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{{alias}}( x, y[, options] )
Computes a Pearson product-moment correlation test between paired samples.
By default, the function performs a t-test for the null hypothesis that the
data in arrays or typed arrays `x` and `y` is not correlated. A test against
a different population correlation can be carried out by supplying the `rho`
option. In this case, a test using the Fisher's z transform is conducted.
The returned object comes with a `.print()` method which when invoked will
print a formatted output of the results of the hypothesis test.
Parameters
----------
x: Array<number>
First data array.
y: Array<number>
Second data array.
options: Object (optional)
Options.
options.alpha: number (optional)
Nnumber in the interval `[0,1]` giving the significance level of the
hypothesis test. Default: `0.05`.
options.alternative: string (optional)
Either `two-sided`, `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'`.
options.rho: number (optional)
Number denoting the correlation under the null hypothesis.
Default: `0`.
Returns
-------
out: Object
Test result object.
out.alpha: number
Used significance level.
out.rejected: boolean
Test decision.
out.pValue: number
p-value of the test.
out.statistic: number
Value of test statistic.
out.ci: Array<number>
1-alpha confidence interval for the Pearson product-moment correlation
coefficient. The confidence interval is calculated using Fisher's
z-transform.
out.nullValue: number
Assumed correlation under H0 (equal to the supplied `rho` option).
out.alternative: string
Alternative hypothesis (`two-sided`, `less` or `greater`).
out.method: string
Name of test.
out.print: Function
Function to print formatted output.
Examples
--------
> var rho = 0.5;
> var x = new Array( 300 );
> var y = new Array( 300 );
> for ( var i = 0; i < 300; i++ ) {
... x[ i ] = {{alias:@stdlib/random/base/normal}}( 0.0, 1.0 );
... y[ i ] = ( rho * x[ i ] ) + {{alias:@stdlib/random/base/normal}}( 0.0,
... {{alias:@stdlib/math/base/special/sqrt}}( 1.0 - (rho*rho) ) );
... }
> var out = {{alias}}( x, y )
{
alpha: 0.05,
rejected: true,
pValue: 0,
statistic: 10.115805615994121,
ci: [ 0.4161679018930295, 0.5853122968949995 ],
alternative: 'two-sided',
method: 't-test for Pearson correlation coefficient',
nullValue: 0,
pcorr: 0.505582072355616,
}
// Print output:
> var table = out.print()
t-test for Pearson correlation coefficient
Alternative hypothesis: True correlation coefficient is not equal to 0
pValue: 0
statistic: 9.2106
95% confidence interval: [0.3776,0.5544]
Test Decision: Reject null in favor of alternative at 5% significance level
See Also
--------
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