zTest
Twosample zTest.
Installation
npm install @stdlib/statsztest2
Usage
var ztest2 = require( '@stdlib/statsztest2' );
ztest2( x, y, sigmax, sigmay[, opts] )
By default, the function performs a twosample ztest 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., =>
Twosample ztest
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:
number
in the interval[0,1]
giving the significance level of the hypothesis test. Default:0.05
. 
alternative: Either
twosided
,less
orgreater
. Indicates whether the alternative hypothesis is thatx
has a larger mean thany
(greater
),x
has a smaller mean thany
(less
) or the means are the same (twosided
). Default:twosided
. 
difference:
number
denoting 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
Twosample ztest
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 twosided test is performed. To perform either of the onesided tests, set the alternative
option to less
or greater
.
var out = ztest2( x, y, {
'alternative': 'less'
});
var table = out.print();
/* e.g., returns
Twosample ztest
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
Twosample ztest
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/randombasenormal' ).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
Twosample ztest
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/randombasenormal' );
var ztest2 = require( '@stdlib/statsztest2' );
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
: onesample and paired zTest.
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 © 20162022. The Stdlib Authors.