Fitting Continuous Models to Effect Size Data

Quantitative methods for research synthesis usually involve calculation of an estimate of effect size for each of a series of studies. Statistical analyses in research synthesis attempt to relate explanatory variables to the effect sizes obtained from the series of studies. Some problems with ad hoc methods, such as ordinary least squares regression analysis using estimates of effect size, are described. Maximum likelihood estimation of the parameters in linear models for effect sizes is discussed and the asymptotic distribution of the estimators is obtained. An alternative estimator is derived which is computationally simpler, but has the same asymptotic distribution as the maximum likelihood estimator. A natural test for model specification is also given. The small sample accuracy of the asymptotic distribution theory derived in this paper is investigated via a simulation study.