time-to-botec/js/node_modules/@stdlib/stats/fligner-test/README.md

<!--

@license Apache-2.0

Copyright (c) 2018 The Stdlib Authors.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

-->

# flignerTest

> Compute the Fligner-Killeen test for equal variances.

<section class="intro">

</section>

<!-- /.intro -->

<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'
];
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 class="links">

</section>

<!-- /.links -->