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, wellwritten, studied, documented, tested, measured, and highquality 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!
bartlettTest
Compute Bartlett’s test for equal variances.
Bartlett's test is used to test the null hypothesis that the variances of k groups are equal against the alternative that at least two of them are different.
For k
groups each with n_i
observations, the test statistic is
where N
is the total number of observations, S_i
are the biased grouplevel variances and S^2
is a (biased) pooled estimate for the variance. Under the null hypothesis, the test statistic follows a chisquare distribution with df = k  1
degrees of freedom.
Installation
npm install @stdlib/statsbartletttest
Usage
var bartlettTest = require( '@stdlib/statsbartletttest' );
bartlettTest( a[,b,...,k][, opts] )
For input arrays a
, b
, ... holding numeric observations, this function calculates Bartlett’s 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 = bartlettTest( x, y, z );
/* returns
{
'rejected': false,
'alpha': 0.05,
'df': 2,
'pValue': ~0.573,
'statistic': ~1.112,
...
}
*/
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 = bartlettTest( x, y, z, {
'alpha': 0.01
});
/* returns
{
'rejected': false,
'alpha': 0.01,
'df': 2,
'pValue': ~0.573,
'statistic': ~1.112,
...
}
*/
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'
];
var out = bartlettTest( 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 = bartlettTest( x, y, z );
console.log( out.print() );
/* =>
Bartlett's test of equal variances
Null hypothesis: The variances in all groups are the same.
pValue: 0.5735
statistic: 1.1122
df: 2
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
Examples
var bartlettTest = require( '@stdlib/statsbartletttest' );
// 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 = bartlettTest( x, y, z );
/* returns
{
'rejected': false,
'alpha': 0.05,
'df': 2,
'pValue': ~0.573,
'statistic': ~1.112,
...
}
*/
var table = out.print();
/* returns
Bartlett's test of equal variances
Null hypothesis: The variances in all groups are the same.
pValue: 0.5735
statistic: 1.1122
df: 2
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
See Also

@stdlib/statsvartest
: twosample Ftest for equal variances 
@stdlib/statslevenetest
: Levene's test for equal variances.
Notice
This package is part of 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, see the main project repository.
Community
License
See LICENSE.
Copyright
Copyright © 20162024. The Stdlib Authors.