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

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# dztest

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> Compute a one-sample Z-test for a double-precision floating-point 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-dztest
```

</section>

<section class="usage">

## Usage

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

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

Computes a one-sample Z-test for a double-precision floating-point strided array.

```javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );

var results = new Results();
var out = dztest( 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 [`Float64Array`][@stdlib/array/float64].
-   **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`,

<!-- eslint-disable max-len -->

```javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 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 = dztest( 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 = dztest( x1.length, 'two-sided', 0.05, 0.0, 1.0, x1, 1, results );
// returns {...}

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

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

Computes a one-sample Z-test for a double-precision floating-point strided array using alternative indexing semantics.

```javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );

var results = new Results();
var out = dztest.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 Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 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 = dztest.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.

</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 dztest = require( '@stdlib/stats-strided-dztest' );

var x = normal( 1000, 0.0, 1.0, {
    'dtype': 'float64'
});

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

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

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/strided/dztest.h"
```

#### stdlib_strided_dztest( N, alternative, alpha, mu, sigma, \*X, strideX, \*results )

Computes a one-sample Z-test for a double-precision floating-point strided array.

```c
#include "stdlib/stats/base/ztest/one-sample/results/float64.h"
#include "stdlib/stats/base/ztest/alternatives.h"

struct stdlib_stats_ztest_one_sample_float64_results results = {
    .rejected = false,
    .alpha = 0.0,
    .alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
    .pValue = 0.0,
    .statistic = 0.0,
    .ci = { 0.0, 0.0 },
    .nullValue = 0.0,
    .sd = 0.0
};

const double x[] = { 4.0, 4.0, 6.0, 6.0, 5.0 };

stdlib_strided_dztest( 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05, 0.0, 1.0, x, 1, &results );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **alternative**: `[in] enum STDLIB_STATS_ZTEST_ALTERNATIVE` [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].
-   **alpha**: `[in] double` significance level.
-   **mu**: `[in] double` value of the mean under the null hypothesis.
-   **sigma** `[in] double` known standard deviation.
-   **X**: `[in] double*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **results**: `[out] struct stdlib_stats_ztest_one_sample_results_float64*` output [results object][@stdlib/stats/base/ztest/one-sample/results/float64].

```c
void stdlib_strided_dztest( const CBLAS_INT N, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const double alpha, const double mu, const double sigma, const double *X, const CBLAS_INT strideX, struct stdlib_stats_ztest_one_sample_float64_results *results );
```

#### stdlib_strided_dztest_ndarray( N, alternative, alpha, mu, sigma, \*X, strideX, offsetX, \*results )

Computes a one-sample Z-test for a double-precision floating-point strided array using alternative indexing semantics.

```c
#include "stdlib/stats/base/ztest/one-sample/results/float64.h"
#include "stdlib/stats/base/ztest/alternatives.h"

struct stdlib_stats_ztest_one_sample_float64_results results = {
    .rejected = false,
    .alpha = 0.0,
    .alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
    .pValue = 0.0,
    .statistic = 0.0,
    .ci = { 0.0, 0.0 },
    .nullValue = 0.0,
    .sd = 0.0
};

const double x[] = { 4.0, 4.0, 6.0, 6.0, 5.0 };

stdlib_strided_dztest_ndarray( 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05, 0.0, 1.0, x, 1, 0, &results );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **alternative**: `[in] enum STDLIB_STATS_ZTEST_ALTERNATIVE` [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].
-   **alpha**: `[in] double` significance level.
-   **mu**: `[in] double` value of the mean under the null hypothesis.
-   **sigma** `[in] double` known standard deviation.
-   **X**: `[in] double*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
-   **results**: `[out] struct stdlib_stats_ztest_one_sample_results_float64*` output [results object][@stdlib/stats/base/ztest/one-sample/results/float64].

```c
void stdlib_strided_dztest_ndarray( const CBLAS_INT N, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const double alpha, const double mu, const double sigma, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, struct stdlib_stats_ztest_one_sample_float64_results *results );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/strided/dztest.h"
#include "stdlib/stats/base/ztest/one-sample/results/float64.h"
#include "stdlib/stats/base/ztest/alternatives.h"
#include <stdbool.h>
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };

    // Specify the number of elements:
    const int N = 4;

    // Specify the stride length:
    const int strideX = 2;

    // Initialize a results object:
    struct stdlib_stats_ztest_one_sample_float64_results results = {
        .rejected = false,
        .alpha = 0.0,
        .alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
        .pValue = 0.0,
        .statistic = 0.0,
        .ci = { 0.0, 0.0 },
        .nullValue = 0.0,
        .sd = 0.0
    };

    // Compute a Z-test:
    stdlib_strided_dztest( N, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05, 5.0, 3.0, x, strideX, &results );

    // Print the result:
    printf( "Statistic: %lf\n", results.statistic );
    printf( "Null hypothesis was %s\n", ( results.rejected ) ? "rejected" : "not rejected" );
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<section class="references">

</section>

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<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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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[@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64

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