Compute a one-sample Z-test for a 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 ≥ μ0versus the alternative hypothesisH1: μ < μ0.H0: μ ≤ μ0versus the alternative hypothesisH1: μ > μ0.H0: μ = μ0versus the alternative hypothesisH1: μ ≠ μ0.
var ztest = require( '@stdlib/stats/strided/ztest' );Computes a one-sample Z-test for a strided array.
var Results = require( '@stdlib/stats/base/ztest/one-sample/results/float64' );
var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var results = new Results();
var out = ztest( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, results );
// returns {...}
var bool = ( out === results );
// returns trueThe 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 array.
- 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 x = [ 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 = ztest( 5, 'two-sided', 0.05, 0.0, 1.0, x, 2, results );
// returns {...}
var bool = ( out === results );
// returns trueNote 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 = ztest( x1.length, 'two-sided', 0.05, 0.0, 1.0, x1, 1, results );
// returns {...}
var bool = ( out === results );
// returns trueComputes a one-sample Z-test for a strided array using alternative indexing semantics.
var Results = require( '@stdlib/stats/base/ztest/one-sample/results/float64' );
var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
var results = new Results();
var out = ztest.ndarray( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, 0, results );
// returns {...}
var bool = ( out === results );
// returns trueThe 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 x = [ 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 = ztest.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. - Both functions support array-like objects having getter and setter accessors for array element access (e.g.,
@stdlib/array/base/accessor). - Depending on the environment, the typed versions (
dztest,sztest, etc.) are likely to be significantly more performant.
var Results = require( '@stdlib/stats/base/ztest/one-sample/results/float64' );
var normal = require( '@stdlib/random/array/normal' );
var ztest = require( '@stdlib/stats/strided/ztest' );
var x = normal( 1000, 0.0, 1.0, {
'dtype': 'generic'
});
var results = new Results();
var out = ztest( x.length, 'two-sided', 0.05, 0.0, 1.0, x, 1, results );
// returns {...}
console.log( out.toString() );