Compute a two-sample Z-test for two double-precision floating-point strided arrays.
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> Compute a two-sample Z-test for two double-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-dztest2
`javascript`
var dztest2 = require( '@stdlib/stats-strided-dztest2' );
#### dztest2( NX, NY, alternative, alpha, diff, sigmax, x, strideX, sigmay, y, strideY, out )
Computes a two-sample Z-test for two double-precision floating-point strided arrays.
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );
var Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );
var y = new Float64Array( [ 3.0, 3.0, 5.0, 7.0, 7.0 ] );
var results = new Results();
var out = dztest2( 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 .Float64Array
- x: first input [][@stdlib/array/float64].x
- strideX: stride length for .y
- sigmay: known standard deviation of .Float64Array
- y: second input [][@stdlib/array/float64].y
- 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 Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0, 0.0 ] );
var y = new Float64Array( [ 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 = dztest2( 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 = dztest2( 5, 5, 'two-sided', 0.05, 0.0, 1.0, x1, 1, 2.0, y1, 1, results );
// returns {...}
var bool = ( out === results );
// returns true
`
#### dztest2.ndarray( NX, NY, alternative, alpha, diff, sigmax, x, strideX, offsetX, sigmay, y, strideY, offsetY, out )
Computes a two-sample Z-test for two double-precision floating-point strided arrays using alternative indexing semantics.
`javascript
var Results = require( '@stdlib/stats-base-ztest-two-sample-results-float64' );
var Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );
var y = new Float64Array( [ 3.0, 3.0, 5.0, 7.0, 7.0 ] );
var results = new Results();
var out = dztest2.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 Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 0.0, 4.0, 0.0, 4.0, 0.0, 6.0, 0.0, 6.0, 0.0, 5.0 ] );
var y = new Float64Array( [ 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 = dztest2.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-float64' );
var normal = require( '@stdlib/random-array-normal' );
var dztest2 = require( '@stdlib/stats-strided-dztest2' );
var x = normal( 1000, 4.0, 2.0, {
'dtype': 'float64'
});
var y = normal( 800, 3.0, 2.0, {
'dtype': 'float64'
});
var results = new Results();
var out = dztest2( 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/dztest2.h"
#### stdlib_strided_dztest2( NX, NY, alternative, alpha, diff, sigmax, \X, strideX, sigmay, \Y, strideY, \*results )
Computes a two-sample Z-test for two double-precision floating-point strided arrays.
`c
#include "stdlib/stats/base/ztest/two-sample/results/float64.h"
#include "stdlib/stats/base/ztest/alternatives.h"
struct stdlib_stats_ztest_two_sample_float64_results results = {
.rejected = false,
.alpha = 0.0,
.alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
.pValue = 0.0,
.statistic = 0.0,
.ci = { 0.0, 0.0 },
.nullValue = 0.0,
.xmean = 0.0,
.ymean = 0.0
};
const double x[] = { 4.0, 4.0, 6.0, 6.0, 5.0 };
const double y[] = { 3.0, 3.0, 5.0, 7.0, 7.0 };
stdlib_strided_dztest2( 5, 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05, 0.0, 1.0, x, 1, 2.0, 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] double
- alpha: significance level.[in] double
- diff: difference in means under the null hypothesis.[in] double
- sigmax known standard deviation of x.[in] double*
- X: first input [Float64Array][@stdlib/array/float64].[in] CBLAS_INT
- strideX: stride length for X.[in] double
- sigmay known standard deviation of y.[in] double*
- Y: second input [Float64Array][@stdlib/array/float64].[in] CBLAS_INT
- strideY: stride length for Y.[out] struct stdlib_stats_ztest_two_sample_results_float64*
- results: output [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
`c`
void stdlib_strided_dztest2( const CBLAS_INT NX, const CBLAS_INT NY, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const double alpha, const double diff, const double sigmax, const double X, const CBLAS_INT strideX, const double sigmay, const double Y, const CBLAS_INT strideY, struct stdlib_stats_ztest_two_sample_float64_results *results );
#### stdlib_strided_dztest2_ndarray( NX, NY, alternative, alpha, diff, sigmax, \X, strideX, offsetX, sigmay, \Y, strideY, offsetY, \*results )
Computes a two-sample Z-test for two double-precision floating-point strided arrays using alternative indexing semantics.
`c
#include "stdlib/stats/base/ztest/two-sample/results/float64.h"
#include "stdlib/stats/base/ztest/alternatives.h"
struct stdlib_stats_ztest_two_sample_float64_results results = {
.rejected = false,
.alpha = 0.0,
.alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
.pValue = 0.0,
.statistic = 0.0,
.ci = { 0.0, 0.0 },
.nullValue = 0.0,
.xmean = 0.0,
.ymean = 0.0
};
const double x[] = { 4.0, 4.0, 6.0, 6.0, 5.0 };
const double y[] = { 3.0, 3.0, 5.0, 7.0, 7.0 };
stdlib_strided_dztest2_ndarray( 5, 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05, 0.0, 1.0, x, 1, 0, 2.0, 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] double
- alpha: significance level.[in] double
- diff: difference in means under the null hypothesis.[in] double
- sigmax known standard deviation of x.[in] double*
- X: first input [Float64Array][@stdlib/array/float64].[in] CBLAS_INT
- strideX: stride length for X.[in] CBLAS_INT
- offsetX: starting index for X.[in] double
- sigmay known standard deviation of y.[in] double*
- Y: second input [Float64Array][@stdlib/array/float64].[in] CBLAS_INT
- strideY: stride length for Y.[in] CBLAS_INT
- offsetY: starting index for Y.[out] struct stdlib_stats_ztest_two_sample_results_float64*
- results: output [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
`c`
void stdlib_strided_dztest2_ndarray( const CBLAS_INT NX, const CBLAS_INT NY, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const double alpha, const double diff, const double sigmax, const double X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double sigmay, const double Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, struct stdlib_stats_ztest_two_sample_float64_results *results );
`c
#include "stdlib/stats/strided/dztest2.h"
#include "stdlib/stats/base/ztest/two-sample/results/float64.h"
#include "stdlib/stats/base/ztest/alternatives.h"
#include
#include
int main( void ) {
// Create a strided arrays:
const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
const double y[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
// 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_float64_results results = {
.rejected = false,
.alpha = 0.0,
.alternative = STDLIB_STATS_ZTEST_TWO_SIDED,
.pValue = 0.0,
.statistic = 0.0,
.ci = { 0.0, 0.0 },
.nullValue = 0.0,
.xmean = 0.0,
.ymean = 0.0
};
// Compute a Z-test:
stdlib_strided_dztest2( NX, NY, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05, 5.0, 3.0, x, strideX, 3.0, y, strideY, &results );
// Print the result:
printf( "Statistic: %lf\n", results.statistic );
printf( "Null hypothesis was %s\n", ( results.rejected ) ? "rejected" : "not rejected" );
}
`
*
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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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