z.transform function

Variance-Stabilizing Transformations of the Correlation Coefficient

z.transform implements Fisher's (1921) first-order and Hotelling's (1953) second-order transformations to stabilize the distribution of the correlation coefficient. After the transformation the data follows approximately a normal distribution with constant variance (i.e. independent of the mean).

The Fisher transformation is simply z.transform(r) = atanh(r).

Hotelling's transformation requires the specification of the degree of freedom kappa of the underlying distribution. This depends on the sample size n used to compute the sample correlation and whether simple ot partial correlation coefficients are considered. If there are p variables, with p-2 variables eliminated, the degree of freedom is kappa=n-p+1. (cf. also dcor0).

z.transform(r)
hotelling.transform(r, kappa)

Arguments

• r: vector of sample correlations
• kappa: degrees of freedom of the distribution of the correlation coefficient

Returns

The vector of transformed sample correlation coefficients.

Author(s)

Korbinian Strimmer (https://strimmerlab.github.io).

References

Fisher, R.A. (1921). On the 'probable error' of a coefficient of correlation deduced from a small sample. Metron, 1 , 1--32.

Hotelling, H. (1953). New light on the correlation coefficient and its transformation. J. Roy. Statist. Soc. B, 15 , 193--232.

See Also

dcor0, kappa2n.

Examples

# load GeneNet library
library("GeneNet")

# small example data set 
r <- c(-0.26074194, 0.47251437, 0.23957283,-0.02187209,-0.07699437,
       -0.03809433,-0.06010493, 0.01334491,-0.42383367,-0.25513041)

# transformed data
z1 <- z.transform(r)
z2 <- hotelling.transform(r,7)
z1
z2