The Fiducialist Papers: Evidence and Likelihood

My comments in this discussion of “Redefine statistical significance”:

The call for smaller significance levels cannot be based only on mathematical arguments that p values tend to be much lower than posterior probabilities, as Andrew Gelman and Christian Robert pointed out in their comment (“Revised evidence for statistical standards”).

In the rejoinder, Valen Johnson made it clear that the call is also based on empirical findings of non-reproducible research results. How many of those findings are significant at the 0.005 level? Should meta-analysis have a less stringent standard?

…

“Irreplicable results can’t possibly add empirical clout to the mathematical argument unless it is already known or assumed to be caused by a given cut-off, and further, that lowering it would diminish those problems.”

The preprint cites empirical results to support its use of the 1:10 prior odds. If that is in fact a reliable estimate of the prior odds for the reference class of previous studies, then, in the absence of other relevant information, it would be reasonable to use as input for Bayes’s theorem.

John Byrd asks, “Is 1:10 replicable?” Is it important to ask whether a 1:1 prior odds can be rejected at the 0.005 significance level?

END