Compute a one-sample Z-test for a single-precision floating-point strided array.
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> Compute a one-sample Z-test for a single-precision floating-point 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-sztest
`javascript`
var sztest = require( '@stdlib/stats-strided-sztest' );
#### sztest( N, alternative, alpha, mu, sigma, x, strideX, out )
Computes a one-sample Z-test for a single-precision floating-point strided array.
`javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float32' );
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );
var results = new Results();
var out = sztest( 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 [Float32Array][@stdlib/array/float32].x
- strideX: stride length for .
- out: output [results object][@stdlib/stats/base/ztest/one-sample/results/float32].
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-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 results = new Results();
var out = sztest( 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-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 results = new Results();
var out = sztest( x1.length, 'two-sided', 0.05, 0.0, 1.0, x1, 1, results );
// returns {...}
var bool = ( out === results );
// returns true
`
#### sztest.ndarray( N, alternative, alpha, mu, sigma, x, strideX, offsetX, out )
Computes a one-sample Z-test for a single-precision floating-point strided array using alternative indexing semantics.
`javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float32' );
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );
var results = new Results();
var out = sztest.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-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 results = new Results();
var out = sztest.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.
`javascript
var Results = require( '@stdlib/stats-base-ztest-one-sample-results-float32' );
var normal = require( '@stdlib/random-array-normal' );
var sztest = require( '@stdlib/stats-strided-sztest' );
var x = normal( 1000, 0.0, 1.0, {
'dtype': 'float32'
});
var results = new Results();
var out = sztest( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, results );
// returns {...}
console.log( out.toString() );
`
*
`c`
#include "stdlib/stats/strided/sztest.h"
#### stdlib_strided_sztest( N, alternative, alpha, mu, sigma, \X, strideX, \results )
Computes a one-sample Z-test for a single-precision floating-point strided array.
`c
#include "stdlib/stats/base/ztest/one-sample/results/float32.h"
#include "stdlib/stats/base/ztest/alternatives.h"
struct stdlib_stats_ztest_one_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,
.sd = 0.0f
};
const float x[] = { 4.0f, 4.0f, 6.0f, 6.0f, 5.0f };
stdlib_strided_sztest( 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05f, 0.0f, 1.0f, x, 1, &results );
`
The function accepts the following arguments:
- N: [in] CBLAS_INT number of indexed elements.[in] enum STDLIB_STATS_ZTEST_ALTERNATIVE
- alternative: [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].[in] float
- alpha: significance level.[in] float
- mu: value of the mean under the null hypothesis.[in] float
- sigma known standard deviation.[in] float*
- X: input array.[in] CBLAS_INT
- strideX: stride length for X.[out] struct stdlib_stats_ztest_one_sample_results_float32*
- results: output [results object][@stdlib/stats/base/ztest/one-sample/results/float32].
`c`
void stdlib_strided_sztest( const CBLAS_INT N, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const float alpha, const float mu, const float sigma, const float X, const CBLAS_INT strideX, struct stdlib_stats_ztest_one_sample_float32_results results );
#### stdlib_strided_sztest_ndarray( N, alternative, alpha, mu, sigma, \X, strideX, offsetX, \results )
Computes a one-sample Z-test for a single-precision floating-point strided array using alternative indexing semantics.
`c
#include "stdlib/stats/base/ztest/one-sample/results/float32.h"
#include "stdlib/stats/base/ztest/alternatives.h"
struct stdlib_stats_ztest_one_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,
.sd = 0.0f
};
const float x[] = { 4.0f, 4.0f, 6.0f, 6.0f, 5.0f };
stdlib_strided_sztest_ndarray( 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05f, 0.0f, 1.0f, x, 1, 0, &results );
`
The function accepts the following arguments:
- N: [in] CBLAS_INT number of indexed elements.[in] enum STDLIB_STATS_ZTEST_ALTERNATIVE
- alternative: [alternative hypothesis][@stdlib/stats/base/ztest/alternatives].[in] float
- alpha: significance level.[in] float
- mu: value of the mean under the null hypothesis.[in] float
- sigma known standard deviation.[in] float*
- X: input array.[in] CBLAS_INT
- strideX: stride length for X.[in] CBLAS_INT
- offsetX: starting index for X.[out] struct stdlib_stats_ztest_one_sample_results_float32*
- results: output [results object][@stdlib/stats/base/ztest/one-sample/results/float32].
`c`
void stdlib_strided_sztest_ndarray( const CBLAS_INT N, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const float alpha, const float mu, const float sigma, const float X, const CBLAS_INT strideX, const CBLAS_INT offsetX, struct stdlib_stats_ztest_one_sample_float32_results results );
`c
#include "stdlib/stats/strided/sztest.h"
#include "stdlib/stats/base/ztest/one-sample/results/float32.h"
#include "stdlib/stats/base/ztest/alternatives.h"
#include
#include
int main( void ) {
// Create a strided array:
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
// Specify the number of elements:
const int N = 4;
// Specify the stride length:
const int strideX = 2;
// Initialize a results object:
struct stdlib_stats_ztest_one_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,
.sd = 0.0f
};
// Compute a Z-test:
stdlib_strided_sztest( N, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05f, 5.0f, 3.0f, x, strideX, &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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