npm package: @stdlib/stats-base-ndarray-ztest
Description: Compute a one-sample Z-test for a one-dimensional ndarray.
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 one-dimensional ndarray.

<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-base-ndarray-ztest
```

</section>

<section class="usage">

## Usage

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

#### ztest( arrays )

Computes a one-sample Z-test for a one-dimensional ndarray.

```javascript
var Float64Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var resolveEnum = require( '@stdlib/stats-base-ztest-alternative-resolve-enum' );
var structFactory = require( '@stdlib/array-struct-factory' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );
var ndarray = require( '@stdlib/ndarray-ctor' );

var opts = {
    'dtype': 'generic'
};
var xbuf = [ 1.0, 3.0, 4.0, 2.0 ];
var x = new ndarray( opts.dtype, xbuf, [ 4 ], [ 1 ], 0, 'row-major' );

var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
    'dtype': 'int8'
});
var alpha = scalar2ndarray( 0.05, opts );
var mu = scalar2ndarray( 0.0, opts );
var sigma = scalar2ndarray( 1.0, opts );

var ResultsArray = structFactory( Float64Results );
var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );

var v = ztest( [ x, out, alt, alpha, mu, sigma ] );

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

The function has the following parameters:

-   **arrays**: array-like object containing the following ndarrays in order:

    1.  a one-dimensional input ndarray.
    2.  a zero-dimensional output ndarray containing a [results object][@stdlib/stats/base/ztest/one-sample/results/float64].
    3.  a zero-dimensional ndarray specifying the alternative hypothesis.
    4.  a zero-dimensional ndarray specifying the significance level.
    5.  a zero-dimensional ndarray specifying the mean under the null hypothesis.
    6.  a zero-dimensional ndarray specifying the known standard deviation.

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var Float64Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var resolveEnum = require( '@stdlib/stats-base-ztest-alternative-resolve-enum' );
var structFactory = require( '@stdlib/array-struct-factory' );
var normal = require( '@stdlib/random-array-normal' );
var ndarray = require( '@stdlib/ndarray-ctor' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );
var ndarray2array = require( '@stdlib/ndarray-to-array' );
var ztest = require( '@stdlib/stats-base-ndarray-ztest' );

var opts = {
    'dtype': 'generic'
};

// Create a one-dimensional ndarray containing pseudorandom numbers drawn from a normal distribution:
var xbuf = normal( 100, 0.0, 1.0, opts );
var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
console.log( ndarray2array( x ) );

// Specify the alternative hypothesis:
var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
    'dtype': 'int8'
});

// Specify the significance level:
var alpha = scalar2ndarray( 0.05, opts );

// Specify the mean under the null hypothesis:
var mu = scalar2ndarray( 0.0, opts );

// Specify the known standard deviation:
var sigma = scalar2ndarray( 1.0, opts );

// Create a zero-dimensional results ndarray:
var ResultsArray = structFactory( Float64Results );
var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );

// Perform a Z-test:
var v = ztest( [ x, out, alt, alpha, mu, sigma ] );
console.log( v.get().toString() );
```

</section>

<!-- /.examples -->

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<section class="related">

</section>

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* * *

## 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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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