A general linear model for estimating effect size in the presence of publication bias

When the process of publication favors studies with small p-values, and hence large effect estimates, combined estimates from many studies may be biased. This paper describes a model for estimation of effect size when there is selection based on one-tailed p-values. The model employs the method of maximum likelihood in the context of a mixed (fixed and random) effects general linear model for effect sizes. It offers a test for the presence of publication bias, and corrected estimates of the parameters of the linear model for effect magnitude. The model is illustrated using a well-known data set on the benefits of psychotherapy.