Compute a Pearson product-moment correlation test between paired samples.
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> Compute a Pearson product-moment correlation test between paired samples.
``bash`
npm install @stdlib/stats-pcorrtest
`javascript`
var pcorrtest = require( '@stdlib/stats-pcorrtest' );
#### pcorrtest( x, y\[, opts] )
By default, the function performs a t-test for the null hypothesis that the paired data in [arrays][mdn-array] or [typed arrays][mdn-typed-array] x and y have a [Pearson correlation coefficient][pearson-correlation] of zero.
`javascript
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.
`javascript
console.log( out.print() );
/* e.g., =>
t-test 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.two-sided
- alternative: Either , less or greater. Indicates whether the alternative hypothesis is that x has a larger mean than y (greater), x has a smaller mean than y (less) or the means are the same (two-sided). Default: two-sided.number
- rho: denoting the correlation between the x and y 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.
`javascript
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
t-test 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 two-sided test is performed. To perform either of the one-sided tests, set the alternative option to less or greater.
`javascript
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
t-test 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
t-test 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 z-transformation][fisher-transform].
`javascript
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
*/
`
`javascript
var rnorm = require( '@stdlib/random-base-normal' );
var sqrt = require( '@stdlib/math-base-special-sqrt' );
var pcorrtest = require( '@stdlib/stats-pcorrtest' );
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 - (rhorho) ) );
}
out = pcorrtest( x, y );
table = out.print();
console.log( table );
out = pcorrtest( x, y, {
'rho': 0.5
});
table = out.print();
console.log( table );
`
*
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
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[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
[fisher-transform]: https://en.wikipedia.org/wiki/Fisher_transformation
[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays