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feat: add stats/base/ndarray/ztest2
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‎lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2025 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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# ztest2
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> Compute a two-sample Z-test for two one-dimensional ndarrays.
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<section class="intro">
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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`:
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- `H0: μX - μY ≥ Δ` versus the alternative hypothesis `H1: μX - μY < Δ`.
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- `H0: μX - μY ≤ Δ` versus the alternative hypothesis `H1: μX - μY > Δ`.
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- `H0: μX - μY = Δ` versus the alternative hypothesis `H1: μX - μY ≠ Δ`.
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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).
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var ztest2 = require( '@stdlib/stats/base/ndarray/ztest2' );
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```
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#### ztest2( arrays )
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Computes a two-sample Z-test for two one-dimensional ndarrays.
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```javascript
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var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
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var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
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var structFactory = require( '@stdlib/array/struct-factory' );
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var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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var ndarray = require( '@stdlib/ndarray/ctor' );
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var opts = {
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'dtype': 'generic'
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};
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var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
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var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );
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var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
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var y = new ndarray( opts.dtype, ybuf, [ 5 ], [ 1 ], 0, 'row-major' );
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var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
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'dtype': 'int8'
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});
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var alpha = scalar2ndarray( 0.05, opts );
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var diff = scalar2ndarray( 0.0, opts );
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var sigmax = scalar2ndarray( 1.0, opts );
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var sigmay = scalar2ndarray( 2.0, opts );
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var ResultsArray = structFactory( Float64Results );
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var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
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var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
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var bool = ( v === out );
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// returns true
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```
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The function has the following parameters:
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- **arrays**: array-like object containing the following ndarrays in order:
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1. first one-dimensional input ndarray.
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1. second one-dimensional input ndarray.
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2. a zero-dimensional output ndarray containing a [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
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3. a zero-dimensional ndarray specifying the alternative hypothesis.
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4. a zero-dimensional ndarray specifying the significance level.
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5. a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
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6. a zero-dimensional ndarray specifying the known standard deviation of first one-dimensional input ndarray.
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7. a zero-dimensional ndarray specifying the known standard deviation of second one-dimensional input ndarray.
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- As a general rule of thumb, a Z-test is most reliable for sample sizes greater than `50`. For smaller sample sizes or when the standard deviation is unknown, prefer a t-test.
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</section>
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<!-- /.notes -->
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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 Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
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var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
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var structFactory = require( '@stdlib/array/struct-factory' );
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var normal = require( '@stdlib/random/array/normal' );
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var ndarray = require( '@stdlib/ndarray/ctor' );
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var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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var ndarray2array = require( '@stdlib/ndarray/to-array' );
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var ztest2 = require( '@stdlib/stats/base/ndarray/ztest2' );
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var opts = {
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'dtype': 'generic'
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};
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// Create a one-dimensional ndarrays containing pseudorandom numbers drawn from a normal distribution:
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var xbuf = normal( 100, 0.0, 1.0, opts );
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var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
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console.log( ndarray2array( x ) );
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var ybuf = normal( 100, 0.0, 1.0, opts );
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var y = new ndarray( opts.dtype, ybuf, [ ybuf.length ], [ 1 ], 0, 'row-major' );
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console.log( ndarray2array( y ) );
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// Specify the alternative hypothesis:
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var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
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'dtype': 'int8'
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});
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// Specify the significance level:
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var alpha = scalar2ndarray( 0.05, opts );
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// Specify the difference in means under the null hypothesis:
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var diff = scalar2ndarray( 0.0, opts );
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// Specify the known standard deviations:
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var sigmax = scalar2ndarray( 1.0, opts );
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var sigmay = scalar2ndarray( 1.0, opts );
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// Create a zero-dimensional results ndarray:
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var ResultsArray = structFactory( Float64Results );
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var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
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// Perform a Z-test:
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var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
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console.log( v.get().toString() );
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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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[@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
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/ndarray/ztest2/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) 2025 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 normal = require( '@stdlib/random/array/normal' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var ndarray = require( '@stdlib/ndarray/base/ctor' );
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var scalar2ndarray = require( '@stdlib/ndarray/base/from-scalar' );
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var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
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var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
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var structFactory = require( '@stdlib/array/struct-factory' );
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var pkg = require( './../package.json' ).name;
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var ztest2 = require( './../lib' );
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// VARIABLES //
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var options = {
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'dtype': 'generic'
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};
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var ResultsArray = structFactory( Float64Results );
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var sigmax;
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var sigmay;
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var alpha;
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var diff;
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var xbuf;
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var ybuf;
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var obuf;
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var out;
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var alt;
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var x;
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var y;
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xbuf = normal( len, 0.0, 1.0, options );
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x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
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ybuf = normal( len, 0.0, 1.0, options );
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y = new ndarray( options.dtype, ybuf, [ len ], [ 1 ], 0, 'row-major' );
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obuf = new ResultsArray( 1 );
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out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
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alt = scalar2ndarray( resolveEnum( 'two-sided' ), 'int8', 'row-major' );
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alpha = scalar2ndarray( 0.05, options.dtype, 'row-major' );
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diff = scalar2ndarray( 0.0, options.dtype, 'row-major' );
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sigmax = scalar2ndarray( 1.0, options.dtype, 'row-major' );
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sigmay = scalar2ndarray( 1.0, options.dtype, 'row-major' );
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return benchmark;
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function benchmark( b ) {
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var v;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
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if ( typeof v !== 'object' ) {
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b.fail( 'should return an ndarray' );
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}
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}
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b.toc();
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if ( isnan( v.get().statistic ) || isnan( v.get().pValue ) ) {
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b.fail( 'should not return NaN' );
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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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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':len='+len, f );
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}
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}
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main();

‎lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt

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{{alias}}( arrays )
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Computes a two-sample Z-test for two one-dimensional ndarrays.
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Parameters
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----------
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arrays: ArrayLikeObject<ndarray>
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Array-like object containing the following ndarrays in order:
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- first one-dimensional input ndarray.
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- second one-dimensional input ndarray.
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- a zero-dimensional output ndarray containing a results object.
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- a zero-dimensional ndarray specifying the alternative hypothesis.
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- a zero-dimensional ndarray specifying the significance level.
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- a zero-dimensional ndarray specifying the difference in means under
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the null hypothesis.
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- a zero-dimensional ndarray specifying the known standard deviation of
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first one-dimensional input ndarray.
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- a zero-dimensional ndarray specifying the known standard deviation of
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second one-dimensional input ndarray.
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Returns
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-------
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out: ndarray
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Output ndarray.
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Examples
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--------
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// Create the input ndarray:
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> var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
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> var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
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> var dt = 'generic';
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> var sh = [ xbuf.length ];
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> var st = [ 1 ];
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> var oo = 0;
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> var ord = 'row-major';
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> var x = new {{alias:@stdlib/ndarray/ctor}}( dt, xbuf, sh, st, oo, ord );
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> var y = new {{alias:@stdlib/ndarray/ctor}}( dt, ybuf, sh, st, oo, ord );
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// Create the output ndarray:
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> var S = {{alias:@stdlib/stats/base/ztest/two-sample/results/float64}};
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> var Results = {{alias:@stdlib/array/struct-factory}}( S );
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> var obuf = new Results( 1 );
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> var out = new {{alias:@stdlib/ndarray/ctor}}( S, obuf, [], [ 0 ], 0, ord );
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// Specify the alternative hypothesis:
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> var alt = {{alias:@stdlib/ndarray/from-scalar}}( 'two-sided' );
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// Specify the significance level:
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> var opts = { 'dtype': dt };
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> var alpha = {{alias:@stdlib/ndarray/from-scalar}}( 0.05, opts );
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// Specify the difference in means under the null hypothesis:
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> var diff = {{alias:@stdlib/ndarray/from-scalar}}( 0.0, opts );
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// Specify the known standard deviations:
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> var sigmax = {{alias:@stdlib/ndarray/from-scalar}}( 1.0, opts );
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> var sigmay = {{alias:@stdlib/ndarray/from-scalar}}( 2.0, opts );
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// Perform a Z-test:
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> {{alias}}( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
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// Print the results:
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> out.get().toString()
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See Also
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--------
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