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ztest2

Compute a two-sample Z-test.

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).

Installation

npm install @stdlib/stats-strided-ztest2

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 ztest2 = require( '@stdlib/stats-strided-ztest2' );

ztest2( NX, NY, alternative, alpha, diff, sigmax, x, strideX, sigmay, y, strideY, out )

Computes a two-sample Z-test.

var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );

var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var y = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];

var results = new Results();
var out = ztest2( x.length, y.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, 2.0, y, 1, results );
// returns {...}

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

The function has the following parameters:

• NX: number of indexed elements in x.
• NY: number of indexed elements in y.
• alternative: alternative hypothesis.
• alpha: significance level.
• diff: difference in means under the null hypothesis.
• sigmax: known standard deviation of x.
• x: first input array.
• strideX: stride length for x.
• sigmay: known standard deviation of y.
• y: second input array.
• strideY: stride length for y.
• out: output results object.

The N and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to perform a two-sample Z-test over every other element in x and y,

var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );

var x = [ 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0, 0.0 ];
var y = [ 3.0, 0.0, 3.0, 0.0, 5.0, 0.0, 7.0, 0.0, 7.0, 0.0 ];

var results = new Results();
var out = ztest2( 5, 5, 'two-sided', 0.05, 0.0, 1.0, x, 2, 2.0, y, 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-two-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 y0 = new Float64Array( [ 0.0, 3.0, 3.0, 5.0, 7.0, 7.0 ] );
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var results = new Results();
var out = ztest2( 5, 5, 'two-sided', 0.05, 0.0, 1.0, x1, 1, 2.0, y1, 1, results );
// returns {...}

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

ztest2.ndarray( NX, NY, alternative, alpha, diff, sigmax, x, strideX, offsetX, sigmay, y, strideY, offsetY, out )

Computes a two-sample Z-test using alternative indexing semantics.

var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );

var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var y = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];

var results = new Results();
var out = ztest2.ndarray( x.length, y.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, 0, 2.0, y, 1, 0, results );
// returns {...}

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

The function has the following additional parameters:

• offsetX: starting index for x.
• offsetY: starting index for y.

While typed array views mandate a view offset based on the underlying buffer, offset parameters support indexing semantics based on starting indices. For example, to perform a two-sample Z-test over every other element in x and y starting from the second element

var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );

var x = [ 0.0, 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0 ];
var y = [ 0.0, 3.0, 0.0, 3.0, 0.0, 5.0, 0.0, 7.0, 0.0, 7.0 ];

var results = new Results();
var out = ztest2.ndarray( 5, 5, 'two-sided', 0.05, 0.0, 1.0, x, 2, 1, 2.0, y, 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 deviations are unknown, prefer a t-test.
• Both functions support array-like objects having getter and setter accessors for array element access (e.g., @stdlib/array-base/accessor).
• Depending on the environment, the typed versions (dztest2, sztest2, etc.) are likely to be significantly more performant.

Examples

var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );
var normal = require( '@stdlib/random-array-normal' );
var ztest2 = require( '@stdlib/stats-strided-ztest2' );

var x = normal( 1000, 4.0, 2.0, {
    'dtype': 'generic'
});
var y = normal( 800, 3.0, 2.0, {
    'dtype': 'generic'
});

var results = new Results();
var out = ztest2( x.length, y.length, 'two-sided', 0.05, 1.0, 2.0, x, 1, 2.0, y, 1, results );
// returns {...}

console.log( out.toString() );

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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.