Correlational meta-analysis: independent and nonindependent cases.

Abstract

The purpose of this study was to determine the effect of the violation of the assumption of independence when combining correlation coefficients in a meta-analysis. In this Monte Carlo simulation the following four parameters were used with the values specified: N-the sample size within a study (20, 50, 100), p-the number of predictors (1, 2, 3, 5), rho( i)-the population intercorrelation among predictors (0, .3, .7), rho( p)-the population correlation between predictors and criterion (0, .3, .7). When cnly one predictor was used or when the intercorrelation among predictors equaled zero, the assumption of independence was not violated. The assumption of independence was violated when more than one predictor with an intercorrelation exceeding zero were used. Therefore, rho( i) the index of nonindependence was the main parameter of interest. For both r's and Fisher's z's, the means, medians, and standard deviations showed no discernible change over levels of rho( i) or p, but the precision of estimation of the expected values improved as N increased. The 90%, 95%, and 99% confidence intervals for both r's and Fisher's z's showed no change over levels of rho( i) or p, but the intervals narrowed as N increased.