npm package: @stdlib/stats-base-ndarray-ztest2
Description: Compute a two-sample Z-test for two one-dimensional ndarrays.
Author: The Stdlib Authors
Latest version: 0.1.1

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# ztest2

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> Compute a two-sample Z-test for two one-dimensional ndarrays.

<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-base-ndarray-ztest2
```

</section>

<section class="usage">

## Usage

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

#### ztest2( arrays )

Computes a two-sample Z-test for two one-dimensional ndarrays.

```javascript
var Float64Results = require( '@stdlib/stats-base-ztest-two-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 = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );

var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
var y = new ndarray( opts.dtype, ybuf, [ 5 ], [ 1 ], 0, 'row-major' );

var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
    'dtype': 'int8'
});
var alpha = scalar2ndarray( 0.05, opts );
var diff = scalar2ndarray( 0.0, opts );
var sigmax = scalar2ndarray( 1.0, opts );
var sigmay = scalar2ndarray( 2.0, opts );

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

var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );

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

The function has the following parameters:

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

    1.  first one-dimensional input ndarray.
    2.  second one-dimensional input ndarray.
    3.  a zero-dimensional output ndarray containing a [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
    4.  a zero-dimensional ndarray specifying the alternative hypothesis.
    5.  a zero-dimensional ndarray specifying the significance level.
    6.  a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
    7.  a zero-dimensional ndarray specifying the known standard deviation of the first one-dimensional input ndarray.
    8.  a zero-dimensional ndarray specifying the known standard deviation of the second one-dimensional input ndarray.

</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-two-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 ztest2 = require( '@stdlib/stats-base-ndarray-ztest2' );

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

// Create one-dimensional ndarrays 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 ) );

var ybuf = normal( 100, 0.0, 1.0, opts );
var y = new ndarray( opts.dtype, ybuf, [ ybuf.length ], [ 1 ], 0, 'row-major' );
console.log( ndarray2array( y ) );

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

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

// Specify the difference in means under the null hypothesis:
var diff = scalar2ndarray( 0.0, opts );

// Specify the known standard deviations:
var sigmax = scalar2ndarray( 1.0, opts );
var sigmay = 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 = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
console.log( v.get().toString() );
```

</section>

<!-- /.examples -->

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<section class="related">

</section>

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* * *

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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