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I like your papers too and cite them. If everyone followed them and Cox's to the letter we would not be in this mess. But that's like saying if everyone was sensible there would have been no World Wars. We must deal with sad human realities, like: words can matter more than math.

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Cox, like me, considers several benchmarks, & a "moderate" P-value is taken as indicating the parameter is < the upper CI bound. It's the data-dependent version of power analysis that gives the SEV for the CI-upper inference. Also relevant is this tweet

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♕Deborah Mayo♕

@learnfromerror

Mar 22, 2019

Replying to @matloff and @R__INDEX

Sure, but just because pts in a CI are not rejectable at the given level doesn't mean there's evidence for them.Rather, there's evidence the parameter is less than various upper CI bounds, say at the .9 level.

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See "Frequentist Statistics as a Theory of Inductive Inference" (Cox and Mayo 2006) phil.vt.edu/dmayo/personal

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Cox & Donnelly is from 2011.

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I know that, what is your pt?

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As an aside, here is another point from John Ioannidis 'Even the most clearly statistically sig results don't go anywhere> With roughly 40 % of the most highly cited papers refuted within a few years after discovery.'

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Where's the criterion for "refutation"? Was it (as often the case) P<0.05 in the initial research and P>0.05 in the subsequent research? Which is just what one should expect when studying small effects even if all the studies were perfect.

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If all studies were perfect this would rarely happen (because you made sure you have 99.x% power for effect sizes you were interested in). And even then, always repeat the experiment a few times. In other words, follow Fisher, 1935. If you work in a field where you can.

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I mean, it is sort of silly to criticize a tool if you use it badly, right? 'Hey, this hammer is not working well. When I throw it from 6 feet at the nail in the wall'.