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feat(stats/mannwhitneyu): add Mann–Whitney U test package
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‎lib/node_modules/@stdlib/stats/mannwhitneyu/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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# Mann-Whitney U Test
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> Nonparametric hypothesis test comparing two independent samples.
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<section class="usage">
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## Usage
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```javascript
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var mannWhitneyU = require( '@stdlib/stats/mannwhitneyu' );
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```
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#### mannWhitneyU( x, y\[, options] )
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Given two independent samples x and y, the function computes the Mann–Whitney U rank-sum test to assess whether the distributions differ.
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```javascript
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var out = mannWhitneyU( [ 7, 8, 9 ], [ 1, 2, 3 ] );
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/* returns
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{
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'U': 0,
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'pValue': 0.025,
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'rejected': true
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}
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*/
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out = mannWhitneyU( [ 10, 11, 10, 12 ], [ 9, 11, 10, 10 ] );
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/* returns
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{
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'U': 4.5,
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'pValue': 0.312,
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'rejected': false
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}
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*/
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```
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<!-- run-disable -->
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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 the direction of the hypothesis test. `'greater'` tests whether values in `x` tend to be larger than those in `y`, `'less'` tests whether values in `x` tend to be smaller than those in `y`, and `'two-sided'` tests for any difference in distributions.
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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 out = mannWhitneyU( [ 7, 8, 9 ], [ 1, 2, 3 ], {
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'alpha': 0.05,
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'alternative': 'greater'
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});
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/* returns
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{
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'U': 0,
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'pValue': 0.025,
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'rejected': true
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}
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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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out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
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'alternative': 'greater',
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'alpha': 0.05
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});
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/* returns
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{
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'U': 0,
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'pValue': 0.0104,
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'rejected': true
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}
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*/
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out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
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'alternative': 'less',
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'alpha': 0.05
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});
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/* returns
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{
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'U': 0,
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'pValue': 0.9896,
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'rejected': false
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}
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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 mannWhitneyU = require( '@stdlib/stats/mannwhitneyu' );
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var x = [ 12, 15, 14, 10, 13 ];
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var y = [ 7, 9, 6, 8, 7 ];
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var out = mannWhitneyU( x, y );
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/* returns
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{
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'U': 0,
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'pValue': 0.009,
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'rejected': true
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}
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*/
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out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ] );
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/* returns
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{
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'U': 0,
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'pValue': 0.0208,
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'rejected': true
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}
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*/
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out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
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'alternative': 'greater'
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});
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/* returns
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{
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'U': 0,
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'pValue': 0.0104,
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'rejected': true
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}
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*/
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out = mannWhitneyU( [ 1, 2, 2, 3 ], [ 2, 3, 4, 5 ], {
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'alternative': 'greater',
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'alpha': 0.05
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});
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/* returns
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{
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'U': 2.5,
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'pValue': 0.057,
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'rejected': false
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}
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*/
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/mannwhitneyu/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 isObject = require( '@stdlib/assert/is-object' );
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var isString = require( '@stdlib/assert/is-string' ).isPrimitive;
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var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
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var pkg = require( './../package.json' ).name;
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var mannWhitneyU = 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 x;
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var y;
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var i;
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x = [];
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y = [];
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for ( i = 0; i < 100; i++ ) {
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x.push( 0 );
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y.push( 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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fillArray( x );
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fillArray( y );
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result = mannWhitneyU( 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 x;
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var y;
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var i;
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opts = {
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'alternative': 'greater'
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};
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x = [];
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y = [];
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for ( i = 0; i < 100; i++ ) {
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x.push( 0 );
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y.push( 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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fillArray( x );
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fillArray( y );
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result = mannWhitneyU( 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 digits;
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var result;
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var output;
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var i;
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result = mannWhitneyU( [ 7, 8, 9 ], [ 1, 2, 3 ] );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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digits = ( i % 8 ) + 1;
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output = result.print({
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'digits': digits
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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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// FUNCTIONS //
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function fillArray( arr ) {
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var i;
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for ( i = 0; i < arr.length; i++ ) {
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arr[ i ] = discreteUniform( 0, 100 );
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}
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}

‎lib/node_modules/@stdlib/stats/mannwhitneyu/docs/repl.txt‎

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{{alias}}( x, y[, options] )
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Computes the Mann–Whitney U rank-sum test for the difference between two
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independent samples.
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The returned object comes with a `.print()` method which when invoked will
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print a formatted output of the results of the hypothesis test.
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Parameters
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----------
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x: Array<number>
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First independent sample.
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y: Array<number>
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Second independent sample.
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options: Object (optional)
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Options.
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options.alpha: number (optional)
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Number in the interval `[0,1]` giving the significance level of the
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hypothesis test. Default: `0.05`.
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options.alternative: string (optional)
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Indicates whether the alternative hypothesis is that the distribution of
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`x` is shifted to the right of `y` (`greater`), to the left of `y`
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(`less`) or that they differ (`two-sided`). Default: `'two-sided'`.
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Returns
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-------
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out: Object
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Test result object.
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out.alpha: number
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Used significance level.
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out.rejected: boolean
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Test decision.
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out.pValue: number
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p-value of the test.
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out.U: number
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Mann–Whitney U statistic.
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out.U1: number
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U value for sample `x`.
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out.U2: number
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U value for sample `y`.
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out.alternative: string
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Alternative hypothesis (`two-sided`, `less` or `greater`).
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out.method: string
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Name of the test.
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out.print: Function
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Function to print formatted output.
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Examples
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--------
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> var out = {{alias}}( [ 7, 8, 9 ], [ 1, 2, 3 ] )
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{ 'U': 0, 'pValue': ~0.025, ... }
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> out = {{alias}}( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
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... 'alternative': 'greater'
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... })
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{ 'U': 0, 'pValue': ~0.0104, ... }
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> out = {{alias}}( [ 1, 2, 2, 3 ], [ 2, 3, 4, 5 ], {
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... 'alternative': 'greater',
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... 'alpha': 0.05
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... })
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{ 'U': 2.5, 'pValue': ~0.057, ... }
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See Also
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--------

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