npm package: @stdlib/stats-fligner-test
Description: Fligner-Killeen test for equal variances.
Author: The Stdlib Authors
Latest version: 0.2.3

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# flignerTest

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> Compute the Fligner-Killeen test for equal variances.

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-fligner-test
```

</section>

<section class="usage">

## Usage

```javascript
var flignerTest = require( '@stdlib/stats-fligner-test' );
```

#### flignerTest( a\[,b,...,k]\[, opts] )

For input arrays `a`, `b`, ... holding numeric observations, this function calculates the Fligner-Killeen test, which tests the null hypothesis that the variances in all `k` groups are the same.

```javascript
// Data from Hollander & Wolfe (1973), p. 116:
var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
var y = [ 3.8, 2.7, 4.0, 2.4 ];
var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];

var out = flignerTest( x, y, z );
/* returns
    {
        'rejected': false,
        'alpha': 0.05,
        'df': 2,
        'pValue': ~0.074,
        'statistic': ~5.209,
        ...
    }
*/
```

The function accepts the following `options`:

-   **alpha**: `number` in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`.
-   **groups**: an `array` of group indicators. If set, the function assumes that only a single numeric array is provided holding all observations.

By default, the test is carried out at a significance level of `0.05`. To choose a custom significance level, set the `alpha` option.

```javascript
var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
var y = [ 3.8, 2.7, 4.0, 2.4 ];
var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];

var out = flignerTest( x, y, z, {
    'alpha': 0.1
});
/* returns
    {
        'rejected': true,
        'alpha': 0.1,
        'df': 2,
        'pValue': ~0.074,
        'statistic': ~5.209,
        ...
    }
*/
```

The 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.

<!-- eslint-disable array-element-newline -->

```javascript
var arr = [
    2.9, 3.0, 2.5, 2.6, 3.2,
    3.8, 2.7, 4.0, 2.4,
    2.8, 3.4, 3.7, 2.2, 2.0
];
var groups = [
    'a', 'a', 'a', 'a', 'a',
    'b', 'b', 'b', 'b',
    'c', 'c', 'c', 'c', 'c'
];
var out = flignerTest( arr, {
    'groups': groups
});
```

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
var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
var y = [ 3.8, 2.7, 4.0, 2.4 ];
var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];

var out = flignerTest( x, y, z );
console.log( out.print() );
/* =>
    Fligner-Killeen test of homogeneity of variances

    Null hypothesis: The variances in all groups are the same.

        pValue: 0.0739
        statistic: 5.2092
        df: 2

    Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var flignerTest = require( '@stdlib/stats-fligner-test' );

// Data from Hollander & Wolfe (1973), p. 116:
var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
var y = [ 3.8, 2.7, 4.0, 2.4 ];
var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];

var out = flignerTest( x, y, z );
/* returns
    {
        'rejected': false,
        'alpha': 0.05,
        'df': 2,
        'pValue': ~0.074,
        'statistic': ~5.209,
        ...
    }
*/

var table = out.print();
/* returns
    Fligner-Killeen test of homogeneity of variances

    Null hypothesis: The variances in all groups are the same.

        pValue: 0.0739
        statistic: 5.2092
        df: 2

    Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
```

</section>

<!-- /.examples -->

<section class="references">

</section>

<!-- /.references -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/stats-bartlett-test`][@stdlib/stats/bartlett-test]</span><span class="delimiter">: </span><span class="description">Bartlett’s test for equal variances.</span>

</section>

<!-- /.related -->

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* * *

## 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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</section>

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