Having discussed the “p-values overstate the evidence against the null fallacy” many times over the past few years, I leave it to readers to disinter the issues (pro and con), and appraise the assumptions, in the most recent rehearsal of the well-known Bayesian argument. There’s nothing intrinsically wrong with demanding everyone work with a lowered p-value–if you’re so inclined to embrace a single, dichotomous standard without context-dependent interpretations, especially if larger sample sizes are required to compensate the loss of power. But lowering the p-value won’t solve the problems that vex people (biasing selection effects), and is very likely to introduce new ones (see my comment). Kelly Servick, a reporter from Science, gives the ingredients of the main argument given by “a megateam of reproducibility-minded scientists” in an article out today:
To explain to a broader audience how weak the .05 statistical threshold really is, Johnson joined with 71 collaborators on the new paper (which partly reprises an argument Johnson made for stricter p-values in a 2013 paper). Among the authors are some big names in the study of scientific reproducibility, including psychologist Brian Nosek of the University of Virginia in Charlottesville, who led a replication effort of high-profile psychology studies through the nonprofit Center for Open Science, and epidemiologist John Ioannidis of Stanford University in Palo Alto, California, known for pointing out systemic flaws in biomedical research.
The authors set up a scenario where the odds are one to 10 that any given hypothesis researchers are testing is inherently true—that a drug really has some benefit, for example, or a psychological intervention really changes behavior. (Johnson says that some recent studies in the social sciences support that idea.) If an experiment reveals an effect with an accompanying p-value of .05, that would actually mean that the null hypothesis—no real effect—is about three times more likely than the hypothesis being tested. In other words, the evidence of a true effect is relatively weak.
But under those same conditions (and assuming studies have 100% power to detect a true effect)—requiring a p-value at or below .005 instead of .05 would make for much stronger evidence: It would reduce the rate of false-positive results from 33% to 5%, the paper explains.
Her article is here.
From the perspective of the Bayesian argument on which the proposal is based, the p-value appears to exaggerate evidence, but from the error statistical perspective, it’s the Bayesian inference (to the alternative) that exaggerates the inference beyond what frequentists allow. Greenland, Senn, Rothman, Carlin, Poole, Goodman, Altman (2016, p. 342) observe, correctly, that whether “P-values exaggerate the evidence” “depends on one’s philosophy of statistics and the precise meaning given to the terms involved”. 
Share your thoughts.
 .”..it has been argued that P values overstate evidence against test hypotheses, based on directly comparing P values against certain quantities (likelihood ratios and Bayes factors) that play a central role as evidence measures in Bayesian analysis … Nonetheless, many other statisticians do not accept these quantities as gold standards” (Greenland et al, p. 342).