(I wanted to stress that the validity of null hypothesis is really an assumption one has to make here and through a lazy mental shortcut iff appeared suitable as a stronger version of if. Later I realised that it is not only false, but rather “not even false”, given that “probability of A if B” is meant to represent p(A|B) - not sure what “probability of A only if B” would represent. But I was too tired to edit the post.)
Is this a typo? I think the ‘iff’ should be an ‘if’. The ‘only if’ implication is false.
Thanks, corrected.
(I wanted to stress that the validity of null hypothesis is really an assumption one has to make here and through a lazy mental shortcut iff appeared suitable as a stronger version of if. Later I realised that it is not only false, but rather “not even false”, given that “probability of A if B” is meant to represent p(A|B) - not sure what “probability of A only if B” would represent. But I was too tired to edit the post.)