Compute a two-sample Z-test for two single-precision floating-point strided arrays.
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> Compute a two-sample Z-test for two single-precision floating-point strided arrays.
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-sztest2
`javascript`
var sztest2 = require( '@stdlib/stats-strided-sztest2' );
#### sztest2( NX, NY, alternative, alpha, diff, sigmax, x, strideX, sigmay, y, strideY, out )
Computes a two-sample Z-test for two single-precision floating-point strided arrays.
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float32' );
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );
var y = new Float32Array( [ 3.0, 3.0, 5.0, 7.0, 7.0 ] );
var results = new Results();
var out = sztest2( 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 .Float32Array
- x: first input [][@stdlib/array/float32].x
- strideX: stride length for .y
- sigmay: known standard deviation of .Float32Array
- y: second input [][@stdlib/array/float32].y
- strideY: stride length for .
- out: output [results object][@stdlib/stats/base/ztest/two-sample/results/float32].
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-float32' );
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0, 0.0 ] );
var y = new Float32Array( [ 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 = sztest2( 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-float32' );
var Float32Array = require( '@stdlib/array-float32' );
var x0 = new Float32Array( [ 0.0, 4.0, 4.0, 6.0, 6.0, 5.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y0 = new Float32Array( [ 0.0, 3.0, 3.0, 5.0, 7.0, 7.0 ] );
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var results = new Results();
var out = sztest2( 5, 5, 'two-sided', 0.05, 0.0, 1.0, x1, 1, 2.0, y1, 1, results );
// returns {...}
var bool = ( out === results );
// returns true
`
#### sztest2.ndarray( NX, NY, alternative, alpha, diff, sigmax, x, strideX, offsetX, sigmay, y, strideY, offsetY, out )
Computes a two-sample Z-test for two single-precision floating-point strided arrays using alternative indexing semantics.
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float32' );
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );
var y = new Float32Array( [ 3.0, 3.0, 5.0, 7.0, 7.0 ] );
var results = new Results();
var out = sztest2.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-float32' );
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 0.0, 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0 ] );
var y = new Float32Array( [ 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 = sztest2.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.
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float32' );
var normal = require( '@stdlib/random-array-normal' );
var sztest2 = require( '@stdlib/stats-strided-sztest2' );
var x = normal( 1000, 4.0, 2.0, {
'dtype': 'float32'
});
var y = normal( 800, 3.0, 2.0, {
'dtype': 'float32'
});
var results = new Results();
var out = sztest2( x.length, y.length, 'two-sided', 0.05, 1.0, 2.0, x, 1, 2.0, y, 1, results );
// returns {...}
console.log( out.toString() );
`
*
`c`
#include "stdlib/stats/strided/sztest2.h"
#### stdlib_strided_sztest2( NX, NY, alternative, alpha, diff, sigmax, \X, strideX, sigmay, \Y, strideY, \*results )
Computes a two-sample Z-test for two single-precision floating-point strided arrays.
`c
#include "stdlib/stats/base/ztest/two-sample/results/float32.h"
#include "stdlib/stats/base/ztest/alternatives.h"
struct stdlib_stats_ztest_two_sample_float32_results results = {
.rejected = false,
.alpha = 0.0f,
.alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
.pValue = 0.0f,
.statistic = 0.0f,
.ci = { 0.0f, 0.0f },
.nullValue = 0.0f,
.xmean = 0.0f,
.ymean = 0.0f
};
const float x[] = { 4.0f, 4.0f, 6.0f, 6.0f, 5.0f };
const float y[] = { 3.0f, 3.0f, 5.0f, 7.0f, 7.0f };
stdlib_strided_sztest2( 5, 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05f, 0.0f, 1.0f, x, 1, 2.0f, y, 1, &results );
`
The function accepts the following arguments:
- NX: [in] CBLAS_INT number of indexed elements in x.[in] CBLAS_INT
- NY: number of indexed elements in y.[in] enum STDLIB_STATS_ZTEST_ALTERNATIVE
- alternative: [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].[in] float
- alpha: significance level.[in] float
- diff: difference in means under the null hypothesis.[in] float
- sigmax known standard deviation of x.[in] float*
- X: first input [Float32Array][@stdlib/array/float32].[in] CBLAS_INT
- strideX: stride length for X.[in] float
- sigmay known standard deviation of y.[in] float*
- Y: second input [Float32Array][@stdlib/array/float32].[in] CBLAS_INT
- strideY: stride length for Y.[out] struct stdlib_stats_ztest_two_sample_results_float32*
- results: output [results object][@stdlib/stats/base/ztest/two-sample/results/float32].
`c`
void stdlib_strided_sztest2( const CBLAS_INT NX, const CBLAS_INT NY, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const float alpha, const float diff, const float sigmax, const float X, const CBLAS_INT strideX, const float sigmay, const float Y, const CBLAS_INT strideY, struct stdlib_stats_ztest_two_sample_float32_results *results );
#### stdlib_strided_sztest2_ndarray( NX, NY, alternative, alpha, diff, sigmax, \X, strideX, offsetX, sigmay, \Y, strideY, offsetY, \*results )
Computes a two-sample Z-test for two single-precision floating-point strided arrays using alternative indexing semantics.
`c
#include "stdlib/stats/base/ztest/two-sample/results/float32.h"
#include "stdlib/stats/base/ztest/alternatives.h"
struct stdlib_stats_ztest_two_sample_float32_results results = {
.rejected = false,
.alpha = 0.0f,
.alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
.pValue = 0.0f,
.statistic = 0.0f,
.ci = { 0.0f, 0.0f },
.nullValue = 0.0f,
.xmean = 0.0f,
.ymean = 0.0f
};
const float x[] = { 4.0f, 4.0f, 6.0f, 6.0f, 5.0f };
const float y[] = { 3.0f, 3.0f, 5.0f, 7.0f, 7.0f };
stdlib_strided_sztest2_ndarray( 5, 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05f, 0.0f, 1.0f, x, 1, 0, 2.0f, y, 1, 0, &results );
`
The function accepts the following arguments:
- NX: [in] CBLAS_INT number of indexed elements in x.[in] CBLAS_INT
- NY: number of indexed elements in y.[in] enum STDLIB_STATS_ZTEST_ALTERNATIVE
- alternative: [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].[in] float
- alpha: significance level.[in] float
- diff: difference in means under the null hypothesis.[in] float
- sigmax known standard deviation of x.[in] float*
- X: first input [Float32Array][@stdlib/array/float32].[in] CBLAS_INT
- strideX: stride length for X.[in] CBLAS_INT
- offsetX: starting index for X.[in] float
- sigmay known standard deviation of y.[in] float*
- Y: second input [Float32Array][@stdlib/array/float32].[in] CBLAS_INT
- strideY: stride length for Y.[in] CBLAS_INT
- offsetY: starting index for Y.[out] struct stdlib_stats_ztest_two_sample_results_float32*
- results: output [results object][@stdlib/stats/base/ztest/two-sample/results/float32].
`c`
void stdlib_strided_sztest2_ndarray( const CBLAS_INT NX, const CBLAS_INT NY, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const float alpha, const float diff, const float sigmax, const float X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const float sigmay, const float Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, struct stdlib_stats_ztest_two_sample_float32_results *results );
`c
#include "stdlib/stats/strided/sztest2.h"
#include "stdlib/stats/base/ztest/two-sample/results/float32.h"
#include "stdlib/stats/base/ztest/alternatives.h"
#include
#include
int main( void ) {
// Create a strided arrays:
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
const float y[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
// Specify the number of elements:
const int NX = 4;
const int NY = 4;
// Specify the stride lengths:
const int strideX = 2;
const int strideY = 2;
// Initialize a results object:
struct stdlib_stats_ztest_two_sample_float32_results results = {
.rejected = false,
.alpha = 0.0f,
.alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
.pValue = 0.0f,
.statistic = 0.0f,
.ci = { 0.0f, 0.0f },
.nullValue = 0.0f,
.xmean = 0.0f,
.ymean = 0.0f
};
// Compute a Z-test:
stdlib_strided_sztest2( NX, NY, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05f, 5.0f, 3.0f, x, strideX, 3.0f, y, strideY, &results );
// Print the result:
printf( "Statistic: %f\n", results.statistic );
printf( "Null hypothesis was %s\n", ( results.rejected ) ? "rejected" : "not rejected" );
}
`
*
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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