In other words, the more “statistically significant” is the result in such an experiment, the more it is evidence for faulty measurement and against the experimenters’ claim (here, FTL neutrinos).
It’s still evidence for the claims, just also evidence for the experiment being faulty.
Technically, when viewed on the log-odds scale, it is exactly the same amount of evidence for either hypothesis.
On the (0;1) scale of probabilities it is, however, stronger evidence for flawed experiment. E.g. if we had a null hypothesis H0 at a prior P of 0.25 and two hypotheses H1 and H2 at 0.25 and 0.5, respectively, and we see evidence that has a likelihood of 5:1 for each of these hypotheses over H0. Then we have posterior P(H0|D)/P(H1|D)=1/5 and P(H0|D)/P(H2|D)=1/10, and after normalization, P(H0)=1/16, P(H1)=5/16, P(H2)=10/16. So, in this situation, P(H2) has increased by 2⁄16 and P(H1) only by 1⁄16. Which is what I meant in my comment: the probability of the more likely hypothesis increases faster, so H2 becomes more more probable than H1 :) Although on the log-odds scale, of course, both H1 and H2 received the same amount of evidence.
It’s still evidence for the claims, just also evidence for the experiment being faulty.
Technically, when viewed on the log-odds scale, it is exactly the same amount of evidence for either hypothesis.
On the (0;1) scale of probabilities it is, however, stronger evidence for flawed experiment. E.g. if we had a null hypothesis H0 at a prior P of 0.25 and two hypotheses H1 and H2 at 0.25 and 0.5, respectively, and we see evidence that has a likelihood of 5:1 for each of these hypotheses over H0. Then we have posterior P(H0|D)/P(H1|D)=1/5 and P(H0|D)/P(H2|D)=1/10, and after normalization, P(H0)=1/16, P(H1)=5/16, P(H2)=10/16. So, in this situation, P(H2) has increased by 2⁄16 and P(H1) only by 1⁄16. Which is what I meant in my comment: the probability of the more likely hypothesis increases faster, so H2 becomes more more probable than H1 :) Although on the log-odds scale, of course, both H1 and H2 received the same amount of evidence.