fisherz: Function to compute Fisher z transformation

In survcomp: Performance Assessment and Comparison for Survival Analysis

Description

The function computes the Fisher z transformation useful to calculate the confidence interval of Pearson's correlation coefficient.

Usage

fisherz(x, inv = FALSE, eps = 1e-16)

Arguments

x	value, e.g. Pearson's correlation coefficient
inv	TRUE for inverse Fisher z transformation, FALSE otherwise
eps	tolerance for extreme cases, i.e. |x| \approx 1 when inv = FALSE and |x| \approx Inf when inv = TRUE

Details

The sampling distribution of Pearson's ρ is not normally distributed. R. A. Fisher developed a transformation now called “Fisher's z transformation” that converts Pearson's ρ to the normally distributed variable z. The formula for the transformation is

z = 1 / 2 [ \log(1 + ρ) - \log(1 - ρ) ]

Two attributes of the distribution of the z statistic: (1) It is normally distributed and (2) it has a known standard error of

σ_z = 1 / √{N - 3}

where N is the number of samples.

Fisher's z is used for computing confidence intervals on Pearson's correlation and for confidence intervals on the difference between correlations.

Value

Fisher's z statistic

Author(s)

Benjamin Haibe-Kains

References

R. A. Fisher (1915) "Frequency distribution of the values of the correlation coefficient in samples of an indefinitely large population". Biometrika, 10,pages 507–521.

See Also

cor

Examples

set.seed(12345)
x1 <- rnorm(100, 50, 10)
x2 <- runif(100,.5,2)
cc <- cor(x1, x2)
z <- fisherz(x=cc, inv=FALSE)
z.se <- 1 / sqrt(100 - 3)
fisherz(z, inv=TRUE)

Example output

Loading required package: survival
Loading required package: prodlim
[1] -0.1327014

survcomp documentation built on Nov. 8, 2020, 4:54 p.m.