Further contributions in estimating an overall correlation coefficient

Our objectives in this research are to further study methodology for estimating an overall correlation coefficient from the combination of a number of bivariate samples. Provided are extensive exploratory simulation studies, theory, and numerical studies. Previous investigations were based on a small number of simulation studies and were very limited in scope. Another aim of the study is to provide guidelines for the applications of methods for estimating an overall correlation coefficient. Independent simulation programs are developed for a broad range of conditions.; We further investigate the methods of NILE, Fisher, Hotelling, and Standard Score for estimating an overall correlation coefficient through a wide range of simulation studies for a large variety of situations. Donner and Roser (1980) and Paul (1988) only completed limited simulation studies. We perform extensive simulation studies based on 10,000 replications in most of the simulation situations, which give us more accurate results.; We further study the standard score estimator through numerical approximation for estimating an overall correlation coefficient for equal correlation coefficients across studies in both equal and unequal sample size situations. We investigate and derive formulas for the MSE (mean square error), variance, and bias of the standard score estimator rs. We investigate the impact of unequal sample size on the estimators through simulation and numerical studies.; Although the exact mean and variance of the sample correlation coefficient is obtained only as infinite series, we show that we can obtain very good approximations of the MSE, variance, and bias by considering the approximation of mean and variance to the order 1ni2 when sample sizes increase to at least 20. We also show that adding more terms in the approximation of the mean and variance resulting in no significant improvement.; We further investigate the standard score estimator for estimating the combined correlation coefficient when outliers are present. We show the impact of outliers on the standard score estimator in a broad range of outlier conditions. We investigate criteria to detect and remove outliers from such bivariate samples. We compare the criteria to find more effective methods for detecting and removing outliers. Independent simulation programs are developed for a broad range of conditions. Another objective of the study is to provide guidelines for the applications of the methods.; We further investigate and develop a robust standard score method for estimating the combined correlation coefficient when outliers are present. We study and compare the criteria for detecting and removing outliers through robust approach and find an effective method that leads to efficient estimators in the presence of outliers. Independent simulation programs are developed for a broad range of conditions.; We investigate and develop a new estimator, the standard score maximum likelihood estimator, which can be obtained in a closed form. The existing MLE can not be obtained in a close form, but can only be obtained through an iteration procedure. We investigate and develop several approximate maximum likelihood estimators, which are easily applied in practice.