Fisher Z Transformation is used to transform the sampling distribution of Pearson’s r (i.e. the correlation coefficient) into a normally distributed variable "Z". The "z" in Fisher Z stands for a z-score. It was developed by Fisher and so it is named as Fisher's Z transformation. Substitute the values of r and size in the Fisher z transformation equation for transforming the Pearson product-moment correlation coefficient into z' (Z_{r}) and to find the standard error (SE_{zr}).

SE

Where,

Z

SE

r = Correlation Coefficient

n = Size

Fisher's z' is used to find confidence intervals for both r and differences between correlations. Use the above Fisher z transformation equation to test the significance of the difference between two correlation coefficients, r1 and r2 from independent samples.