Bias and Precision of Alternate Estimators in Meta

We describe a new estimator (labeled Morris) for meta-analysis. The Morris estimator combines elements of both the Schmidt-Hunter and Hedges estimators. The new estimator is compared to (a) the Schmidt-Hunter estimator, (b) the Schmidt-Hunter estimator with variance correction for the number of studies (“k correction”), (c) the Hedges random-effects estimator, and (d) the Bonett unit weights estimator in a Monte Carlo simulation. The simulation was designed to represent realistic conditions faced by researchers, including population random-effects distributions, numbers of studies, and skewed sample size distributions. The simulation was used to evaluate the estimators with respect to bias, coverage of the 95% confidence interval of the mean, and root mean square error of estimates of the population mean. We also evaluated the quality of credibility intervals. Overall, the new estimator provides better coverage and slightly better credibility values than other commonly used methods. Thus it has advantages of both commonly used approaches without the apparent disadvantages. The new estimator can be implemented easily with existing software; software used in the study is available online, and an example is included in the appendix in the Supplemental Material available online