Increasing the replicability for linear models via adaptive significance levels

We put forward an adaptive \(\alpha \) (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) general i.i.d. The calibration proposed this paper may be interpreted a Bayes–non-Bayes compromise, of simple translation Bayes factor on frequentist terms leads to statistical consistency, most importantly, it is step toward statistics promotes replicable scientific findings.