z_fisher_test: Fisher's Z test for Pearson's correlation.
In gilberto-sassi/power:

Description Usage Arguments Details Value Examples

z_fisher_test performs test on Pearson's correlation using Fisher's Z transform.

1 2	z_fisher_test(x, y, rho0 = 0, alternative = "two.sided", conf_level = 0.95)

`x`	a numeric vector.
`y`	a numeric vector.
`rho0`	Pearson's correlation under null hypothesis.
`alternative`	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
`conf_level`	confidence level of the interval

It can be proved that \frac{1}{2}\ln≤ft(\frac{1 + r}{1- r} \right) has normal distribution with mean \frac{1}{2}\ln≤ft(\frac{1 + ρ}{1- ρ} \right) and variance σ^2 = \frac{1}{n - 3}.

z_fisher_test return a list with the following components:

statistic: statistic of test
p_value: p-value
alternative: a character string specifying the alternative hypothesis
lower_ci: lower bound in the confidence interval
upper_ci: upper bound in the confidence interval
conf_level: confidence level of the interval

# x and y are not correlated
Sigma <- matrix(c(1, 0, 0, 1), ncol = 2)
m <- MASS::mvrnorm(500, mu = c(0, 1), Sigma = Sigma)
z_fisher_test(m[, 1], m[, 2])
# x and y are correlated
Sigma <- matrix(c(1, 0.85, 0.85, 1), ncol = 2)
m <- MASS::mvrnorm(500, mu = c(0, 1), Sigma = Sigma)
z_fisher_test(m[, 1], m[, 2])