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z-Test
Two-sample z-Test.
Installation
npm install @stdlib/stats-ztest2Usage
var ztest2 = require( '@stdlib/stats-ztest2' );ztest2( x, y, sigmax, sigmay[, opts] )
By default, the function performs a two-sample z-test for the null hypothesis that the data in arrays or typed arrays x and y is independently drawn from normal distributions with equal means and known standard deviations sigmax and sigmay.
var x = [ 2.66, 1.5, 3.25, 0.993, 2.31, 2.41, 1.76, 2.57, 2.62, 1.23 ]; // Drawn from N(2,1)
var y = [ 4.88, 2.93, 2.96, 4.5, -0.0603, 4.62, 3.35, 2.98 ]; // Drawn from N(3,2)
var out = ztest2( x, y, 1.0, 2.0 );
/* e.g., returns
{
'rejected': false,
'pValue': ~0.141,
'statistic': ~-1.471,
'ci': [ ~-2.658, ~0.379 ],
// ...
}
*/The returned object comes with a .print() method which when invoked will print a formatted output of the results of the hypothesis test. 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.
console.log( out.print() );
/* e.g., =>
Two-sample z-test
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.1412
statistic: -1.4713
95% confidence interval: [-2.6578,0.3785]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/The 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 thatxhas a larger mean thany(greater),xhas a smaller mean thany(less) or the means are the same (two-sided). Default:two-sided. -
difference:
numberdenoting the difference in means 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 out = ztest2( x, y, 1.0, 2.0, {
'alpha': 0.2
});
var table = out.print();
/* e.g., returns
Two-sample z-test
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.1412
statistic: -1.4713
80% confidence interval: [-2.1323,-0.147]
Test Decision: Reject null in favor of alternative at 20% significance level
*/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 out = ztest2( x, y, {
'alternative': 'less'
});
var table = out.print();
/* e.g., returns
Two-sample z-test
Alternative hypothesis: True difference in means is less than 0
pValue: 0.0706
statistic: -1.4713
95% confidence interval: [-Infinity,0.1344]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
out = ztest2( x, y, {
'alternative': 'greater'
});
table = out.print();
/* e.g., returns
Two-sample z-test
Alternative hypothesis: True difference in means is greater than 0
pValue: 0.9294
statistic: -1.4713
95% confidence interval: [-2.4138,Infinity]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/To test whether the difference in the population means is equal to some other value than 0, set the difference option.
var normal = require( '@stdlib/random-base-normal' ).factory;
var rnorm = normal({
'seed': 372
});
var x = new Array( 100 );
var i;
for ( i = 0; i < x.length; i++ ) {
x[ i ] = rnorm( 2.0, 1.0 );
}
var y = new Array( 100 );
for ( i = 0; i < x.length; i++ ) {
y[ i ] = rnorm( 1.0, 1.0 );
}
var out = ztest2( x, y, 1.0, 1.0, {
'difference': 1.0
});
/* e.g., returns
{
'rejected': false,
'pValue': ~0.74,
'statistic': ~0.332,
'ci': [ ~0.77, ~1.324 ],
// ...
}
*/
var table = out.print();
/* e.g., returns
Two-sample z-test
Alternative hypothesis: True difference in means is not equal to 1
pValue: 0.7395
statistic: 0.3325
95% confidence interval: [0.7698,1.3242]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/Examples
var rnorm = require( '@stdlib/random-base-normal' );
var ztest2 = require( '@stdlib/stats-ztest2' );
var table;
var out;
var x;
var y;
var i;
// Values drawn from a Normal(4,2) distribution
x = new Array( 100 );
for ( i = 0; i < 100; i++ ) {
x[ i ] = rnorm( 4.0, 2.0 );
}
// Values drawn from a Normal(3,2) distribution
y = new Array( 80 );
for ( i = 0; i < 80; i++ ) {
y[ i ] = rnorm( 3.0, 2.0 );
}
out = ztest2( x, y, 2.0, 2.0 );
table = out.print();
console.log( table );
out = ztest2( x, y, 2.0, 2.0, {
'difference': 1.0
});
table = out.print();
console.log( table );See Also
-
@stdlib/stats-ztest: one-sample and paired 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.