npm package: @stdlib/stats-strided-ztest2
Description: Compute a two-sample Z-test.
Author: The Stdlib Authors
Latest version: 0.1.1

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# ztest2

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute a two-sample Z-test.

<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="installation">

## Installation

```bash
npm install @stdlib/stats-strided-ztest2
```

</section>

<section class="usage">

## Usage

```javascript
var ztest2 = require( '@stdlib/stats-strided-ztest2' );
```

#### ztest2( NX, NY, alternative, alpha, diff, sigmax, x, strideX, sigmay, y, strideY, out )

Computes a two-sample Z-test.

```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, x, 1, 2.0, 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`.
-   **x**: first input array.
-   **strideX**: stride length for `x`.
-   **sigmay**: known standard deviation of `y`.
-   **y**: second 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 arrays 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, x, 2, 2.0, 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, x1, 1, 2.0, y1, 1, results );
// returns {...}

var bool = ( out === results );
// returns true
```

#### ztest2.ndarray( NX, NY, alternative, alpha, diff, sigmax, x, strideX, offsetX, sigmay, y, strideY, offsetY, out )

Computes a two-sample Z-test 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, x, 1, 0, 2.0, 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, offset parameters support indexing semantics based on starting indices. 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, x, 2, 1, 2.0, 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 deviations are 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, x, 1, 2.0, y, 1, results );
// returns {...}

console.log( out.toString() );
```

</section>

<!-- /.examples -->

<section class="references">

</section>

<!-- /.references -->

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<section class="related">

</section>

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* * *

## Notice

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For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[@stdlib/stats/base/ztest/alternatives]: https://www.npmjs.com/package/@stdlib/stats-base-ztest-alternatives

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