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@stdlib/stats-ttest2

Two-sample Student's t-Test.

https://github.com/stdlib-js/stats-ttest2

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hypothesis javascript math mathematics mean node node-js nodejs normal statistics stats stdlib summary test two-sample welch
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Two-sample Student's t-Test.

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hypothesis javascript math mathematics mean node node-js nodejs normal statistics stats stdlib summary test two-sample welch
Created over 4 years ago · Last pushed 8 months ago
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README.md

About stdlib...

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.

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Student's t-Test

NPM version Build Status Coverage Status <!-- dependencies -->

Two-sample Student's t-Test.

## Installation ```bash npm install @stdlib/stats-ttest2 ``` 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 ttest2 = require( '@stdlib/stats-ttest2' ); ``` #### ttest2( x, y\[, opts] ) By default, the function performs a two-sample t-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. ```javascript // Student's sleep data: var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ]; var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ]; var out = ttest2( x, y ); /* e.g., returns { 'rejected': false, 'pValue': ~0.079, 'statistic': ~-1.861, 'ci': [ ~-3.365, ~0.205 ], // ... } */ ``` 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., => Welch two-sample t-test Alternative hypothesis: True difference in means is not equal to 0 pValue: 0.0794 statistic: -1.8608 95% confidence interval: [-3.3655,0.2055] 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`. - **variance**: `string` indicating if the test should be conducted under the assumption that the unknown variances of the normal distributions are `equal` or `unequal`. Default: `unequal`. 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 x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ]; var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ]; var out = ttest2( x, y, { 'alpha': 0.1 }); var table = out.print(); /* e.g., returns Welch two-sample t-test Alternative hypothesis: True difference in means is not equal to 0 pValue: 0.0794 statistic: -1.8608 90% confidence interval: [-3.0534,-0.1066] Test Decision: Reject null in favor of alternative at 10% 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 // Student's sleep data: var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ]; var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ]; var out = ttest2( x, y, { 'alternative': 'less' }); var table = out.print(); /* e.g., returns Welch two-sample t-test Alternative hypothesis: True difference in means is less than 0 pValue: 0.0397 statistic: -1.8608 df: 17.7765 95% confidence interval: [-Infinity,-0.1066] Test Decision: Reject null in favor of alternative at 5% significance level */ out = ttest2( x, y, { 'alternative': 'greater' }); table = out.print(); /* e.g., returns Welch two-sample t-test Alternative hypothesis: True difference in means is greater than 0 pValue: 0.9603 statistic: -1.8608 df: 17.7765 95% confidence interval: [-3.0534,Infinity] Test Decision: Fail to reject null in favor of alternative at 5% significance level */ ``` As a default choice, the `ttest2` function carries out the Welch test (using the Satterthwaite approximation for the degrees of freedom), which does not have the requirement that the variances of the underlying distributions are equal. If the equal variances assumption seems warranted, set the `variance` option to `equal`. ```javascript var x = [ 2, 3, 1, 4 ]; var y = [ 1, 2, 3, 1, 2, 5, 3, 4 ]; var out = ttest2( x, y, { 'variance': 'equal' }); var table = out.print(); /* e.g., returns Two-sample t-test Alternative hypothesis: True difference in means is not equal to 0 pValue: 0.8848 statistic: -0.1486 df: 10 95% confidence interval: [-1.9996,1.7496] 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 = []; var i; for ( i = 0; i < x.length; i++ ) { x.push( rnorm( 2.0, 3.0 ) ); } var y = []; for ( i = 0; i < x.length; i++ ) { y.push( rnorm( 1.0, 3.0 ) ); } var out = ttest2( x, y, { 'difference': 1.0, 'variance': 'equal' }); /* e.g., returns { 'rejected': false, 'pValue': ~0.642, 'statistic': ~-0.466, 'ci': [ ~-0.0455, ~1.646 ], // ... } */ var table = out.print(); /* e.g., returns Two-sample t-test Alternative hypothesis: True difference in means is not equal to 1 pValue: 0.6419 statistic: -0.4657 df: 198 95% confidence interval: [-0.0455,1.646] Test Decision: Fail to reject null in favor of alternative at 5% significance level */ ```
## Examples ```javascript var incrspace = require( '@stdlib/array-base-incrspace' ); var ttest2 = require( '@stdlib/stats-ttest2' ); var a = incrspace( 1, 11, 1 ); var b = incrspace( 7, 21, 1 ); var out = ttest2( a, b ); var table = out.print(); /* e.g., returns Welch two-sample t-test Alternative hypothesis: True difference in means is not equal to 0 pValue: 0 statistic: -5.4349 95% confidence interval: [-11.0528,-4.9472] Test Decision: Reject null in favor of alternative at 5% significance level */ ```
* * * ## See Also - [`@stdlib/stats-ttest`][@stdlib/stats/ttest]: one-sample and paired Student's t-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 © 2016-2025. 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
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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:
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  - 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-ttest2

Two-sample Student's t-Test.

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