dztest

Compute a one-sample Z-test for a double-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-dztest

Usage

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.

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.
• alpha: significance level.
• mu: mean value under the null hypothesis.
• sigma: known standard deviation.
• x: input Float64Array.
• 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-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 views.

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.

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 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-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

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-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() );

C APIs

Usage

#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.

#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.
• 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.

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.

#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.
• 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.

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 );

Examples

#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" );
}

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.

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License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.