A basic introduction to fixed-effect and random-effects models for meta-analysis

Res Synth Methods. 2010 Apr;1(2):97-111. doi: 10.1002/jrsm.12. Epub 2010 Nov 21.


There are two popular statistical models for meta-analysis, the fixed-effect model and the random-effects model. The fact that these two models employ similar sets of formulas to compute statistics, and sometimes yield similar estimates for the various parameters, may lead people to believe that the models are interchangeable. In fact, though, the models represent fundamentally different assumptions about the data. The selection of the appropriate model is important to ensure that the various statistics are estimated correctly. Additionally, and more fundamentally, the model serves to place the analysis in context. It provides a framework for the goals of the analysis as well as for the interpretation of the statistics. In this paper we explain the key assumptions of each model, and then outline the differences between the models. We conclude with a discussion of factors to consider when choosing between the two models. Copyright © 2010 John Wiley & Sons, Ltd.

Keywords: fixed‐effect; meta‐analysis; random‐effects; research synthesis; statistical models; systematic reviews.