Have you ever noticed that some leading advocates of a statistical account, say a testing account A, upon discovering account A is unable to handle a certain kind of important testing problem that a rival testing account, account B, has no trouble at all with, will mount an argument that being able to handle that kind of problem is actually a bad thing? In fact, they might argue that testing account B is not a “real” testing account because it can handle such a problem? You have? Sure you have, if you read this blog. But that’s only a subliminal point of this post.
I’ve had three posts recently on the Law of Likelihood (LL): Breaking the [LL](a)(b), [c], and [LL] is bankrupt. Please read at least one of them for background. All deal with Royall’s comparative likelihoodist account, which some will say only a few people even use, but I promise you that these same points come up again and again in foundational criticisms from entirely other quarters.[i]
[M]edical researchers are interested in the success probability, θ, associated with a new treatment. They are particularly interested in how θ relates to the old treatment’s success probability, believed to be about 0.2. They have reason to hope θ is considerably greater, perhaps 0.8 or even greater. To obtain evidence about θ, they carry out a study in which the new treatment is given to 17 subjects, and find that it is successful in nine.
Let me interject at this point that of all of Stephen Senn’s posts on this blog, my favorite is the one where he zeroes in on the proper way to think about the discrepancy we hope to find (the .8 in this example). (See note [ii]) Continue reading