Modelling publication bias and p‐hacking

Publication bias and p‐hacking are two well‐known phenomena that strongly affect the scientific literature and cause severe problems in meta‐analyses. Due to these phenomena, the assumptions of meta‐analyses are seriously violated and the results of the studies cannot be trusted. While publication bias is very often captured well by the weighting function selection model, p‐hacking is much harder to model and no definitive solution has been found yet. In this paper, we advocate the selection model approach to model publication bias and propose a mixture model for p‐hacking. We derive some properties for these models, and we compare them formally and through simulations. Finally, two real data examples are used to show how the models work in practice.