feat: add stats/mannwhitneyu

lib/node_modules/@stdlib/stats/mannwhitneyu/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2018 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# Mann-Whitney U Test
+
+> Nonparametric hypothesis test comparing two independent samples.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var mannWhitneyU = require( '@stdlib/stats/mannwhitneyu' );
+```
+
+#### mannWhitneyU( x, y\[, options] )
+
+Given two independent samples x and y, the function computes the Mann–Whitney U rank-sum test to assess whether the distributions differ.
+
+```javascript
+var out = mannWhitneyU( [ 7, 8, 9 ], [ 1, 2, 3 ] );
+/* returns
+    {
+        'U': 0,
+        'pValue': 0.025,
+        'rejected': true
+    }
+*/
+
+out = mannWhitneyU( [ 10, 11, 10, 12 ], [ 9, 11, 10, 10 ] );
+/* returns
+    {
+        'U': 4.5,
+        'pValue': 0.312,
+        'rejected': false
+    }
+*/
+```
+
+<!-- run-disable -->
+
+The function accepts the following `options`:
+
+-   **alpha**: `number` in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`.
+-   **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.
+
+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.
+
+```javascript
+var out = mannWhitneyU( [ 7, 8, 9 ], [ 1, 2, 3 ], {
+    'alpha': 0.05,
+    'alternative': 'greater'
+});
+/* returns
+    {
+        'U': 0,
+        'pValue': 0.025,
+        'rejected': true
+    }
+*/
+```
+
+By default, a two-sided test is performed. To perform either of the one-sided tests, set the `alternative` option to `less` or `greater`.
+
+```javascript
+var out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
+    'alternative': 'greater',
+    'alpha': 0.05
+});
+/* returns
+    {
+        'U': 0,
+        'pValue': 0.0104,
+        'rejected': true
+    }
+*/
+
+out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
+    'alternative': 'less',
+    'alpha': 0.05
+});
+/* returns
+    {
+        'U': 0,
+        'pValue': 0.9896,
+        'rejected': false
+    }
+*/
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var mannWhitneyU = require( '@stdlib/stats/mannwhitneyu' );
+
+var x = [ 12, 15, 14, 10, 13 ];
+var y = [ 7, 9, 6, 8, 7 ];
+
+var out = mannWhitneyU( x, y );
+/* returns
+    {
+       'U': 0,
+       'pValue': 0.009,
+       'rejected': true
+    }
+*/
+
+out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ] );
+/* returns
+    {
+        'U': 0,
+        'pValue': 0.0208,
+        'rejected': true
+    }
+*/
+
+out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
+    'alternative': 'greater'
+});
+/* returns
+    {
+        'U': 0,
+        'pValue': 0.0104,
+        'rejected': true
+    }
+*/
+
+out = mannWhitneyU( [ 1, 2, 2, 3 ], [ 2, 3, 4, 5 ], {
+    'alternative': 'greater',
+    'alpha': 0.05
+});
+/* returns
+    {
+        'U': 2.5,
+        'pValue': 0.057,
+        'rejected': false
+    }
+*/
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var isObject = require( '@stdlib/assert/is-object' );
+var isString = require( '@stdlib/assert/is-string' ).isPrimitive;
+var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
+var pkg = require( './../package.json' ).name;
+var mannWhitneyU = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var result;
+	var x;
+	var y;
+	var i;
+
+	x = [];
+	y = [];
+	for ( i = 0; i < 100; i++ ) {
+		x.push( 0 );
+		y.push( 0 );
+	}
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		fillArray( x );
+		fillArray( y );
+		result = mannWhitneyU( x, y );
+		if ( typeof result !== 'object' ) {
+			b.fail( 'should return an object' );
+		}
+	}
+	b.toc();
+	if ( !isObject( result ) ) {
+		b.fail( 'should return an object' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::one-sided', function benchmark( b ) {
+	var result;
+	var opts;
+	var x;
+	var y;
+	var i;
+
+	opts = {
+		'alternative': 'greater'
+	};
+	x = [];
+	y = [];
+	for ( i = 0; i < 100; i++ ) {
+		x.push( 0 );
+		y.push( 0 );
+	}
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		fillArray( x );
+		fillArray( y );
+		result = mannWhitneyU( x, y, opts );
+		if ( typeof result !== 'object' ) {
+			b.fail( 'should return an object' );
+		}
+	}
+	b.toc();
+	if ( !isObject( result ) ) {
+		b.fail( 'should return an object' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+':print', function benchmark( b ) {
+	var digits;
+	var result;
+	var output;
+	var i;
+
+	result = mannWhitneyU( [ 7, 8, 9 ], [ 1, 2, 3 ] );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		digits = ( i % 8 ) + 1;
+		output = result.print({
+			'digits': digits
+		});
+		if ( typeof output !== 'string' ) {
+			b.fail( 'should return a string' );
+		}
+	}
+	b.toc();
+	if ( !isString( output ) ) {
+		b.fail( 'should return a string' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+
+// FUNCTIONS //
+
+function fillArray( arr ) {
+	var i;
+	for ( i = 0; i < arr.length; i++ ) {
+		arr[ i ] = discreteUniform( 0, 100 );
+	}
+}

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

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