A new method to explore inferential risks associated with each study in a meta-analysis: An approach based on Design Analysis

In the last ten years, scientific research has experienced an unprecedented “credibility’s crisis” of results. This means that researchers couldn't find the same results as in the original ones when conducting replication studies. In fact, the results showed that effects size were often not as strong as in the original studies and sometimes no effect was found. However, an important side-effect of the replicability crisis is that it increased the awareness of the problematic issues in the published literature and it promoted the development of new practices which would guarantee rigour, transparency and reproducibility. In the current work, the aim is to propose a new method to explore the inferential risks associated with each study in a meta-analysis. Specifically, this method is based on Design Analysis, a power analysis approach developed by @gelmanPowerCalculationsAssessing2014, which allows to analyse two other type of errors that are not commonly considered: the Type M (Magnitude) error and the Type S (Sign) error, concerning the magnitude and direction of the effects. We chose the Design Analysis approach because it allows to put more emphasis on the estimate of the effect size and it can be a valid tool available to researchers to make more conscious and informed decisions.