Averaging Correlation Coefficients: Influence of Heterogeneity and Set Size

Silver and Dunlap (1987) recently investigated two methods for averaging correlations: (a) simple average of rs, and (b) average of Fisher's z transformations of r backtransformed to r. The latter method was found to be less positively biased than the simple average of rs was negatively biased. The current study extends these results by demonstrating that the z-transformation method is less susceptible to heterogeneity in the correlations that are averaged, but that the absolute magnitude of bias in the two approaches becomes similar as set size increases.