feat: add stats/strided/ztest2

lib/node_modules/@stdlib/stats/strided/ztest2/README.md

@@ -0,0 +1,238 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+<!-- lint disable max-heading-length -->
+
+# ztest2
+
+> Compute a two-sample Z-test for a strided array.
+
+<section class="intro">
+
+A Z-test commonly refers to a two-sample location test which compares the means of two independent sets of measurements `X` and `Y` when the population standard deviations are known. A Z-test supports testing three different null hypotheses `H0`:
+
+-   `H0: μX - μY ≥ Δ` versus the alternative hypothesis `H1: μX - μY < Δ`.
+-   `H0: μX - μY ≤ Δ` versus the alternative hypothesis `H1: μX - μY > Δ`.
+-   `H0: μX - μY = Δ` versus the alternative hypothesis `H1: μX - μY ≠ Δ`.
+
+Here, `μX` and `μY` are the true population means of samples `X` and `Y`, respectively, and `Δ` is the hypothesized difference in means (typically `0` by default).
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var ztest2 = require( '@stdlib/stats/strided/ztest2' );
+```
+
+#### ztest2( NX, NY, alternative, alpha, diff, sigmax, sigmay, x, strideX, y, strideY, out )
+
+Computes a two-sample Z-test for a strided array.
+
+```javascript
+var Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+
+var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
+var y = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
+
+var results = new Results();
+var out = ztest2( x.length, y.length, 'two-sided', 0.05, 0.0, 1.0, 2.0, x, 1, y, 1, results );
+// returns {...}
+
+var bool = ( out === results );
+// returns true
+```
+
+The function has the following parameters:
+
+-   **NX**: number of indexed elements in `x`.
+-   **NY**: number of indexed elements in `y`.
+-   **alternative**: [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].
+-   **alpha**: significance level.
+-   **diff**: difference in means under the null hypothesis.
+-   **sigmax**: known standard deviation of `x`.
+-   **sigmay**: known standard deviation of `y`.
+-   **x**: input array.
+-   **strideX**: stride length for `x`.
+-   **y**: input array.
+-   **strideY**: stride length for `y`.
+-   **out**: output [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
+
+The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to perform a two-sample Z-test over every other element in `x` and `y`,
+
+```javascript
+var Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+
+var x = [ 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0, 0.0 ];
+var y = [ 3.0, 0.0, 3.0, 0.0, 5.0, 0.0, 7.0, 0.0, 7.0, 0.0 ];
+
+var results = new Results();
+var out = ztest2( 5, 5, 'two-sided', 0.05, 0.0, 1.0, 2.0, x, 2, y, 2, results );
+// returns {...}
+
+var bool = ( out === results );
+// returns true
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x0 = new Float64Array( [ 0.0, 4.0, 4.0, 6.0, 6.0, 5.0 ] );
+var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var y0 = new Float64Array( [ 0.0, 3.0, 3.0, 5.0, 7.0, 7.0 ] );
+var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var results = new Results();
+var out = ztest2( 5, 5, 'two-sided', 0.05, 0.0, 1.0, 2.0, x1, 1, y1, 1, results );
+// returns {...}
+
+var bool = ( out === results );
+// returns true
+```
+
+#### ztest2.ndarray( NX, NY, alternative, alpha, diff, sigmax, sigmay, x, strideX, offsetX, y, strideY, offsetY, out )
+
+Computes a two-sample Z-test for a strided array using alternative indexing semantics.
+
+```javascript
+var Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+
+var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
+var y = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
+
+var results = new Results();
+var out = ztest2.ndarray( x.length, y.length, 'two-sided', 0.05, 0.0, 1.0, 2.0, x, 1, 0, y, 1, 0, results );
+// returns {...}
+
+var bool = ( out === results );
+// returns true
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index for `x`.
+-   **offsetY**: starting index for `y`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to perform a two-sample Z-test over every other element in `x` and `y` starting from the second element
+
+```javascript
+var Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+
+var x = [ 0.0, 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0 ];
+var y = [ 0.0, 3.0, 0.0, 3.0, 0.0, 5.0, 0.0, 7.0, 0.0, 7.0 ];
+
+var results = new Results();
+var out = ztest2.ndarray( 5, 5, 'two-sided', 0.05, 0.0, 1.0, 2.0, x, 2, 1, y, 2, 1, results );
+// returns {...}
+
+var bool = ( out === results );
+// returns true
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   As a general rule of thumb, a Z-test is most reliable when `N >= 50`. For smaller sample sizes or when the standard deviation is unknown, prefer a t-test.
+-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
+-   Depending on the environment, the typed versions ([`dztest2`][@stdlib/stats/strided/dztest2], [`sztest2`][@stdlib/stats/strided/sztest2], etc.) are likely to be significantly more performant.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+var normal = require( '@stdlib/random/array/normal' );
+var ztest2 = require( '@stdlib/stats/strided/ztest2' );
+
+var x = normal( 1000, 4.0, 2.0, {
+    'dtype': 'generic'
+});
+var y = normal( 800, 3.0, 2.0, {
+    'dtype': 'generic'
+});
+
+var results = new Results();
+var out = ztest2( x.length, y.length, 'two-sided', 0.05, 1.0, 2.0, 2.0, x, 1, y, 1, results );
+// returns {...}
+
+console.log( out.toString() );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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">
+
+[variance]: https://en.wikipedia.org/wiki/Variance
+
+[@stdlib/stats/base/ztest/alternatives]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/ztest/alternatives
+
+[@stdlib/stats/base/ztest/two-sample/results/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/ztest/two-sample/results/float64
+
+[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
+
+[@stdlib/stats/strided/dztest2]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/strided/dztest
+
+[@stdlib/stats/strided/sztest2]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/strided/sztest
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/strided/ztest2/benchmark/benchmark.js

@@ -0,0 +1,104 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 normal = require( '@stdlib/random/array/normal' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+var pkg = require( './../package.json' ).name;
+var ztest2 = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var results;
+	var x;
+	var y;
+
+	results = new Results();
+	x = normal( len, 0.0, 1.0, options );
+	y = normal( len, 0.0, 1.0, options );
+
+	return benchmark;
+
+	function benchmark( b ) {
+		var out;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			out = ztest2( x.length, y.length, 'two-sided', 0.05, 0.0, 1.0, 1.0, x, 1, y, 1, results );
+			if ( isnan( out.statistic ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( out.statistic ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( pkg+':len='+len, f );
+	}
+}
+
+main();