dztest

Compute a one-sample Z-test for a double-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.

Usage

var dztest = require( '@stdlib/stats/strided/dztest' );

dztest( N, alternative, alpha, mu, sigma, x, strideX, out )

Computes a one-sample Z-test for a double-precision floating-point strided array.

var Results = require( '@stdlib/stats/base/ztest/one-sample/results/float64' );
var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );

var results = new Results();
var out = dztest( 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.
alpha: significance level.
mu: mean value under the null hypothesis.
sigma: known standard deviation.
x: input Float64Array.
strideX: stride length for x.
out: output results object.

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,

var Results = require( '@stdlib/stats/base/ztest/one-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 results = new Results();
var out = dztest( 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 views.

var Results = require( '@stdlib/stats/base/ztest/one-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 results = new Results();
var out = dztest( x1.length, 'two-sided', 0.05, 0.0, 1.0, x1, 1, results );
// returns {...}

var bool = ( out === results );
// returns true

dztest.ndarray( N, alternative, alpha, mu, sigma, x, strideX, offsetX, out )

Computes a one-sample Z-test for a double-precision floating-point strided array using alternative indexing semantics.

var Results = require( '@stdlib/stats/base/ztest/one-sample/results/float64' );
var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 4.0, 4.0, 6.0, 6.0, 5.0 ] );

var results = new Results();
var out = dztest.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 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

var Results = require( '@stdlib/stats/base/ztest/one-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 results = new Results();
var out = dztest.ndarray( 5, 'two-sided', 0.05, 0.0, 1.0, x, 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 deviation is unknown, prefer a t-test.

Examples

var Results = require( '@stdlib/stats/base/ztest/one-sample/results/float64' );
var normal = require( '@stdlib/random/array/normal' );
var dztest = require( '@stdlib/stats/strided/dztest' );

var x = normal( 1000, 0.0, 1.0, {
    'dtype': 'float64'
});

var results = new Results();
var out = dztest( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, results );
// returns {...}

console.log( out.toString() );

C APIs

Usage

#include "stdlib/stats/strided/dztest.h"

stdlib_strided_dztest( N, alternative, alpha, mu, sigma, X, strideX, results )

Computes a one-sample Z-test for a double-precision floating-point strided array.

#include "stdlib/stats/base/ztest/one-sample/results/float64.h"
#include "stdlib/stats/base/ztest/alternatives.h"

struct stdlib_stats_ztest_one_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,
    .sd = 0.0
};

const double x[] = { 4.0, 4.0, 6.0, 6.0, 5.0 };

stdlib_strided_dztest( 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05, 0.0, 1.0, x, 1, &results );

The function accepts the following arguments:

N: [in] CBLAS_INT number of indexed elements.
alternative: [in] enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative hypothesis.
alpha: [in] double significance level.
mu: [in] double value of the mean under the null hypothesis.
sigma [in] double known standard deviation.
X: [in] double* input array.
strideX: [in] CBLAS_INT stride length for X.
results: [out] struct stdlib_stats_ztest_one_sample_results_float64* output results object.

void stdlib_strided_dztest( const CBLAS_INT N, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const double alpha, const double mu, const double sigma, const double *X, const CBLAS_INT strideX, struct stdlib_stats_ztest_one_sample_float64_results *results );

stdlib_strided_dztest_ndarray( N, alternative, alpha, mu, sigma, X, strideX, offsetX, results )

Computes a one-sample Z-test for a double-precision floating-point strided array using alternative indexing semantics.

#include "stdlib/stats/base/ztest/one-sample/results/float64.h"
#include "stdlib/stats/base/ztest/alternatives.h"

struct stdlib_stats_ztest_one_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,
    .sd = 0.0
};

const double x[] = { 4.0, 4.0, 6.0, 6.0, 5.0 };

stdlib_strided_dztest_ndarray( 5, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05, 0.0, 1.0, x, 1, 0, &results );

The function accepts the following arguments:

N: [in] CBLAS_INT number of indexed elements.
alternative: [in] enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative hypothesis.
alpha: [in] double significance level.
mu: [in] double value of the mean under the null hypothesis.
sigma [in] double known standard deviation.
X: [in] double* input array.
strideX: [in] CBLAS_INT stride length for X.
offsetX: [in] CBLAS_INT starting index for X.
results: [out] struct stdlib_stats_ztest_one_sample_results_float64* output results object.

void stdlib_strided_dztest_ndarray( const CBLAS_INT N, const enum STDLIB_STATS_ZTEST_ALTERNATIVE alternative, const double alpha, const double mu, const double sigma, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, struct stdlib_stats_ztest_one_sample_float64_results *results );

Examples

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

int main( void ) {
    // Create a strided array:
    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };

    // 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_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,
        .sd = 0.0
    };

    // Compute a Z-test:
    stdlib_strided_dztest( N, STDLIB_STATS_ZTEST_TWO_SIDED, 0.05, 5.0, 3.0, x, strideX, &results );

    // Print the result:
    printf( "Statistic: %lf\n", results.statistic );
    printf( "Null hypothesis was %s\n", ( results.rejected ) ? "rejected" : "not rejected" );
}

Name		Name	Last commit message	Last commit date
parent directory ..
benchmark		benchmark
docs		docs
examples		examples
include/stdlib/stats/strided		include/stdlib/stats/strided
lib		lib
src		src
test		test
README.md		README.md
binding.gyp		binding.gyp
include.gypi		include.gypi
manifest.json		manifest.json
package.json		package.json

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README.md

dztest

Usage

dztest( N, alternative, alpha, mu, sigma, x, strideX, out )

dztest.ndarray( N, alternative, alpha, mu, sigma, x, strideX, offsetX, out )

Notes

Examples

C APIs

Usage

stdlib_strided_dztest( N, alternative, alpha, mu, sigma, X, strideX, results )

stdlib_strided_dztest_ndarray( N, alternative, alpha, mu, sigma, X, strideX, offsetX, results )

Examples

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README.md

dztest

Usage

dztest( N, alternative, alpha, mu, sigma, x, strideX, out )

dztest.ndarray( N, alternative, alpha, mu, sigma, x, strideX, offsetX, out )

Notes

Examples

C APIs

Usage

stdlib_strided_dztest( N, alternative, alpha, mu, sigma, *X, strideX, *results )

stdlib_strided_dztest_ndarray( N, alternative, alpha, mu, sigma, *X, strideX, offsetX, *results )

Examples

stdlib_strided_dztest( N, alternative, alpha, mu, sigma, X, strideX, results )

stdlib_strided_dztest_ndarray( N, alternative, alpha, mu, sigma, X, strideX, offsetX, results )