Compute a two-sample Z-test for two one-dimensional ndarrays.
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> Compute a two-sample Z-test for two one-dimensional ndarrays.
A Z-test commonly refers to a two-sample location test which compares the means of two independent sets of measurements X and Y when the population standard deviations are known. A Z-test supports testing three different null hypotheses H0:
- H0: μX - μY ≥ Δ versus the alternative hypothesis H1: μX - μY < Δ.
- H0: μX - μY ≤ Δ versus the alternative hypothesis H1: μX - μY > Δ.
- H0: μX - μY = Δ versus the alternative hypothesis H1: μX - μY ≠ Δ.
Here, μX and μY are the true population means of samples X and Y, respectively, and Δ is the hypothesized difference in means (typically 0 by default).
``bash`
npm install @stdlib/stats-base-ndarray-ztest2
`javascript`
var ztest2 = require( '@stdlib/stats-base-ndarray-ztest2' );
#### ztest2( arrays )
Computes a two-sample Z-test for two one-dimensional ndarrays.
`javascript
var Float64Results = require( '@stdlib/stats-base-ztest-two-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 = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );
var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
var y = new ndarray( opts.dtype, ybuf, [ 5 ], [ 1 ], 0, 'row-major' );
var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
'dtype': 'int8'
});
var alpha = scalar2ndarray( 0.05, opts );
var diff = scalar2ndarray( 0.0, opts );
var sigmax = scalar2ndarray( 1.0, opts );
var sigmay = scalar2ndarray( 2.0, opts );
var ResultsArray = structFactory( Float64Results );
var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
var bool = ( v === out );
// returns true
`
The function has the following parameters:
- arrays: array-like object containing the following ndarrays in order:
1. first one-dimensional input ndarray.
2. second one-dimensional input ndarray.
3. a zero-dimensional output ndarray containing a [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
4. a zero-dimensional ndarray specifying the alternative hypothesis.
5. a zero-dimensional ndarray specifying the significance level.
6. a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
7. a zero-dimensional ndarray specifying the known standard deviation of the first one-dimensional input ndarray.
8. a zero-dimensional ndarray specifying the known standard deviation of the second one-dimensional input ndarray.
- 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.
`javascript
var Float64Results = require( '@stdlib/stats-base-ztest-two-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 ztest2 = require( '@stdlib/stats-base-ndarray-ztest2' );
var opts = {
'dtype': 'generic'
};
// Create one-dimensional ndarrays 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 ) );
var ybuf = normal( 100, 0.0, 1.0, opts );
var y = new ndarray( opts.dtype, ybuf, [ ybuf.length ], [ 1 ], 0, 'row-major' );
console.log( ndarray2array( y ) );
// Specify the alternative hypothesis:
var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
'dtype': 'int8'
});
// Specify the significance level:
var alpha = scalar2ndarray( 0.05, opts );
// Specify the difference in means under the null hypothesis:
var diff = scalar2ndarray( 0.0, opts );
// Specify the known standard deviations:
var sigmax = scalar2ndarray( 1.0, opts );
var sigmay = 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 = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
console.log( v.get().toString() );
`
*
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