Fisher's z'

The sampling distribution of Pearson's r is not normally distributed (click here for an illustration). Fisher developed a transformation now called "Fisher's z' transformation" that converts Pearson's r's to the normally distributed variable z'. The formula for the transformation is:

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

where ln is the natural logarithm. It is not important to understand how Fisher came up with this formula. What is important are two attributes of the distribution of the z' statistic: (1) It is normal and (2) it has a known standard error of:

Fisher's z' is used for computing confidence intervals on Pearson's correlation and for confidence intervals on the difference between correlations. You can use the r to z' table. to convert from r to z' and back.