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dztest2

README.md

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).

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" );
}