  We put forward a novel calibration of p values, the "Adaptive Robust Lower
Bound" (ARLB) which maps p values into approximations of posterior
probabilities taking into account the effect of sample sizes. We build on the
Robust Lower Bound proposed by Sellke, Bayarri and Berger (2001), but we
incorporate a simple power of the sample size to make it adaptive to different
amounts of data.
  We present several illustrations from where it is apparent that the ARLB
closely approximates exact Bayes Factors. In particular, it has the same
asymptotics as posterior probabilities but avoiding the problems of "Bayesian
Information Criterion" (BIC) for small samples relative to the number of
parameters.
  We prove that the ARLB is consistent as the sample size grows, and that it is
information consistent (Berger and Pericchi, 2001) for the canonical Normal
case, but with methods that are keen to be generalized. So ARLB also avoids the
problems of certain conjugate priors as g-priors.
  In summary, this is a novel criterion easy to apply, as it only requires a
real p value, a sample size and parameter dimensionality. This method is
intended to aid the practitioners, who are increasingly aware of the lack of
reproducibility of traditional hypothesis testing "findings" but at the same
time, lack of concrete simple alternatives. Here is one.
