Fisher-Transformation for Correlation to z-Score
Convert a correlation to a z score or z to r using the Fisher transformation or find the confidence intervals for a specified correlation.
FisherZ(rho)
FisherZInv(z)
CorCI(rho, n, conf.level = 0.95, alternative = c("two.sided", "less", "greater"))rho |
the Pearson's correlation coefficient |
z |
a Fisher z transformed value |
n |
sample size used for calculating the confidence intervals |
alternative |
is a character string, one of |
conf.level |
confidence level for the returned confidence interval, restricted to lie between zero and one. |
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≤ft ( \frac{1+r}{1-r}\right )
z value corresponding to r (in FisherZ)
r corresponding to z (in FisherZInv)
rho, lower and upper confidence intervals (CorCI)
William Revelle <revelle@northwestern.edu>,
slight modifications Andri Signorell <andri@signorell.net> based on R-Core code
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)
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