npm package: @stdlib/stats-strided-ztest
Description: Compute a one-sample Z-test for a strided array.
Author: The Stdlib Authors
Latest version: 0.1.1

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# ztest

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> Compute a one-sample Z-test for a strided array.

<section class="intro">

A Z-test commonly refers to a one-sample location test which compares the mean of a set of measurements `X` to a given constant when the standard deviation is known. A Z-test supports testing three different null hypotheses `H0`:

-   `H0: μ ≥ μ0` versus the alternative hypothesis `H1: μ < μ0`.
-   `H0: μ ≤ μ0` versus the alternative hypothesis `H1: μ > μ0`.
-   `H0: μ = μ0` versus the alternative hypothesis `H1: μ ≠ μ0`.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### ztest( N, alternative, alpha, mu, sigma, x, strideX, out )

Computes a one-sample Z-test for a strided array.

```javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );

var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];

var results = new Results();
var out = ztest( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, results );
// returns {...}

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

The function has the following parameters:

-   **N**: number of indexed elements.
-   **alternative**: [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].
-   **alpha**: significance level.
-   **mu**: mean value under the null hypothesis.
-   **sigma**: known standard deviation.
-   **x**: input array.
-   **strideX**: stride length for `x`.
-   **out**: output [results object][@stdlib/stats/base/ztest/one-sample/results/float64].

The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to perform a one-sample Z-test over every other element in `x`,

```javascript
var Results = require( '@stdlib/stats-base-ztest-one-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 results = new Results();
var out = ztest( 5, 'two-sided', 0.05, 0.0, 1.0, x, 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-one-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 results = new Results();
var out = ztest( x1.length, 'two-sided', 0.05, 0.0, 1.0, x1, 1, results );
// returns {...}

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

#### ztest.ndarray( N, alternative, alpha, mu, sigma, x, strideX, offsetX, out )

Computes a one-sample Z-test for a strided array using alternative indexing semantics.

```javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );

var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];

var results = new Results();
var out = ztest.ndarray( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, 0, results );
// returns {...}

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

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.

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 one-sample Z-test over every other element in `x` starting from the second element

```javascript
var Results = require( '@stdlib/stats-base-ztest-one-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 results = new Results();
var out = ztest.ndarray( 5, 'two-sided', 0.05, 0.0, 1.0, x, 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 ([`dztest`][@stdlib/stats/strided/dztest], [`sztest`][@stdlib/stats/strided/sztest], 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-one-sample-results-float64' );
var normal = require( '@stdlib/random-array-normal' );
var ztest = require( '@stdlib/stats-strided-ztest' );

var x = normal( 1000, 0.0, 1.0, {
    'dtype': 'generic'
});

var results = new Results();
var out = ztest( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 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>

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

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].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-strided-ztest/main/LICENSE

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

[@stdlib/stats/base/ztest/one-sample/results/float64]: https://www.npmjs.com/package/@stdlib/stats-base-ztest-one-sample-results-float64

[@stdlib/array/base/accessor]: https://www.npmjs.com/package/@stdlib/array-base-accessor

[@stdlib/stats/strided/dztest]: https://www.npmjs.com/package/@stdlib/stats-strided-dztest

[@stdlib/stats/strided/sztest]: https://www.npmjs.com/package/@stdlib/stats-strided-sztest

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

</section>

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