https://github.com/stdlib-js/stats-incr-grubbs

Grubbs' test for outliers.
https://github.com/stdlib-js/stats-incr-grubbs

deviate esd extreme grubbs hypothesis hypothesis-test javascript math mathematics maximum node node-js nodejs normalized residual statistics stats stdlib studentized test

Last synced: 24 days ago
JSON representation

Grubbs' test for outliers.

Host: GitHub
URL: https://github.com/stdlib-js/stats-incr-grubbs
Owner: stdlib-js
License: apache-2.0
Created: 2021-06-15T17:47:27.000Z (over 4 years ago)
Default Branch: main
Last Pushed: 2026-02-08T16:44:26.000Z (about 1 month ago)
Last Synced: 2026-02-08T22:32:45.445Z (about 1 month ago)
Topics: deviate, esd, extreme, grubbs, hypothesis, hypothesis-test, javascript, math, mathematics, maximum, node, node-js, nodejs, normalized, residual, statistics, stats, stdlib, studentized, test
Language: JavaScript
Homepage: https://github.com/stdlib-js/stdlib
Size: 6.07 MB
Stars: 6
Watchers: 2
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
- Notice: NOTICE

Awesome Lists containing this project

README

          

  

    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.

  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!


# incrgrubbs

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 

> [Grubbs' test][grubbs-test] for outliers.

[Grubbs' test][grubbs-test] (also known as the **maximum normalized residual test** or **extreme studentized deviate test**) is a statistical test used to detect outliers in a univariate dataset assumed to come from a normally distributed population. [Grubbs' test][grubbs-test] is defined for the hypothesis:

-   **H_0**: the dataset does **not** contain outliers.

-   **H_1**: the dataset contains **exactly** one outlier.

The [Grubbs' test][grubbs-test] statistic for a two-sided alternative hypothesis is defined as

```math

G = \frac{\max_{i=0,\ldots,N-1} |Y_i - \bar{Y}|}{s}

```

where `s` is the sample standard deviation. The [Grubbs test][grubbs-test] statistic is thus the largest absolute deviation from the sample mean in units of the sample standard deviation.

The [Grubbs' test][grubbs-test] statistic for the alternative hypothesis that the minimum value is an outlier is defined as

```math

G = \frac{\bar{Y} - Y_{\textrm{min}}}{s}

```

The [Grubbs' test][grubbs-test] statistic for the alternative hypothesis that the maximum value is an outlier is defined as

```math

G = \frac{Y_{\textrm{max}} - \bar{Y}}{s}

```

For a two-sided test, the hypothesis that a dataset does **not** contain an outlier is rejected at significance level α if

```math

G > \frac{N-1}{\sqrt{N}} \sqrt{\frac{t^2_{\alpha/(2N),N-2}}{N - 2 + t^2_{\alpha/(2N),N-2}}}

```

where `t` denotes the upper critical value of the _t_-distribution with `N-2` degrees of freedom and a significance level of `α/(2N)`.

For a one-sided test, the hypothesis that a dataset does **not** contain an outlier is rejected at significance level α if

```math

G > \frac{N-1}{\sqrt{N}} \sqrt{\frac{t^2_{\alpha/N,N-2}}{N - 2 + t^2_{\alpha/N,N-2}}}

```

where `t` denotes the upper critical value of the _t_-distribution with `N-2` degrees of freedom and a significance level of `α/N`.

## Installation

```bash

npm install @stdlib/stats-incr-grubbs

```

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 incrgrubbs = require( '@stdlib/stats-incr-grubbs' );

```

#### incrgrubbs( \[options] )

Returns an accumulator `function` which incrementally performs [Grubbs' test][grubbs-test] for outliers.

```javascript

var accumulator = incrgrubbs();

```

The function accepts the following `options`:

-   **alpha**: significance level. Default: `0.05`.

-   **alternative**: alternative hypothesis. The option may be one of the following values:

    -   `'two-sided'`: test whether the minimum or maximum value is an outlier.

    -   `'min'`: test whether the minimum value is an outlier.

    -   `'max'`: test whether the maximum value is an outlier.

    Default: `'two-sided'`.

-   **init**: number of data points the accumulator should use to compute initial statistics **before** testing for an outlier. Until the accumulator is provided the number of data points specified by this option, the accumulator returns `null`. Default: `100`.

#### accumulator( \[x] )

If provided an input value `x`, the accumulator function returns updated test results. If not provided an input value `x`, the accumulator function returns the current test results.

```javascript

var rnorm = require( '@stdlib/random-base-normal' );

var opts = {

    'init': 0

};

var accumulator = incrgrubbs( opts );

var results = accumulator( rnorm( 10.0, 5.0 ) );

// returns null

results = accumulator( rnorm( 10.0, 5.0 ) );

// returns null

results = accumulator( rnorm( 10.0, 5.0 ) );

// returns 

results = accumulator();

// returns 

```

The accumulator function returns an `object` having the following fields:

-   **rejected**: boolean indicating whether the null hypothesis should be rejected.

-   **alpha**: significance level.

-   **criticalValue**: critical value.

-   **statistic**: test statistic.

-   **df**: degrees of freedom.

-   **mean**: sample mean.

-   **sd**: corrected sample standard deviation.

-   **min**: minimum value.

-   **max**: maximum value.

-   **alt**: alternative hypothesis.

-   **method**: method name.

-   **print**: method for pretty-printing test output.

The `print` method accepts the following options:

-   **digits**: number of digits after the decimal point. Default: `4`.

-   **decision**: `boolean` indicating whether to print the test decision. Default: `true`.

## Notes

-   [Grubbs' test][grubbs-test] **assumes** that data is normally distributed. Accordingly, one should first **verify** that the data can be _reasonably_ approximated by a normal distribution before applying the [Grubbs' test][grubbs-test].

-   The accumulator must be provided **at least** three data points before performing [Grubbs' test][grubbs-test]. Until at least three data points are provided, the accumulator returns `null`.

-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the test statistic is `NaN` for **all** future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.

## Examples

```javascript

var incrgrubbs = require( '@stdlib/stats-incr-grubbs' );

var data;

var opts;

var acc;

var i;

// Define a data set (8 mass spectrometer measurements of a uranium isotope; see Tietjen and Moore. 1972. "Some Grubbs-Type Statistics for the Detection of Several Outliers".)

data = [ 199.31, 199.53, 200.19, 200.82, 201.92, 201.95, 202.18, 245.57 ];

// Create a new accumulator:

opts = {

    'init': data.length,

    'alternative': 'two-sided'

};

acc = incrgrubbs( opts );

// Update the accumulator:

for ( i = 0; i < data.length; i++ ) {

    acc( data[ i ] );

}

// Print the test results:

console.log( acc().print() );

/* e.g., =>

Grubbs' Test

Alternative hypothesis: The maximum value (245.57) is an outlier

    criticalValue: 2.1266

    statistic: 2.4688

    df: 6

Test Decision: Reject null in favor of alternative at 5% significance level

*/

```

* * *

## References

-   Grubbs, Frank E. 1950. "Sample Criteria for Testing Outlying Observations." _The Annals of Mathematical Statistics_ 21 (1). The Institute of Mathematical Statistics: 27–58. doi:[10.1214/aoms/1177729885][@grubbs:1950a].

-   Grubbs, Frank E. 1969. "Procedures for Detecting Outlying Observations in Samples." _Technometrics_ 11 (1). Taylor & Francis: 1–21. doi:[10.1080/00401706.1969.10490657][@grubbs:1969a].

* * *

## See Also

-   [`@stdlib/stats-incr/mgrubbs`][@stdlib/stats/incr/mgrubbs]: moving Grubbs' test for outliers.

* * *

## 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 © 2016-2026. The Stdlib [Authors][stdlib-authors].

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-incr-grubbs.svg

[npm-url]: https://npmjs.org/package/@stdlib/stats-incr-grubbs

[test-image]: https://github.com/stdlib-js/stats-incr-grubbs/actions/workflows/test.yml/badge.svg?branch=v0.2.3

[test-url]: https://github.com/stdlib-js/stats-incr-grubbs/actions/workflows/test.yml?query=branch:v0.2.3

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-incr-grubbs/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/stats-incr-grubbs?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg

[chat-url]: https://stdlib.zulipchat.com

[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-incr-grubbs/tree/deno

[deno-readme]: https://github.com/stdlib-js/stats-incr-grubbs/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/stats-incr-grubbs/tree/umd

[umd-readme]: https://github.com/stdlib-js/stats-incr-grubbs/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/stats-incr-grubbs/tree/esm

[esm-readme]: https://github.com/stdlib-js/stats-incr-grubbs/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/stats-incr-grubbs/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-grubbs/main/LICENSE

[grubbs-test]: https://en.wikipedia.org/wiki/Grubbs%27_test_for_outliers

[@grubbs:1950a]: https://doi.org/10.1214/aoms/1177729885

[@grubbs:1969a]: https://doi.org/10.1080/00401706.1969.10490657

[@stdlib/stats/incr/mgrubbs]: https://github.com/stdlib-js/stats-incr-mgrubbs

ecosyste.ms

Data

Tools

Indexes

Applications

Experiments

Awesome

https://github.com/stdlib-js/stats-incr-grubbs

Awesome Lists containing this project

README