z.transform {GeneTS} | R Documentation |
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)
r |
vector of sample correlations |
kappa |
degrees of freedom of the distribution of the correlation coefficient |
The vector of transformed sample correlation coefficients.
Korbinian Strimmer (http://www.statistik.lmu.de/~strimmer/).
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.
# load GeneTS library library("GeneTS") # 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