# FisherZ: Fisher-Transformation for Correlation to z-Score In DescTools: Tools for Descriptive Statistics

## 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

 1 2 3 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 <[email protected]>,
slight modifications Andri Signorell <[email protected]> based on R-Core code

cor.test

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 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) 

### Example output

 [1] -1.47 -1.10 -0.87 -0.69 -0.55 -0.42 -0.31 -0.20 -0.10  0.00  0.10  0.20
[13]  0.31  0.42  0.55  0.69  0.87  1.10  1.47
r    z lower upper     t    p
1  0.0 0.00 -0.36  0.36  0.00 0.25
2  0.1 0.10 -0.27  0.44  0.53 0.15
3  0.2 0.20 -0.17  0.52  1.08 0.07
4  0.3 0.31 -0.07  0.60  1.66 0.03
5  0.4 0.42  0.05  0.66  2.31 0.01
6  0.5 0.55  0.17  0.73  3.06 0.00
7  0.6 0.69  0.31  0.79  3.97 0.00
8  0.7 0.87  0.45  0.85  5.19 0.00
9  0.8 1.10  0.62  0.90  7.06 0.00
10 0.9 1.47  0.80  0.95 10.93 0.00


DescTools documentation built on Sept. 13, 2017, 9:04 a.m.