Feature/sumithraju 17 spearman correlation

lib/node_modules/@stdlib/stats/spearman-test/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# Spearman Correlation Test
+
+> Compute a Spearman rank correlation test between paired samples.
+
+<section class="intro">
+
+The [Spearman rank correlation coefficient][spearman-correlation] is a non-parametric measure of rank correlation that assesses how well the relationship between two variables can be described using a monotonic function. Unlike the [Pearson correlation][pearson-correlation], which assesses linear relationships, the Spearman correlation assesses monotonic relationships (whether linear or not).
+
+For a sample of size `n`, the Spearman rank correlation coefficient is defined as the [Pearson correlation coefficient][pearson-correlation] between the rank variables.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var spearmanTest = require( '@stdlib/stats/spearman-test' );
+```
+
+#### spearmanTest( x, y\[, opts] )
+
+By default, the function performs a t-test for the null hypothesis that the paired data in [arrays][mdn-array] or [typed arrays][mdn-typed-array] `x` and `y` have a [Spearman correlation coefficient][spearman-correlation] of zero.
+
+```javascript
+var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
+var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
+
+var out = spearmanTest( x, y );
+/* e.g., returns
+    {
+        'alpha': 0.05,
+        'rejected': true,
+        'pValue': ~0.014,
+        'statistic': ~2.98,
+        'ci': [ ~0.162, ~0.95 ],
+        'nullValue': 0,
+        'scorr': ~0.745,
+        // ...
+    }
+*/
+```
+
+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.
+
+<!-- run-disable -->
+
+```javascript
+console.log( out.print() );
+/* e.g., =>
+    t-test for Spearman's rank correlation coefficient
+
+    Alternative hypothesis: True correlation coefficient is not equal to 0
+
+        pValue: 0.014
+        statistic: 2.9848
+        95% confidence interval: [0.1623,0.9504]
+
+    Test Decision: Reject null in favor of alternative at 5% significance level
+*/
+```
+
+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 whether the alternative hypothesis is that `x` has a larger (or smaller) Spearman rank correlation with `y` than `rho` (`two-sided`), that `x` has a larger rank correlation than `rho` (`greater`) or a smaller rank correlation than `rho` (`less`). Default: `two-sided`.
+-   **rho**: `number` denoting the correlation under the null hypothesis. Default: `0`.
+
+By default, a two-sided test is performed. To perform either of the one-sided tests, set the `alternative` option.
+
+```javascript
+var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
+var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
+
+var out = spearmanTest( x, y, {
+    'alternative': 'less'
+});
+/* e.g., returns
+    {
+        'alpha': 0.05,
+        'rejected': false,
+        'pValue': ~0.993,
+        // ...
+    }
+*/
+
+out = spearmanTest( x, y, {
+    'alternative': 'greater'
+});
+/* e.g., returns
+    {
+        'alpha': 0.05,
+        'rejected': true,
+        'pValue': ~0.007,
+        // ...
+    }
+*/
+```
+
+By default, the null hypothesis is that the correlation coefficient is `0`. To test against a different value, set the `rho` option.
+
+```javascript
+var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
+var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
+
+var out = spearmanTest( x, y, {
+    'rho': 0.8
+});
+```
+
+To change the significance level, set the `alpha` option.
+
+```javascript
+var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
+var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
+
+var out = spearmanTest( x, y, {
+    'alpha': 0.01
+});
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var rnorm = require( '@stdlib/random/base/normal' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var spearmanTest = require( '@stdlib/stats/spearman-test' );
+
+var table;
+var out;
+var rho;
+var x;
+var y;
+var i;
+
+rho = 0.5;
+x = [];
+y = [];
+for ( i = 0; i < 300; i++ ) {
+    x.push( rnorm( 0.0, 1.0 ) );
+    y.push( ( rho * x[ i ] ) + rnorm( 0.0, sqrt( 1.0 - (rho*rho) ) ) );
+}
+
+out = spearmanTest( x, y );
+table = out.print();
+console.log( table );
+
+out = spearmanTest( x, y, {
+    'rho': 0.5
+});
+table = out.print();
+console.log( table );
+```
+
+</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">
+
+[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays
+
+[spearman-correlation]: https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient
+
+[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/spearman-test/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 rnorm = require( '@stdlib/random/base/normal' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var pkg = require( './../package.json' ).name;
+var spearmanTest = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var result;
+	var rho;
+	var idx;
+	var y;
+	var x;
+	var i;
+
+	rho = 0.5;
+	x = [];
+	y = [];
+	for ( i = 0; i < 300; i++ ) {
+		x.push( rnorm( 0.0, 1.0 ) );
+		y.push( ( rho * x[ i ] ) + rnorm( 0.0, sqrt( 1.0 - (rho*rho) ) ) );
+	}
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		idx = i % x.length;
+		y[ idx ] = ( rho * x[ i ] ) + rnorm( 0.0, sqrt( 1.0 - (rho*rho) ) );
+		result = spearmanTest( 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 rho;
+	var idx;
+	var y;
+	var x;
+	var i;
+
+	rho = 0.5;
+	x = [];
+	y = [];
+	for ( i = 0; i < 300; i++ ) {
+		x.push( rnorm( 0.0, 1.0 ) );
+		y.push( ( rho * x[ i ] ) + rnorm( 0.0, sqrt( 1.0 - (rho*rho) ) ) );
+	}
+	opts = {
+		'alternative': 'less'
+	};
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		idx = i % x.length;
+		y[ idx ] = ( rho * x[ i ] ) + rnorm( 0.0, sqrt( 1.0 - (rho*rho) ) );
+		result = spearmanTest( 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 rho;
+	var y;
+	var x;
+	var i;
+
+	rho = 0.5;
+	x = [];
+	y = [];
+	for ( i = 0; i < 300; i++ ) {
+		x.push( rnorm( 0.0, 1.0 ) );
+		y.push( ( rho * x[ i ] ) + rnorm( 0.0, sqrt( 1.0 - (rho*rho) ) ) );
+	}
+	result = spearmanTest( x, y );
+
+	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();
+});