New paper by @Sander_Greenland on the distinction between p-values as measures of divergence, and p-values as inputs to choose a decision.
Perhaps it would be better to refer to p-values (for an explicit data set) as percentiles and not probabilities. The “probability” of a p-value is conditional upon a model and entirely hypothetical replication under the assumed model. The actual p-value is retrospective.
I think Crane notion of “academic” (model outputs) vs “real” probabilities (prices at which bets are made) has relevance to the flawed probability interpretation of p-values.