A Monte Carlo Investigation of the Fisher Z Transformation for Normal and Nonnormal Distributions

The Fisher transformation of the sample correlation coefficient r (1915, 1921) and two related techniques by Gayen (1951) and Jeyaratnam (1992) are examined for robustness to nonnormality. Monte Carlo analyses compare combinations of sample sizes and population parameters for seven bivariate distributions. The Fisher, Gayen, and Jeyaratnam approaches are shown to provide useful results for a bivariate normal distribution with any population correlation coefficient rho and for nonnormal bivariate distributions when rho = 0. In contrast, the techniques are virtually useless for nonnormal bivariate distributions when rho not equal to 0.0. Surprisingly, small samples are found to provide better estimates than large samples for skewed and symmetric heavy-tailed bivariate distributions.