Increasing the replicability for linear models via adaptive significance levels

We put forward an adaptive α (type I error) that decreases as the information grows for hypothesis tests comparing nested linear models. A less elaborate adaptation was presented in Pérez and Pericchi (Stat Probab Lett 85:20–24, 2014) for general i.i.d. models. The calibration proposed in this paper may be interpreted as a Bayes–non-Bayes compromise, of a simple translation of a Bayes factor on frequentist terms that leads to statistical consistency, and most importantly, it is a step toward statistics that promotes replicable scientific findings.