Baruch Eitam writes:
So I have been convinced by the futility of NHT for my scientific goals and by the futility of of significance testing (in the sense of using p-values as a measure of the strength of evidence against the null). So convinced that I have been teaching this for the last 2 years. Yesterday I bump intothis paper [“To P or not to P: on the evidential nature of P-values and their place in scientific inference,” by Michael Lew] which I thought makes a very strong argument for the validity of using significance testing for the above purpose. Furthermore—by his 1:1 mapping of p-values to likelihood functions he kind of obliterates the difference between the Bayesian and frequentist perspectives. My questions are 1. is his argument sound? 2.what does this mean regarding the use of p-values as measures of strength of evidence?
I replied that it all seems a bit nuts to me. If you’re not going to use p-values for hypothesis testing (and I agree with the author that this is not a good idea), why bother with p-values at all. It seems weird to use p-values to summarize the likelihood; why not just use the likelihood and do Bayesian inference directly? Regarding that latter point, see this paper of mine on p-values.
Eitam followed up:
But aren’t you surprised that the p-values do summarize the likelihood?
I replied that I did not read the paper in detail, but or any given model and sample size, I guess it makes sense that any two measures of evidence can be mapped to each other.