Fisher's z transformation

the logarithmic transformation of Pearson's correlation coefficient. Its common use is in the z test which compares the size of two correlation coefficients from two unrelated samples. (This is obviously different from the more conventional test of whether a single correlation coefficient differs from zero.) Without [Page 67] the transformation, the distribution of differences between the two correlation coefficients becomes very skewed and unmanageable.

Table F.5 r to z transformation

This transformation may be found by looking up the appropriate value in a table or by computing it directly using the following formula where loge stands for the natural logarithm and r for Pearson's correlation:

The values of Pearson's correlation vary from 0 to ± 1 as shown in Table F.5 and the values of the z correlation from 0 to about ±3 (though, effectively, infinity).