Lower the statistical significance threshold to 0.005—or 0.001?
D. R. Bickel, “Sharpen statistical significance: Evidence thresholds and Bayes factors sharpened into Occam’s razors,” Working Paper, University of Ottawa, <hal-01851322> https://hal.archives-ouvertes.fr/hal-01851322 (2018). 2018 preprint
“The Fiducialist Papers” archived in favor of “sIBEe”
The name of the website The Fiducialist Papers: Evidence and Likelihood was just broadened to Statistical Inference to the Best Explanation of the Evidence (sIBEe).
Pre-data insights update priors via Bayes’s theorem
D. R. Bickel, “Bayesian revision of a prior given prior-data conflict, expert opinion, or a similar insight: A large-deviation approach,” Statistics 52, 552-570 (2018). Full text | 2015 preprint | Simple explanation
How to adjust statistical inferences for the simplicity of distributions
D. R. Bickel, “Confidence intervals, significance values, maximum likelihood estimates, etc. sharpened into Occam’s razors,” Working Paper, University of Ottawa, <hal-01799519> https://hal.archives-ouvertes.fr/hal-01799519 (2018). 2018 preprint | Slides
Should the default significance level be changed from 0.05 to 0.005?
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?
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“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?
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