Nick_Tarleton comments on Beautiful Probability - Less Wrong
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Are P(r>70|effective) and P(r>70|~effective) really the same in those two experiments? Trivially, at least, in the second one P(r<60)=0, unlike in the first, so the distribution of r over successive runs must be different. The sequences of experimental outcomes happened to be the same in this case, but not in the counterfactual case where fewer than 60 of the first 100 patients were cured, and it seems that in fact that would affect the likelihood ratio. (I may run a simulation when I have the time.)