two-sided`). Default: `two-sided`.
- **difference**: `number` denoting the difference in means under the null hypothesis. Default: `0`.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 out = ztest2( x, y, 1.0, 2.0, {
'alpha': 0.2
});
var table = out.print();
/* e.g., returns
Two-sample z-testAlternative hypothesis: True difference in means is not equal to 0
pValue: 0.1412
statistic: -1.4713
80% confidence interval: [-2.1323,-0.147]Test Decision: Reject null in favor of alternative at 20% significance level
*/
```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 out = ztest2( x, y, {
'alternative': 'less'
});
var table = out.print();
/* e.g., returns
Two-sample z-testAlternative hypothesis: True difference in means is less than 0
pValue: 0.0706
statistic: -1.4713
95% confidence interval: [-Infinity,0.1344]Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/out = ztest2( x, y, {
'alternative': 'greater'
});
table = out.print();
/* e.g., returns
Two-sample z-testAlternative hypothesis: True difference in means is greater than 0
pValue: 0.9294
statistic: -1.4713
95% confidence interval: [-2.4138,Infinity]Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
```To test whether the difference in the population means is equal to some other value than `0`, set the `difference` option.
```javascript
var normal = require( '@stdlib/random-base-normal' ).factory;var rnorm = normal({
'seed': 372
});var x = new Array( 100 );
var i;
for ( i = 0; i < x.length; i++ ) {
x[ i ] = rnorm( 2.0, 1.0 );
}
var y = new Array( 100 );
for ( i = 0; i < x.length; i++ ) {
y[ i ] = rnorm( 1.0, 1.0 );
}var out = ztest2( x, y, 1.0, 1.0, {
'difference': 1.0
});
/* e.g., returns
{
'rejected': false,
'pValue': ~0.74,
'statistic': ~0.332,
'ci': [ ~0.77, ~1.324 ],
// ...
}
*/var table = out.print();
/* e.g., returns
Two-sample z-testAlternative hypothesis: True difference in means is not equal to 1
pValue: 0.7395
statistic: 0.3325
95% confidence interval: [0.7698,1.3242]Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
```## Examples
```javascript
var rnorm = require( '@stdlib/random-base-normal' );
var ztest2 = require( '@stdlib/stats-ztest2' );var table;
var out;
var x;
var y;
var i;// Values drawn from a Normal(4,2) distribution
x = new Array( 100 );
for ( i = 0; i < 100; i++ ) {
x[ i ] = rnorm( 4.0, 2.0 );
}
// Values drawn from a Normal(3,2) distribution
y = new Array( 80 );
for ( i = 0; i < 80; i++ ) {
y[ i ] = rnorm( 3.0, 2.0 );
}out = ztest2( x, y, 2.0, 2.0 );
table = out.print();
console.log( table );out = ztest2( x, y, 2.0, 2.0, {
'difference': 1.0
});
table = out.print();
console.log( table );
```* * *
## See Also
- [`@stdlib/stats-ztest`][@stdlib/stats/ztest]: one-sample and paired z-Test.
* * *
## 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 © 2016-2024. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-ztest2.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-ztest2[test-image]: https://github.com/stdlib-js/stats-ztest2/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-ztest2/actions/workflows/test.yml?query=branch:main[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-ztest2/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-ztest2?branch=main[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules[deno-url]: https://github.com/stdlib-js/stats-ztest2/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-ztest2/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-ztest2/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-ztest2/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-ztest2/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-ztest2/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-ztest2/blob/main/branches.md[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-ztest2/main/LICENSE
[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays
[@stdlib/stats/ztest]: https://github.com/stdlib-js/stats-ztest