Good post (along with the first entry). I particularly appreciate this bit:
“Consider, for instance, if instead of viewing the “two-sided” significance test as such, we understood it as two one-sided tests with a correction (doubling the p value).”
It seems obvious now that I’ve seen it stated so plainly. And I suppose it’s reasonably likely that I’ve seen it stated plainly before, but that it didn’t sink in for whatever reason. In any case, it’s a useful point to make about the logic of NHST.
I also think your point that “The problem is at the level of philosophy of science, not verbal labels for p values” is important to keep in mind.
At least partially related to this latter point, I’ve written a couple blog posts addressing various aspects of Redefine Statistical Significance. You end this post by saying that the third entry will explore responses to RSS. Here are links to my posts, in case they’re worth including in that exploration:
Benjamin et (many) al recently proposed that the p-value for declaring a (new) result "statistically significant…www.nhsilbert.net
This post is a response, of sorts, to the most recent episode of The Black Goat podcast. It is "of sorts" because it's…www.nhsilbert.net
The first is a direct response to RSS, and the second is a response to an episode of The Black Goat podcast in which they discussed RSS and related issues.