Glenn Shafer writes:
I have joined the immense crowd writing about p-values. My proposal is to replace them with betting outcomes: the factor by which a bet against the hypothesis multiplies the money it risks. This addresses the desideratum you and Carlin identify: embrace all the uncertainty. No one will forget that the outcome of a bet is uncertain. See Working Paper 54 here.
And here’s the two-minute version, on a poster:
I sent this to Anna Dreber who suggested using prediction market prices as priors, to which Shafer replied:
See the paragraph entitled “Bayesian interpretation?” on page 7 of the paper I called to your attention, which I attach this time.
My proposal is to report the outcome of a bet instead of a p-value or odds for a proposed bet. As I say on my poster, a 5% significance test is like an all-or-nothing bet: you multiply your money by 0 or 20. People want to report a p-value as the outcome instead of “reject at 5%” or “do not reject at 5%” because they want a more graded report. We can get this with bets that have many possible payoffs.
I think this whole 95% confidence attitude is a bad idea and I think that Shafer’s in a dead end here; I don’t see these methods being useful now or in the future. But, hey, I could be wrong—it’s happened lots of times before!—so I’m sharing it all with you here. I think Dan Kahan might like this stuff.