z.transform {GeneTS} R Documentation

## Variance-Stabilizing Transformations of the Correlation Coefficient

### Description

`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`).

### Usage

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

### Arguments

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

### Value

The vector of transformed sample correlation coefficients.

### Author(s)

Korbinian Strimmer (http://www.stat.uni-muenchen.de/~strimmer/).

### 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.

`cor0.estimate.kappa`, `dcor0`, `kappa2N`.

### Examples

```# 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
```

[Package GeneTS version 2.3 Index]