Does Every Study? Implementing Ordinal Constraint in Meta-Analysis

The most prominent goal when conducting a meta-analysis is to estimate the true effect size across a set of studies. This approach is problematic whenever the analyzed studies have qualitatively different results, i.e. some studies show an effect in the predicted direction while others show no effect and still others show an effect in the opposite direction. In case of such qualitative differences, the average effect may be a product of different mechanisms, and therefore uninterpretable. The first question in any meta-analysis should therefore be whether all studies show an effect in the same, expected direction. To tackle this question a model with ordinal constraints is proposed where the ordinal constraint holds each study in the set. This "every study" model is compared to a set of alternative models, such as an unconstrained model that predicts effects in both directions. If the ordinal constraints hold, one underlying mechanism may suffice to explain the results from all studies, and this result could be supported by reduced between-study heterogeneity. A major implication is then that average effects become interpretable. We illustrate the model comparison approach using Carbajal et al.'s (2021) meta-analysis on the familiar-word-recognition effect, show how predictor analyses can be incorporated in the approach, and provide R-code for interested researchers. As common in meta-analysis, only surface statistics (such as effect size and sample size) are provided from each study, and the modeling approach can be adapted to suit these conditions.