DescTools (version 0.99.60)

FisherZ: Fisher z-Transformation

Description

Convert a correlation to a z score or z to r using the Fisher transformation.

Usage

FisherZ(rho)
FisherZInv(z)

Value

z value corresponding to r (in FisherZ)
r corresponding to z (in FisherZInv)

Arguments

rho

the Pearson's correlation coefficient

z

a Fisher z transformed value

Author

William Revelle ,
slight modifications Andri Signorell based on R-Core code

Details

The sampling distribution of Pearson's r is not normally distributed. Fisher developed a transformation now called "Fisher's z-transformation" that converts Pearson's r to the normally distributed variable z. The formula for the transformation is:

$$z_r = tanh^{-1}(r) = \frac{1}{2}log\left ( \frac{1+r}{1-r}\right )$$

See Also

cor.test

Examples

cors <- seq(-.9, .9, .1)

zs <- FisherZ(cors)
rs <- FisherZInv(zs)
round(zs, 2)
n <- 30
r <- seq(0, .9, .1)
rc <- t(sapply(r, CorCI, n=n))
t <- r * sqrt(n-2) / sqrt(1-r^2)
p <- (1 - pt(t, n-2)) / 2

r.rc <- data.frame(r=r, z=FisherZ(r), lower=rc[,2], upper=rc[,3], t=t, p=p)

round(r.rc,2)