Compute a two-sample Z-test.
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> Compute a two-sample Z-test.
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-strided-ztest2
`javascript`
var ztest2 = require( '@stdlib/stats-strided-ztest2' );
#### ztest2( NX, NY, alternative, alpha, diff, sigmax, x, strideX, sigmay, y, strideY, out )
Computes a two-sample Z-test.
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );
var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var y = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
var results = new Results();
var out = ztest2( x.length, y.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, 2.0, y, 1, results );
// returns {...}
var bool = ( out === results );
// returns true
`
The function has the following parameters:
- NX: number of indexed elements in x.y
- NY: number of indexed elements in .x
- alternative: [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].
- alpha: significance level.
- diff: difference in means under the null hypothesis.
- sigmax: known standard deviation of .x
- x: first input array.
- strideX: stride length for .y
- sigmay: known standard deviation of .y
- y: second input array.
- strideY: stride length for .
- out: output [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
The N and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to perform a two-sample Z-test over every other element in x and y,
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-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 y = [ 3.0, 0.0, 3.0, 0.0, 5.0, 0.0, 7.0, 0.0, 7.0, 0.0 ];
var results = new Results();
var out = ztest2( 5, 5, 'two-sided', 0.05, 0.0, 1.0, x, 2, 2.0, y, 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-two-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 y0 = new Float64Array( [ 0.0, 3.0, 3.0, 5.0, 7.0, 7.0 ] );
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var results = new Results();
var out = ztest2( 5, 5, 'two-sided', 0.05, 0.0, 1.0, x1, 1, 2.0, y1, 1, results );
// returns {...}
var bool = ( out === results );
// returns true
`
#### ztest2.ndarray( NX, NY, alternative, alpha, diff, sigmax, x, strideX, offsetX, sigmay, y, strideY, offsetY, out )
Computes a two-sample Z-test using alternative indexing semantics.
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );
var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var y = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
var results = new Results();
var out = ztest2.ndarray( x.length, y.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, 0, 2.0, y, 1, 0, results );
// returns {...}
var bool = ( out === results );
// returns true
`
The function has the following additional parameters:
- offsetX: starting index for x.y
- offsetY: starting index for .
While [typed array][mdn-typed-array] views mandate a view offset based on the underlying buffer, offset parameters support indexing semantics based on starting indices. For example, to perform a two-sample Z-test over every other element in x and y starting from the second element
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-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 y = [ 0.0, 3.0, 0.0, 3.0, 0.0, 5.0, 0.0, 7.0, 0.0, 7.0 ];
var results = new Results();
var out = ztest2.ndarray( 5, 5, 'two-sided', 0.05, 0.0, 1.0, x, 2, 1, 2.0, y, 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 deviations are 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]).dztest2
- Depending on the environment, the typed versions ([][@stdlib/stats/strided/dztest2], [sztest2][@stdlib/stats/strided/sztest2], etc.) are likely to be significantly more performant.
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );
var normal = require( '@stdlib/random-array-normal' );
var ztest2 = require( '@stdlib/stats-strided-ztest2' );
var x = normal( 1000, 4.0, 2.0, {
'dtype': 'generic'
});
var y = normal( 800, 3.0, 2.0, {
'dtype': 'generic'
});
var results = new Results();
var out = ztest2( x.length, y.length, 'two-sided', 0.05, 1.0, 2.0, x, 1, 2.0, y, 1, results );
// returns {...}
console.log( out.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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