Compute a one-sample Z-test for a one-dimensional ndarray.
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> Compute a one-sample Z-test for a one-dimensional ndarray.
A Z-test commonly refers to a one-sample location test which compares the mean of a set of measurements X to a given constant when the standard deviation is known. A Z-test supports testing three different null hypotheses H0:
- H0: μ ≥ μ0 versus the alternative hypothesis H1: μ < μ0.
- H0: μ ≤ μ0 versus the alternative hypothesis H1: μ > μ0.
- H0: μ = μ0 versus the alternative hypothesis H1: μ ≠ μ0.
``bash`
npm install @stdlib/stats-base-ndarray-ztest
`javascript`
var ztest = require( '@stdlib/stats-base-ndarray-ztest' );
#### ztest( arrays )
Computes a one-sample Z-test for a one-dimensional ndarray.
`javascript
var Float64Results = require( '@stdlib/stats-base-ztest-one-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 = [ 1.0, 3.0, 4.0, 2.0 ];
var x = new ndarray( opts.dtype, xbuf, [ 4 ], [ 1 ], 0, 'row-major' );
var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
'dtype': 'int8'
});
var alpha = scalar2ndarray( 0.05, opts );
var mu = scalar2ndarray( 0.0, opts );
var sigma = scalar2ndarray( 1.0, opts );
var ResultsArray = structFactory( Float64Results );
var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
var v = ztest( [ x, out, alt, alpha, mu, sigma ] );
var bool = ( v === out );
// returns true
`
The function has the following parameters:
- arrays: array-like object containing the following ndarrays in order:
1. a one-dimensional input ndarray.
2. a zero-dimensional output ndarray containing a [results object][@stdlib/stats/base/ztest/one-sample/results/float64].
3. a zero-dimensional ndarray specifying the alternative hypothesis.
4. a zero-dimensional ndarray specifying the significance level.
5. a zero-dimensional ndarray specifying the mean under the null hypothesis.
6. a zero-dimensional ndarray specifying the known standard deviation.
- 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-one-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 ztest = require( '@stdlib/stats-base-ndarray-ztest' );
var opts = {
'dtype': 'generic'
};
// Create a one-dimensional ndarray 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 ) );
// Specify the alternative hypothesis:
var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
'dtype': 'int8'
});
// Specify the significance level:
var alpha = scalar2ndarray( 0.05, opts );
// Specify the mean under the null hypothesis:
var mu = scalar2ndarray( 0.0, opts );
// Specify the known standard deviation:
var sigma = 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 = ztest( [ x, out, alt, alpha, mu, sigma ] );
console.log( v.get().toString() );
`
*
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For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
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