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Add two-sample variance test
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‎lib/node_modules/@stdlib/stats/vartest/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Two-sample F-test
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> Two-sample F-test for equal variances.
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<section class="usage">
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## Usage
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```javascript
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var vartest = require( '@stdlib/stats/vartest' );
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```
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#### vartest( x, y\[, opts] )
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By default, the function performs a two-sample F-test for the null hypothesis that the data in [arrays][mdn-array] or [typed arrays][mdn-typed-array] `x` and `y` is independently drawn from normal distributions with _equal_ variances.
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```javascript
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var x = [ 610, 610, 550, 590, 565, 570 ];
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var y = [ 560, 550, 580, 550, 560, 590, 550, 590 ];
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var out = vartest( x, y );
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/* returns
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{
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'rejected': false,
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'pValue': ~0.399,
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'statistic': ~1.976,
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'ci': [ ~0.374, ~13.542 ],
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// ...
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}
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*/
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```
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The returned object comes with a `.print()` method which when invoked will print a formatted output of the results of the hypothesis test.
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<!-- run-disable -->
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```javascript
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console.log( out.print() );
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/* e.g., =>
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F test for comparing two variances
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Alternative hypothesis: True ratio in variances is not equal to 1
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pValue: 0.3992
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statistic: 1.976
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variance of x: 617.5 (df of x: 5)
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variance of y: 312.5 (df of y: 7)
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95% confidence interval: [0.3739,13.5417]
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Test Decision: Fail to reject null in favor of alternative at 5% significance level
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*/
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```
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The function accepts the following `options`:
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- **alpha**: `number` in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`.
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- **alternative**: Either `two-sided`, `less` or `greater`. 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`.
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- **difference**: `number` denoting the difference in means under the null hypothesis. Default: `0`.
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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.
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```javascript
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var x = [ 610, 610, 550, 590, 565, 570, 500, 650, 500, 650 ];
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var y = [ 560, 550, 580, 550, 560, 590, 550, 590 ];
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var out = vartest( x, y, {
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'alpha': 0.01
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});
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var table = out.print();
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/* e.g., returns
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F test for comparing two variances
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Alternative hypothesis: True ratio in variances is not equal to 1
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pValue: 0.0081
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statistic: 9.1458
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variance of x: 2858.0556 (df of x: 9)
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variance of y: 312.5 (df of y: 7)
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90% confidence interval: [2.4875,30.1147]
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Test Decision: Reject null in favor of alternative at 1% significance level
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Exited with status 0
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*/
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```
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By default, a two-sided test is performed. To perform either of the one-sided tests, set the `alternative` option to `less` or `greater`.
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```javascript
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var x = [ 610, 610, 550, 590, 565, 570, 500, 650, 500, 650 ];
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var y = [ 560, 550, 580, 550, 560, 590, 550, 590 ];
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var out = vartest( x, y, {
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'alternative': 'less'
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});
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var table = out.print();
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/* e.g., returns
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Alternative hypothesis: True ratio in variances is less than 1
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pValue: 0.996
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statistic: 9.1458
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variance of x: 2858.0556 (df of x: 9)
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variance of y: 312.5 (df of y: 7)
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95% confidence interval: [0,30.1147]
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Test Decision: Fail to reject null in favor of alternative at 5% significance level
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Exited with status 0
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*/
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out = vartest( x, y, {
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'alternative': 'greater'
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});
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table = out.print();
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/* e.g., returns
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Alternative hypothesis: True ratio in variances is greater than 1
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pValue: 0.004
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statistic: 9.1458
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variance of x: 2858.0556 (df of x: 9)
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variance of y: 312.5 (df of y: 7)
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95% confidence interval: [2.4875,Infinity]
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Test Decision: Reject null in favor of alternative at 5% significance level
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Exited with status 0
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*/
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```
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To test whether the ratio in the population variances is equal to some other value than `1`, set the `ratio` option.
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```javascript
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var x = [ 610, 610, 550, 590, 565, 570, 500, 650, 500, 650 ];
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var y = [ 560, 550, 580, 550, 560, 590, 550, 590 ];
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var out = vartest( x, y, {
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'ratio': 10.0
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});
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/* e.g., returns
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{
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'rejected': false,
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'pValue': ~0.879,
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'statistic': ~-0.915,
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'ci': [ ~1.896, ~38.385 ],
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// ...
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}
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*/
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var table = out.print();
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/* e.g., returns
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F test for comparing two variances
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Alternative hypothesis: True ratio in variances is not equal to 10
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pValue: 0.8794
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statistic: 0.9146
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variance of x: 2858.0556 (df of x: 9)
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variance of y: 312.5 (df of y: 7)
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95% confidence interval: [1.8962,38.3853]
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Test Decision: Fail to reject null in favor of alternative at 5% significance level
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*/
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var rnorm = require( '@stdlib/random/base/normal' );
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var vartest = require( '@stdlib/stats/vartest' );
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var table;
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var out;
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var x;
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var y;
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var i;
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x = new Array( 60 );
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for ( i = 0; i < x.length; i++ ) {
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x[ i ] = rnorm( 2.0, 1.0 );
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}
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y = new Array( 40 );
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for ( i = 0; i < y.length; i++ ) {
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y[ i ] = rnorm( 1.0, 2.0 );
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}
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// Test whether the variances of `x` and `y` are the same:
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out = vartest( x, y );
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table = out.print();
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/* e.g., returns
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F test for comparing two variances
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Alternative hypothesis: True ratio in variances is not equal to 1
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pValue: 0
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statistic: 0.1717
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variance of x: 0.6406 (df of x: 60)
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variance of y: 3.7306 (df of y: 40)
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95% confidence interval: [0.0953,0.2995]
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Test Decision: Reject null in favor of alternative at 5% significance level
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*/
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// Test whether the variance of `x` is one fourth of the variance of `y`:
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out = vartest( x, y, {
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'ratio': 0.25
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});
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table = out.print();
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/* e.g., returns
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F test for comparing two variances
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Alternative hypothesis: True ratio in variances is not equal to 0.25
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pValue: 0.1847
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statistic: 0.6869
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variance of x: 0.6406 (df of x: 60)
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variance of y: 3.7306 (df of y: 40)
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95% confidence interval: [0.0953,0.2995]
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Test Decision: Fail to reject null in favor of alternative at 5% significance level
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*/
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/vartest/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/base/randu' );
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var isObject = require( '@stdlib/assert/is-object' );
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var isString = require( '@stdlib/assert/is-string' ).isPrimitive;
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var pkg = require( './../package.json' ).name;
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var vartest = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var result;
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var y;
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var x;
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var i;
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x = new Array( 100 );
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for ( i = 0; i < x.length; i++ ) {
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x[ i ] = ( randu()*2.0 ) + 1.0;
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}
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y = new Array( 120 );
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for ( i = 0; i < y.length; i++ ) {
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y[ i ] = ( randu()*4.0 ) + 1.0;
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}
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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x[ i % x.length ] = randu()*2.0;
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result = vartest( x, y );
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if ( typeof result !== 'object' ) {
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b.fail( 'should return an object' );
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}
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}
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b.toc();
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if ( !isObject( result ) ) {
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b.fail( 'should return an object' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::one-sided', function benchmark( b ) {
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var result;
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var opts;
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var y;
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var x;
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var i;
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x = new Array( 100 );
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for ( i = 0; i < x.length; i++ ) {
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x[ i ] = ( randu()*2.0 ) + 1.0;
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}
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y = new Array( 120 );
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for ( i = 0; i < y.length; i++ ) {
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y[ i ] = ( randu()*2.0 ) + 1.0;
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}
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opts = {
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'alternative': 'less'
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};
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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x[ i % x.length ] = randu()*2.0;
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result = vartest( x, y, opts );
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if ( typeof result !== 'object' ) {
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b.fail( 'should return an object' );
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}
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}
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b.toc();
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if ( !isObject( result ) ) {
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b.fail( 'should return an object' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+':print', function benchmark( b ) {
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var numdigits;
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var result;
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var output;
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var y;
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var x;
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var i;
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x = new Array( 100 );
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for ( i = 0; i < x.length; i++ ) {
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x[ i ] = ( randu()*2.0 ) + 1.0;
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}
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y = new Array( 120 );
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for ( i = 0; i < y.length; i++ ) {
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y[ i ] = ( randu()*2.0 ) + 1.0;
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}
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result = vartest( x, y );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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numdigits = ( i % 8 ) + 1;
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output = result.print({
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'numdigits': numdigits
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});
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if ( typeof output !== 'string' ) {
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b.fail( 'should return a string' );
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}
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}
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b.toc();
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if ( !isString( output ) ) {
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b.fail( 'should return a string' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

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