The statistical basis of meta-analysis

Two models for study-to-study variation in a meta-analysis are presented, critiqued and illustrated. One, the fixed effects model, takes the studies being analysed as the universe of interest; the other, the random effects model, takes these studies as representing a sample from a larger population of possible studies. With emphasis on clinical trials, this paper illustrates in some detail the application of both models to three summary measures of the effect of an experimental intervention versus a control: the standardized difference for comparing two means, and the relative risk and odds ratio for comparing two proportions.