A Monte Carlo investigation of the Fisher Z transformation for normal and nonnormal distributions

The Fisher transformation of the sample correlation coefficient r (1915, 19 21) and two related techniques by Gayen (1951) and Jeyaratnam (1992) are ex amined for robustness to nonnormality. Monte Carlo analyses compare combina tions of sample sizes and population parameters for seven bivariate distrib utions. The Fisher, Gayen, and Jeyaratnam approaches are shown to provide u seful results for a bivariate normal distribution with any population corre lation coefficient rho and for nonnormal bivariate distributions when rho = 0. In contrast, the techniques are virtually useless for nonnormal bivaria te distributions when rho not equal 0.0. Surprisingly, small samples are fo und to provide better estimates than large samples for skewed and symmetric heavy-tailed bivariate distributions.