dztest2

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).

Installation

npm install @stdlib/stats-strided-dztest2

Usage

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.

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.
• NY: number of indexed elements in y.
• alternative: alternative hypothesis.
• alpha: significance level.
• diff: difference in means under the null hypothesis.
• sigmax: known standard deviation of x.
• x: first input Float64Array.
• strideX: stride length for x.
• sigmay: known standard deviation of y.
• y: second input Float64Array.
• strideY: stride length for y.
• out: output results object.

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,

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 views.

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.

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.
• offsetY: starting index for y.

While 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

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

Notes

• 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.

Examples

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 APIs

Usage

#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.

#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.
• NY: [in] CBLAS_INT number of indexed elements in y.
• alternative: [in] enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative hypothesis.
• alpha: [in] double significance level.
• diff: [in] double difference in means under the null hypothesis.
• sigmax [in] double known standard deviation of x.
• X: [in] double* first input Float64Array.
• strideX: [in] CBLAS_INT stride length for X.
• sigmay [in] double known standard deviation of y.
• Y: [in] double* second input Float64Array.
• strideY: [in] CBLAS_INT stride length for Y.
• results: [out] struct stdlib_stats_ztest_two_sample_results_float64* output results object.

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.

#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.
• NY: [in] CBLAS_INT number of indexed elements in y.
• alternative: [in] enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative hypothesis.
• alpha: [in] double significance level.
• diff: [in] double difference in means under the null hypothesis.
• sigmax [in] double known standard deviation of x.
• X: [in] double* first input Float64Array.
• strideX: [in] CBLAS_INT stride length for X.
• offsetX: [in] CBLAS_INT starting index for X.
• sigmay [in] double known standard deviation of y.
• Y: [in] double* second input Float64Array.
• strideY: [in] CBLAS_INT stride length for Y.
• offsetY: [in] CBLAS_INT starting index for Y.
• results: [out] struct stdlib_stats_ztest_two_sample_results_float64* output results object.

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 );

Examples

#include "stdlib/stats/strided/dztest2.h"
#include "stdlib/stats/base/ztest/two-sample/results/float64.h"
#include "stdlib/stats/base/ztest/alternatives.h"
#include <stdbool.h>
#include <stdio.h>

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" );
}

Notice

This package is part of 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, see the main project repository.

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License

See LICENSE.

Copyright

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