`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.

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.

# NOT RUN { # 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 # }