Fig. 2: Bias: p-hacking selection; MAIVE denotes the estimator’s unweighted version.

Notes: The true effect in the simulation is set to 1. The vertical axis shows the bias of meta-analysis estimators. A higher correlation (on the bottom horizontal axis) between the main and control regression variables is associated with more relative importance of spurious precision (top horizontal axis). In the Methods section and the Supplementary Information (S1) we provide details on the simulations. The dashed line shows the performance of the simple mean of published estimates. Panels show (a) a comparison of biases for all unadjusted estimators; bias for (b) the fixed effect or weighted least squares estimator with adjustment, (c) the adjusted precision-effect test and precision-effect estimate with standard errors, (d) the adjusted endogenous kink estimator, (e) the adjusted weighted average of adequately powered, (f) the adjusted Andrews and Kasy estimator, (g) the adjusted p-uniform* method; and (h) a comparison of biases for all adjusted estimators. All estimators in panel (h) use MAIVE-adjusted standard errors; the default is the MAIVE version of PET-PEESE without weights.