R: Fisher-Transformation for Correlation to z-Score

FisherZ {DescTools} | R Documentation

## Fisher-Transformation for Correlation to z-Score

### Description

Convert a correlation to a z score or z to r using the Fisher transformation or find the confidence intervals for a specified correlation.

### Usage

    FisherZ(rho)
    FisherZInv(z)
    CorCI(rho, n, conf.level = 0.95, alternative = c("two.sided", "less", "greater"))

### Arguments

`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 `"greater"`, `"less"`, or `"two.sided"`, or the initial letter of each, indicating the specification of the alternative hypothesis. `"greater"` corresponds to positive association, `"less"` to negative association.
`conf.level` | confidence level for the returned confidence interval, restricted to lie between zero and one.

### 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's to the normally distributed variable z'. The formula for the transformation is:

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

### Value

z value corresponding to r (in FisherZ)
r corresponding to z (in FisherZInv)
rho, lower and upper confidence intervals (CorCI)

### Author(s)

William Revelle <revelle@northwestern.edu>,
slight modifications Andri Signorell <andri@signorell.net> based on R-Core code

### 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)

[Package DescTools version 0.99.26 Index]