Beyond Overall Effects: A Bayesian Approach to Finding Constraints in Meta-Analysis

Most meta-analyses focus on the behavior of meta-analytic means. In many cases, however, this mean is difficult to defend as a construct because the underlying distribution of studies reflects many factors, including how we as researchers choose to design studies. We present an alternative goal for meta-analysis. The analyst may ask about relations that are stable across all the studies. In a typical meta-analysis, there is a hypothesized direction (e.g., that violent video games increase, rather than decrease, aggressive behavior). We ask whether all studies in a meta-analysis have true effects in the hypothesized direction. If so, this is an example of a stable relation across all the studies. We propose 4 models: (a) all studies are truly null; (b) all studies share a single true nonzero effect; (c) studies differ, but all true effects are in the same direction; and (d) some study effects are truly positive, whereas others are truly negative. We develop Bayes factor model comparison for these models and apply them to 4 extant meta-analyses to show their usefulness.