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One-sample z-Test.
npm install @stdlib/stats-ztestAlternatively,
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scripttag without installation and bundlers, use the ES Module available on theesmbranch (see README). - If you are using Deno, visit the
denobranch (see README for usage intructions). - For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the
umdbranch (see README).
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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.
var ztest = require( '@stdlib/stats-ztest' );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-array-normal' );
// Create an array of random numbers:
var arr = normal( 300, 0.0, 2.0 );
// Test whether true mean is equal to 0.0:
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:
numberin the interval[0,1]giving the significance level of the hypothesis test. Default:0.05. - alternative: Either
two-sided,lessorgreater. Indicates whether the alternative hypothesis is that the mean ofxis larger thanmu(greater), smaller thanmu(less) or equal tomu(two-sided). Default:two-sided. - mu:
numberdenoting 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 arr = [ 2, 4, 3, 1, 0 ];
var out = ztest( arr, 2.0, {
'alpha': 0.01
});
var 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 arr = [ 4, 4, 6, 6, 5 ];
var out = ztest( arr, 1.0, {
'mu': 5.0
});
/* e.g., returns
{
'rejected': false,
'pValue': 1.0,
'statistic': 0.0,
'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 arr = [ 4, 4, 6, 6, 5 ];
var out = ztest( arr, 1.0, {
'alternative': 'less'
});
var table = out.print();
/* e.g., returns
One-sample z-test
Alternative hypothesis: True mean is less than 0
pValue: 1.0
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: 0.0
statistic: 11.1803
95% confidence interval: [4.2644,Infinity]
Test Decision: Reject null in favor of alternative at 5% significance level
*/var normal = require( '@stdlib/random-array-normal' );
var ztest = require( '@stdlib/stats-ztest' );
// Create an array of random numbers:
var arr = normal( 500, 5.0, 4.0 );
// Test whether true mean is equal to 0.0:
var 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: 0.0
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 5.0:
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
*/@stdlib/stats-ztest2: two-sample z-Test.
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.
See LICENSE.
Copyright © 2016-2025. The Stdlib Authors.
