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sztest

Compute a one-sample Z-test for a single-precision floating-point strided array.

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.

Installation

npm install @stdlib/stats-strided-sztest

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var sztest = require( '@stdlib/stats-strided-sztest' );

sztest( N, alternative, alpha, mu, sigma, x, strideX, out )

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

var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float32' );
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );

var results = new Results();
var out = sztest( 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.
• alpha: significance level.
• mu: mean value under the null hypothesis.
• sigma: known standard deviation.
• x: input Float32Array.
• strideX: stride length for x.
• out: output results object.

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,

var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float32' );
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 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 = sztest( 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 views.

var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float32' );
var Float32Array = require( '@stdlib/array-float32' );

var x0 = new Float32Array( [ 0.0, 4.0, 4.0, 6.0, 6.0, 5.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var results = new Results();
var out = sztest( x1.length, 'two-sided', 0.05, 0.0, 1.0, x1, 1, results );
// returns {...}

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

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

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

var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float32' );
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );

var results = new Results();
var out = sztest.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 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

var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float32' );
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 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 = sztest.ndarray( 5, 'two-sided', 0.05, 0.0, 1.0, x, 2, 1, results );
// returns {...}

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

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.

Examples

var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float32' );
var normal = require( '@stdlib/random-array-normal' );
var sztest = require( '@stdlib/stats-strided-sztest' );

var x = normal( 1000, 0.0, 1.0, {
    'dtype': 'float32'
});

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

console.log( out.toString() );

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C APIs

Usage

#include "stdlib/stats/strided/sztest.h"

stdlib_strided_sztest( N, alternative, alpha, mu, sigma, *X, strideX, *results )

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

#include "stdlib/stats/base/ztest/one-sample/results/float32.h"
#include "stdlib/stats/base/ztest/alternatives.h"

struct stdlib_stats_ztest_one_sample_float32_results results = {
    .rejected = false,
    .alpha = 0.0f,
    .alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
    .pValue = 0.0f,
    .statistic = 0.0f,
    .ci = { 0.0f, 0.0f },
    .nullValue = 0.0f,
    .sd = 0.0f
};

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

stdlib_strided_sztest( 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05f, 0.0f, 1.0f, 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.
• alpha: [in] float significance level.
• mu: [in] float value of the mean under the null hypothesis.
• sigma [in] float known standard deviation.
• X: [in] float* input array.
• strideX: [in] CBLAS_INT stride length for X.
• results: [out] struct stdlib_stats_ztest_one_sample_results_float32* output results object.

void stdlib_strided_sztest( const CBLAS_INT N, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const float alpha, const float mu, const float sigma, const float *X, const CBLAS_INT strideX, struct stdlib_stats_ztest_one_sample_float32_results *results );

stdlib_strided_sztest_ndarray( N, alternative, alpha, mu, sigma, *X, strideX, offsetX, *results )

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

#include "stdlib/stats/base/ztest/one-sample/results/float32.h"
#include "stdlib/stats/base/ztest/alternatives.h"

struct stdlib_stats_ztest_one_sample_float32_results results = {
    .rejected = false,
    .alpha = 0.0f,
    .alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
    .pValue = 0.0f,
    .statistic = 0.0f,
    .ci = { 0.0f, 0.0f },
    .nullValue = 0.0f,
    .sd = 0.0f
};

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

stdlib_strided_sztest_ndarray( 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05f, 0.0f, 1.0f, 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.
• alpha: [in] float significance level.
• mu: [in] float value of the mean under the null hypothesis.
• sigma [in] float known standard deviation.
• X: [in] float* 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_float32* output results object.

void stdlib_strided_sztest_ndarray( const CBLAS_INT N, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const float alpha, const float mu, const float sigma, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, struct stdlib_stats_ztest_one_sample_float32_results *results );

Examples

#include "stdlib/stats/strided/sztest.h"
#include "stdlib/stats/base/ztest/one-sample/results/float32.h"
#include "stdlib/stats/base/ztest/alternatives.h"
#include <stdbool.h>
#include <stdio.h>

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

    // 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_float32_results results = {
        .rejected = false,
        .alpha = 0.0f,
        .alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
        .pValue = 0.0f,
        .statistic = 0.0f,
        .ci = { 0.0f, 0.0f },
        .nullValue = 0.0f,
        .sd = 0.0f
    };

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

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

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.