# flignerTest

Compute the Fligner-Killeen test for equal variances.

## Usage

``````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.

``````// 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.

``````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.

``````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.

``````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
*/
``````

## Examples

``````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
*/
``````