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ztest

Compute a one-sample Z-test for a one-dimensional ndarray.

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-base-ndarray-ztest

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

ztest( arrays )

Computes a one-sample Z-test for a one-dimensional ndarray.

var Float64Results = require( '@stdlib/stats-base-ztest-one-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 = [ 1.0, 3.0, 4.0, 2.0 ];
var x = new ndarray( opts.dtype, xbuf, [ 4 ], [ 1 ], 0, 'row-major' );

var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
    'dtype': 'int8'
});
var alpha = scalar2ndarray( 0.05, opts );
var mu = scalar2ndarray( 0.0, opts );
var sigma = scalar2ndarray( 1.0, opts );

var ResultsArray = structFactory( Float64Results );
var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );

var v = ztest( [ x, out, alt, alpha, mu, sigma ] );

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

The function has the following parameters:

• arrays: array-like object containing the following ndarrays in order:

  1. a one-dimensional input ndarray.
  2. a zero-dimensional output ndarray containing a results object.
  3. a zero-dimensional ndarray specifying the alternative hypothesis.
  4. a zero-dimensional ndarray specifying the significance level.
  5. a zero-dimensional ndarray specifying the mean under the null hypothesis.
  6. a zero-dimensional ndarray specifying the known standard deviation.

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-one-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 ztest = require( '@stdlib/stats-base-ndarray-ztest' );

var opts = {
    'dtype': 'generic'
};

// Create a one-dimensional ndarray 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 ) );

// Specify the alternative hypothesis:
var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
    'dtype': 'int8'
});

// Specify the significance level:
var alpha = scalar2ndarray( 0.05, opts );

// Specify the mean under the null hypothesis:
var mu = scalar2ndarray( 0.0, opts );

// Specify the known standard deviation:
var sigma = 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 = ztest( [ x, out, alt, alpha, mu, sigma ] );
console.log( v.get().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

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