The Use of Fisher’s Z in Schmidt-Hunter–type Meta-Analyses

Abstract

Over the past few years, there has been some dispute as to whether Fisher’s Z or the Pearson correlation (r) should be used in Schmidt-Hunter–type meta-analyses. The two major reasons that Z has not been recommended are the possibly larger positive bias in estimating mean population correlation (M_ρ) and the problem of estimating the standard deviation of population correlations (SD_ρ). In this study, two new methods of estimating M_ρ and SD_ρ by using Z are suggested and tested by Monte Carlo simulations. The results show no consistent advantage to using r instead of Z or vice versa in estimating both M_ρ and SD_ρ In fact, the estimated M_ρ and SD_ρ from all three methods were highly similar and were almost identical when rounded off.