fisherz {survcomp} | R Documentation

## Function to compute Fisher z transformation

### 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)

[Package survcomp version 1.40.0 Index]