Fisher z' Transformation (Pearson r to z')

The sampling distribution of Pearson's correlation coefficient r does not follow the normal distribution. The so-called "Fisher z transformation" converts the standard Pearson's r to a normally distributed variable z', via:

z' = .5*[ln(1+r) - ln(1-r)]

where ln is the natural (base e) logarithm. The standard error of z is:

Fisher's z' is used for computing confidence intervals for the Pearson correlation coefficient, and for testing the significance of differences between correlation coefficients.

The Fisher z transformation can be computed via STATISTICA's Probability calculator facilities; see also Pearson Product Moment Correlation Distribution for details.