Z-Test

One-sample z-Test.

Installation

npm install @stdlib/stats-ztest

Usage

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

ztest( x, sigma[, opts] )

The function performs a one-sample z-test for the null hypothesis that the data in array or typed array x is drawn from a normal distribution with mean zero and known standard deviation sigma.

var normal = require( '@stdlib/random-base-normal' ).factory;

var rnorm = normal( 0.0, 2.0, {
    'seed': 5776
});

var arr = new Array( 300 );
var i;
for ( i = 0; i < arr.length; i++ ) {
    arr[ i ] = rnorm();
}

var out = ztest( arr, 2.0 );
/* e.g., returns
    {
        'rejected': false,
        'pValue': ~0.155,
        'statistic': -1.422,
        'ci': [~-0.391,~0.062],
        // ...
    }
*/

The returned object comes with a .print() method which when invoked will print a formatted output of the hypothesis test results. print accepts a digits option that controls the number of decimal digits displayed for the outputs and a decision option which when set to false will hide the test decision.

var table = out.print({
    'digits': 3
});
console.log( table );
/* e.g., =>
    One-sample z-test

    Alternative hypothesis: True mean is not equal to 0

        pValue: 0.155
        statistic: -1.422
        95% confidence interval: [-0.391,0.062]

    Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/

The ztest function accepts the following options:

• alpha: number in the interval [0,1] giving the significance level of the hypothesis test. Default: 0.05.
• alternative: Either two-sided, less or greater. Indicates whether the alternative hypothesis is that the mean of x is larger than mu (greater), smaller than mu (less) or equal to mu (two-sided). Default: two-sided.
• mu: number denoting the hypothesized true mean under the null hypothesis. Default: 0.

By default, the hypothesis test is carried out at a significance level of 0.05. To choose a different significance level, set the alpha option.

var table;
var out;
var arr;

arr = [ 2, 4, 3, 1, 0 ];

out = ztest( arr, 2.0, {
    'alpha': 0.01
});
table = out.print();
/* e.g., returns
    One-sample z-test

    Alternative hypothesis: True mean is not equal to 0

        pValue: 0.0253
        statistic: 2.2361
        99% confidence interval: [-0.3039,4.3039]

    Test Decision: Fail to reject null in favor of alternative at 1% significance level
*/

out = ztest( arr, 2.0, {
    'alpha': 0.1
});
table = out.print();
/* e.g., returns
    One-sample z-test

    Alternative hypothesis: True mean is not equal to 0

        pValue: 0.0253
        statistic: 2.2361
        90% confidence interval: [0.5288,3.4712]

    Test Decision: Reject null in favor of alternative at 10% significance level
*/

To test whether the data comes from a distribution with a mean different than zero, set the mu option.

var out;
var arr;

arr = [ 4, 4, 6, 6, 5 ];

out = ztest( arr, 1.0, {
    'mu': 5.0
});
/* e.g., returns
    {
        'rejected': false,
        'pValue': 1,
        'statistic': 0,
        'ci': [ ~4.123, ~5.877 ],
        // ...
    }
*/

By default, a two-sided test is performed. To perform either of the one-sided tests, set the alternative option to less or greater.

var table;
var out;
var arr;

arr = [ 4, 4, 6, 6, 5 ];

out = ztest( arr, 1.0, {
    'alternative': 'less'
});
table = out.print();
/* e.g., returns
    One-sample z-test

    Alternative hypothesis: True mean is less than 0

        pValue: 1
        statistic: 11.1803
        95% confidence interval: [-Infinity,5.7356]

    Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/

out = ztest( arr, 1.0, {
    'alternative': 'greater'
});
table = out.print();
/* e.g., returns
    One-sample z-test

    Alternative hypothesis: True mean is greater than 0

        pValue: 0
        statistic: 11.1803
        95% confidence interval: [4.2644,Infinity]

    Test Decision: Reject null in favor of alternative at 5% significance level
*/

Examples

var normal = require( '@stdlib/random-base-normal' ).factory;
var ztest = require( '@stdlib/stats-ztest' );

var rnorm;
var arr;
var out;
var i;

rnorm = normal( 5.0, 4.0, {
    'seed': 37827
});
arr = new Array( 500 );
for ( i = 0; i < arr.length; i++ ) {
    arr[ i ] = rnorm();
}

// Test whether true mean is equal to zero:
out = ztest( arr, 4.0 );
console.log( out.print() );
/* e.g., =>
    One-sample z-test

    Alternative hypothesis: True mean is not equal to 0

        pValue: 0
        statistic: 28.6754
        95% confidence interval: [4.779,5.4802]

    Test Decision: Reject null in favor of alternative at 5% significance level
*/

// Test whether true mean is equal to five:
out = ztest( arr, 4.0, {
    'mu': 5.0
});
console.log( out.print() );
/* e.g., =>
    One-sample z-test

    Alternative hypothesis: True mean is not equal to 5

        pValue: 0.4688
        statistic: 0.7245
        95% confidence interval: [4.779,5.4802]

    Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/

See Also

• @stdlib/stats-ztest2: two-sample z-Test.

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 © 2016-2024. The Stdlib Authors.