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).
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 G variables, with G-2 variables eliminated, the degree of freedom is kappa=N-G+1.
(cf. also cor0.estimate.kappa
and 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.stat.uni-muenchen.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.
cor0.estimate.kappa
, dcor0
, kappa2N
.
# 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