Inference for Pearson correlation

Installation & Usage

npm install fisher-transform

Require as follows:

var fisher = require('fisher-transform');

fisher exports the following functions:

fisherTest(rho, n, [alpha, alternative, rho_0])

The function parameters are:

• rho: the Pearson correlation for which inference should be carried out
• n: the number of sample observations
• alpha: the significance level of the test, default value is 0.05
• alternative: default value "two-sided", for one-sided tests options "greater" and "less" exist
• rho_0: the value of rho assumed under the null hypothesis, default value is 0

Specifically, the two-sided test is

H_0: rho = rho_0 vs. H_1: rho != rho_0

and the one-sided tests are

H_0: rho = rho_0 vs. H_1: rho >= rho_0

and

H_0: rho = rho_0 vs. H_1: rho <= rho_0

For the chosen test, its p-value is calculated. In addition, a 1-alpha confidence interval is constructed by inverting the test statistic. The function returns an object with with two keys: pvalue and CI. The former holds the pvalue, while the latter is an Array with two elements, the lower and upper bounds of the calculated confidence interval.

r2z(r)

Applies the Fisher transformation to r to obtain z, where z = arctanh(r)

z2r(z)

Applies the inverse Fisher transformation to z in order to recover r, where r = tanh(z)

zScore(r, r_0, n)

Returns the Fisher z-score for Pearson correlation r under the null hypothesis that r = r_0. Approximately, the z-score follows a standard normal distribution.

Unit Tests

Run tests via the command npm test

---

License

MIT license.