Estimation of and testing significance for a common correlation coefficient

The new estimators, based on Hotelling's (Hotelling, 1953) adjusted Z statistic (Fisher, 1921), of a common corrlation coefficient ρ from k≧2 independent random samples drawn from bivariate normal population are developed. By using a simulation study these estimators are compared with three estimators studied by Donner and Rosner (Applied Statistics, 1980). For testing the significance of the common ρ we derive the C(α) test statistic and the likelihood ratio statistic. By using the same simulation study we compare the performance of these statistics with a few others based on estimators of the common ρ. An estimator based on Hotelling's adjusted Z-statistic, applicable to both equal and unequal sample sizes, perform best for ρ < 5 whereas an estimator based on Fisher's Z statistic performs best for ρ≧.5. For testing significance of the common correlation the C(α) test statistic (Neyman, 1959) performs best with respect to both size and power and also it has a remarkably simple form.