Meta-analyzing dependent correlations with correction for artifacts that multiplicatively attenuate the true correlation.

Previous procedures for meta-analyzing dependent correlations have been found to overestimate or underestimate the true variation in effect sizes. Samplewise-adjusted procedures have been shown to perform better than simple within-study means when meta-analyzing dependent correlations. However, such procedures cannot be applied when correction for artifacts such as unreliability is desired. In the present study, we extended the procedures to correct for attenuation due to artifacts when meta-analyzing dependent correlations. Monte Carlo simulation was conducted in order to examine conditions with various degrees of dependence, degrees of heterogeneity, sample sizes, and numbers of studies, among other factors. The previous procedures, including the samplewise-adjusted procedures without correction, yielded biased point estimates and confidence intervals with low coverage probabilities of the population mean correlation and degree of heterogeneity. More importantly, the bias and undercoverage of the confidence interval increased with the mean sample size and number of studies in many conditions. The new samplewise-adjusted procedures with correction for attenuation yielded negligible biases when estimating the mean population correlation, even in the presence of dependent correlations. Given that the need for correction for attenuation due to artifacts is becoming more recognized in meta-analysis, our findings highlight the importance of such considerations when meta-analyzing dependent correlations. Conditions under which these procedures can be further improved are also discussed.