*p*-values average over possible observations because statistical procedures need to consider what observations might have occurred as well as what did in fact occur. In response, B & W argue that LP procedures

*do*consider observations that did not occur. A statistician can't determine their likelihood function without taking into account what would be the evidential impact of all possible realisations of the random variable to be observed.

But I think this misses the point of the frequentist objection. The frequentist would argue that they are not responding to the 'intuition' that unlikely observations under the null constitute evidence against the null. They think (rightly or wrongly) that the intuition they are really responding to is that

*extreme*observations count as evidence against the null. Obviously, any statistical procedure will at some point have to take into consideration observations that did not occur.

[I AGREE. GOOD POINT.

(AND, AS YOU PROBABLY KNOW, I THINK THE INTUITION IS WRONG, UNLESS IT'S SPELLED OUT IN A WAY WHICH THE FREQUENTISTS CAN'T SATISFY EITHER, BUT THAT'S A SEPARATE ISSUE.) Jason 2017-08-08]