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Two-sample F-test
Two-sample F-test for equal variances.
Installation
npm install @stdlib/stats-vartestUsage
var vartest = require( '@stdlib/stats-vartest' );vartest( x, y[, opts] )
By default, the function performs a two-sample F-test for the null hypothesis that the data in arrays or typed arrays x and y is independently drawn from normal distributions with equal variances.
var x = [ 610, 610, 550, 590, 565, 570 ];
var y = [ 560, 550, 580, 550, 560, 590, 550, 590 ];
var out = vartest( x, y );
/* returns
{
'rejected': false,
'pValue': ~0.399,
'statistic': ~1.976,
'ci': [ ~0.374, ~13.542 ],
// ...
}
*/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.
console.log( out.print() );
/* e.g., =>
F test for comparing two variances
Alternative hypothesis: True ratio in variances is not equal to 1
pValue: 0.3992
statistic: 1.976
variance of x: 617.5 (df of x: 5)
variance of y: 312.5 (df of y: 7)
95% confidence interval: [0.3739,13.5417]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/The function accepts the following options:
-
alpha:
numberin the interval[0,1]giving the significance level of the hypothesis test. Default:0.05. -
alternative: Either
two-sided,lessorgreater. Indicates whether the alternative hypothesis is that the true ratio of variances is greater than one (greater), smaller than one (less), or that the variances are the same (two-sided). Default:two-sided. -
ratio: positive
numberdenoting the ratio of the two population variances under the null hypothesis. Default:1.
By default, the hypothesis test is carried out at a significance level of 0.05. To choose a different significance level, set the alpha option.
var x = [ 610, 610, 550, 590, 565, 570, 500, 650, 500, 650 ];
var y = [ 560, 550, 580, 550, 560, 590, 550, 590 ];
var out = vartest( x, y, {
'alpha': 0.01
});
var table = out.print();
/* e.g., returns
F test for comparing two variances
Alternative hypothesis: True ratio in variances is not equal to 1
pValue: 0.0081
statistic: 9.1458
variance of x: 2858.0556 (df of x: 9)
variance of y: 312.5 (df of y: 7)
90% confidence interval: [2.4875,30.1147]
Test Decision: Reject null in favor of alternative at 1% significance level
Exited with status 0
*/By default, a two-sided test is performed. To perform either of the one-sided tests, set the alternative option to less or greater.
var x = [ 610, 610, 550, 590, 565, 570, 500, 650, 500, 650 ];
var y = [ 560, 550, 580, 550, 560, 590, 550, 590 ];
var out = vartest( x, y, {
'alternative': 'less'
});
var table = out.print();
/* e.g., returns
Alternative hypothesis: True ratio in variances is less than 1
pValue: 0.996
statistic: 9.1458
variance of x: 2858.0556 (df of x: 9)
variance of y: 312.5 (df of y: 7)
95% confidence interval: [0,30.1147]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
Exited with status 0
*/
out = vartest( x, y, {
'alternative': 'greater'
});
table = out.print();
/* e.g., returns
Alternative hypothesis: True ratio in variances is greater than 1
pValue: 0.004
statistic: 9.1458
variance of x: 2858.0556 (df of x: 9)
variance of y: 312.5 (df of y: 7)
95% confidence interval: [2.4875,Infinity]
Test Decision: Reject null in favor of alternative at 5% significance level
Exited with status 0
*/To test whether the ratio in the population variances is equal to some other value than 1, set the ratio option.
var x = [ 610, 610, 550, 590, 565, 570, 500, 650, 500, 650 ];
var y = [ 560, 550, 580, 550, 560, 590, 550, 590 ];
var out = vartest( x, y, {
'ratio': 10.0
});
/* e.g., returns
{
'rejected': false,
'pValue': ~0.879,
'statistic': ~-0.915,
'ci': [ ~1.896, ~38.385 ],
// ...
}
*/
var table = out.print();
/* e.g., returns
F test for comparing two variances
Alternative hypothesis: True ratio in variances is not equal to 10
pValue: 0.8794
statistic: 0.9146
variance of x: 2858.0556 (df of x: 9)
variance of y: 312.5 (df of y: 7)
95% confidence interval: [1.8962,38.3853]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/Examples
var rnorm = require( '@stdlib/random-base-normal' );
var vartest = require( '@stdlib/stats-vartest' );
var table;
var out;
var x;
var y;
var i;
x = new Array( 60 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = rnorm( 2.0, 1.0 );
}
y = new Array( 40 );
for ( i = 0; i < y.length; i++ ) {
y[ i ] = rnorm( 1.0, 2.0 );
}
// Test whether the variances of `x` and `y` are the same:
out = vartest( x, y );
table = out.print();
/* e.g., returns
F test for comparing two variances
Alternative hypothesis: True ratio in variances is not equal to 1
pValue: 0
statistic: 0.1717
variance of x: 0.6406 (df of x: 60)
variance of y: 3.7306 (df of y: 40)
95% confidence interval: [0.0953,0.2995]
Test Decision: Reject null in favor of alternative at 5% significance level
*/
// Test whether the variance of `x` is one fourth of the variance of `y`:
out = vartest( x, y, {
'ratio': 0.25
});
table = out.print();
/* e.g., returns
F test for comparing two variances
Alternative hypothesis: True ratio in variances is not equal to 0.25
pValue: 0.1847
statistic: 0.6869
variance of x: 0.6406 (df of x: 60)
variance of y: 3.7306 (df of y: 40)
95% confidence interval: [0.0953,0.2995]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/See Also
-
@stdlib/stats-bartlett-test: Bartlett’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.
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License
See LICENSE.
Copyright
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