ztest2

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

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-base-ndarray-ztest2

Usage

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

ztest2( arrays )

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

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.
  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.

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.

Examples

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() );

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

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.