Compute a one-sample Z-test for a strided array.
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> Compute a one-sample Z-test for a strided array.
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-strided-ztest
`javascript`
var ztest = require( '@stdlib/stats-strided-ztest' );
#### ztest( N, alternative, alpha, mu, sigma, x, strideX, out )
Computes a one-sample Z-test for a strided array.
`javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var results = new Results();
var out = ztest( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, results );
// returns {...}
var bool = ( out === results );
// returns true
`
The function has the following parameters:
- N: number of indexed elements.
- alternative: [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].
- alpha: significance level.
- mu: mean value under the null hypothesis.
- sigma: known standard deviation.
- x: input array.
- strideX: stride length for x.
- out: output [results object][@stdlib/stats/base/ztest/one-sample/results/float64].
The N and stride parameters determine which elements in the strided array are accessed at runtime. For example, to perform a one-sample Z-test over every other element in x,
`javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var x = [ 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0, 0.0 ];
var results = new Results();
var out = ztest( 5, 'two-sided', 0.05, 0.0, 1.0, x, 2, results );
// returns {...}
var bool = ( out === results );
// returns true
`
Note that indexing is relative to the first index. To introduce an offset, use [typed array][mdn-typed-array] views.
`javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var Float64Array = require( '@stdlib/array-float64' );
var x0 = new Float64Array( [ 0.0, 4.0, 4.0, 6.0, 6.0, 5.0 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var results = new Results();
var out = ztest( x1.length, 'two-sided', 0.05, 0.0, 1.0, x1, 1, results );
// returns {...}
var bool = ( out === results );
// returns true
`
#### ztest.ndarray( N, alternative, alpha, mu, sigma, x, strideX, offsetX, out )
Computes a one-sample Z-test for a strided array using alternative indexing semantics.
`javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var results = new Results();
var out = ztest.ndarray( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, 0, results );
// returns {...}
var bool = ( out === results );
// returns true
`
The function has the following additional parameters:
- offsetX: starting index for x.
While [typed array][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to perform a one-sample Z-test over every other element in x starting from the second element
`javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var x = [ 0.0, 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0 ];
var results = new Results();
var out = ztest.ndarray( 5, 'two-sided', 0.05, 0.0, 1.0, x, 2, 1, results );
// returns {...}
var bool = ( out === results );
// returns true
`
- As a general rule of thumb, a Z-test is most reliable when N >= 50. For smaller sample sizes or when the standard deviation is unknown, prefer a t-test.@stdlib/array-base/accessor
- Both functions support array-like objects having getter and setter accessors for array element access (e.g., [][@stdlib/array/base/accessor]).dztest
- Depending on the environment, the typed versions ([][@stdlib/stats/strided/dztest], [sztest][@stdlib/stats/strided/sztest], etc.) are likely to be significantly more performant.
`javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float64' );
var normal = require( '@stdlib/random-array-normal' );
var ztest = require( '@stdlib/stats-strided-ztest' );
var x = normal( 1000, 0.0, 1.0, {
'dtype': 'generic'
});
var results = new Results();
var out = ztest( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, results );
// returns {...}
console.log( out.toString() );
`
*
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
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[@stdlib/stats/base/ztest/alternatives]: https://www.npmjs.com/package/@stdlib/stats-base-ztest-alternatives
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