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Correlation Test
Compute a Pearson productmoment correlation test between paired samples.
Installation
npm install @stdlib/statspcorrtest
Usage
var pcorrtest = require( '@stdlib/statspcorrtest' );
pcorrtest( x, y[, opts] )
By default, the function performs a ttest for the null hypothesis that the paired data in arrays or typed arrays x
and y
have a Pearson correlation coefficient of zero.
var x = [ 0.7, 1.6, 0.2, 1.2, 0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
var y = [ 1.9, 0.8, 1.1, 0.1, 0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
var out = pcorrtest( x, y );
/* e.g., returns
{
'alpha': 0.05,
'rejected': true,
'pValue': ~0.006,
'statistic': ~3.709,
'ci': [ ~0.332, ~0.95 ],
'nullValue': 0,
'pcorr': ~0.795,
// ...
}
*/
The returned object comes with a .print()
method which when invoked will print a formatted output of the results of the hypothesis test. print
accepts a digits
option that controls the number of decimal digits displayed for the outputs and a decision
option, which when set to false
will hide the test decision.
console.log( out.print() );
/* e.g., =>
ttest for Pearson correlation coefficient
Alternative hypothesis: True correlation coefficient is not equal to 0
pValue: 0.006
statistic: 3.709
95% confidence interval: [0.3315,0.9494]
Test Decision: Reject null in favor of alternative at 5% significance level
*/
The function accepts the following options
:

alpha:
number
in the interval[0,1]
giving the significance level of the hypothesis test. Default:0.05
. 
alternative: Either
twosided
,less
orgreater
. Indicates whether the alternative hypothesis is thatx
has a larger mean thany
(greater
),x
has a smaller mean thany
(less
) or the means are the same (twosided
). Default:twosided
. 
rho:
number
denoting the correlation between thex
andy
variables under the null hypothesis. Default:0
.
By default, the hypothesis test is carried out at a significance level of 0.05
. To choose a different significance level, set the alpha
option.
var x = [ 0.7, 1.6, 0.2, 1.2, 0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
var y = [ 1.9, 0.8, 1.1, 0.1, 0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
var out = pcorrtest( x, y, {
'alpha': 0.1
});
var table = out.print();
/* e.g., returns
ttest for Pearson correlation coefficient
Alternative hypothesis: True correlation coefficient is not equal to 0
pValue: 0.006
statistic: 3.709
90% confidence interval: [0.433,0.9363]
Test Decision: Reject null in favor of alternative at 10% significance level
*/
By default, a twosided test is performed. To perform either of the onesided tests, set the alternative
option to less
or greater
.
var x = [ 0.7, 1.6, 0.2, 1.2, 0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
var y = [ 1.9, 0.8, 1.1, 0.1, 0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
var out = pcorrtest( x, y, {
'alternative': 'less'
});
var table = out.print();
/* e.g., returns
ttest for Pearson correlation coefficient
Alternative hypothesis: True correlation coefficient is less than 0
pValue: 0.997
statistic: 3.709
95% confidence interval: [1,0.9363]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
out = pcorrtest( x, y, {
'alternative': 'greater'
});
table = out.print();
/* e.g., returns
ttest for Pearson correlation coefficient
Alternative hypothesis: True correlation coefficient is greater than 0
pValue: 0.003
statistic: 3.709
95% confidence interval: [0.433,1]
Test Decision: Reject null in favor of alternative at 5% significance level
*/
To test whether the correlation coefficient is equal to some other value than 0
, set the rho
option. Hypotheses tests for correlation coefficients besides zero are carried out using the Fisher ztransformation.
var x = [ 0.7, 1.6, 0.2, 1.2, 0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
var y = [ 1.9, 0.8, 1.1, 0.1, 0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
var out = pcorrtest( x, y, {
'rho': 0.8
});
/* e.g., returns
{
'alpha': 0.05,
'rejected': false,
'pValue': ~0.972,
'statistic': ~0.035,
'ci': [ ~0.332, ~0.949 ],
'nullValue': 0.8,
'pcorr': ~0.795,
// ...
}
*/
var table = out.print();
/* e.g., returns
Fisher's z transform test for Pearson correlation coefficient
Alternative hypothesis: True correlation coefficient is not equal to 0.8
pValue: 0.972
statistic: 0.0351
95% confidence interval: [0.3315,0.9494]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
Examples
var rnorm = require( '@stdlib/randombasenormal' );
var sqrt = require( '@stdlib/mathbasespecialsqrt' );
var pcorrtest = require( '@stdlib/statspcorrtest' );
var table;
var out;
var rho;
var x;
var y;
var i;
rho = 0.5;
x = new Array( 300 );
y = new Array( 300 );
for ( i = 0; i < 300; i++ ) {
x[ i ] = rnorm( 0.0, 1.0 );
y[ i ] = ( rho * x[ i ] ) + rnorm( 0.0, sqrt( 1.0  (rho*rho) ) );
}
out = pcorrtest( x, y );
table = out.print();
console.log( table );
out = pcorrtest( x, y, {
'rho': 0.5
});
table = out.print();
console.log( table );
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.
Community
License
See LICENSE.
Copyright
Copyright © 20162024. The Stdlib Authors.