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It's easy to challenge the subjectivity of a prior, pretending that frequentist testing is objective... until you design your own experiment, rather than just a
by 6gvONxR4sf7o 7y ago
It's easy to challenge the subjectivity of a prior, pretending that frequentist testing is objective... until you design your own experiment, rather than just analyze one. Turns out this is a more important part. It'd be illustrative to explain that process.
A p-value of 0.05 (or a test with 95% significance) will, if there's actually nothing there, tell you'll think there's something there 5% of the time (wrongly). It says nothing about error rates if there is something there, which is presumably what we're interested in. So for that, you'll do what's called a power analysis. Power of the conventional 80% tells you, if there's actually an effect size of X and you know all about your noise, you'll think there's nothing there 20% of the time (wrongly).
5% comes out of nowhere. 80% comes out of nowhere. A priori knowing your noise is often feasible, but not always. X, the presumed effect size you have to magically know before you run your experiment, comes out of nowhere. Getting this right is crucial to a reliable experiment, and it needs to really reflect your prior belief, even though it's frequentist. It's totally subjective.
What's worse is that X is often taken to be whatever leads to a feasible/fundable experiment that'll be done fast enough, not anything scientific.
It's waaay harder to understand the impact of the subjective 5%/80%/X decisions than it is to understand the impact of your prior. A prior takes way less training. Better yet, you can report your results assuming many different priors and let your reader subjectively decide what to think, so you don't have to commit as hard.
tl;dr The "gold standard" way of doing science is already really subjective and that's okay. Equally subjective alternatives can still be better science.