Meta-Analysis Calculations Based on Independent and Nonindependent Cases

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Abstract
Meta-analysis calculations, including both validity generalization and reliability generalization, are based on the assumption that the correlations or standardized mean differences are statistically independent. This assumption is frequently violated because studies often report more than one correlation or effect size based on the same sample. The purpose of this study was to determine the effect of including nonindependent correlations in Hunter and Schmidt’s meta-analysis method on the estimated population standard deviation. First, the method for estimating the population standard deviation was examined and four new estimation methods were suggested and evaluated. The evaluation indicated that the Hunter and Schmidt method will underestimate the true population standard deviation, and the new methods were developed to correct for this. Second, a pseudo–Monte Carlo study consisting of 36 different simulated cases was conducted to illustrate the behavior of both the Hunter and Schmidt estimators and the new methods.