filtherton

There are plenty of things wrong with 95/5 hypothesis test paradigm. One of the primary problems is that it can shift the focus from clinical significance to statistical significance. So you'll have papers that get press for finding a statistically significant correlation between an exposure and a disease with little attention paid to the magnitude of the correlation. This is why many journals require more than boilerplate statements about acceptance and rejection of hypothesis tests, like p-values and/or confidence intervals. Any discerning reader of medical research should be fairly skeptical of any research which doesn't mention effect size and a p-value or confidence interval. Another problem with the 95/5 is that it doesn't take into account multiple tests. These problems are widely known and accepted and various workarounds exist. Finally, 95/5 is completely arbitrary, and if you think about it, being wrong every one in twenty times isn't really that discerning a criterion in light of the sheer number of papers published every year.

With regards to Bayesian analysis, there is no small amount of controversy between Frequentists and Bayesians about which method is "better". That being said, medical research, ie, the randomized, controlled clinical trial, is one of the few places that the underlying assumptions of Frequentist methods really obtain well, so that Bayesian statistics aren't necessarily preferable for hypothesis testing in medical research (at least, I have yet to see much Bayesian analysis in any of the literature searches I've done).

Bayesian methods are useful for epidemiologic research, like observational or case control studies, where one can't really make the assumptions required by Frequentist methods. That Frequentist methods are typically used anyway is possibly a cause of the problems mentioned in the OP.