Regarding the stopping rule issue, it really depends how you decide the stopping. I believe sequential inference lets you do that without any problem but it’s not the same as saying that the p-value is within the wanted bounds. But basically all of this derives from working with p-values instead of workable values like log-odds. The other problem of p-values is that it only lets you work with binary hypotheses and makes you believe that writing things like P(H0) actually carry a meaning, when in reality you can’t test an hypothesis in a vacuum, you have to test it against an other hypothesis (unless once again it’s binary of course).
An other common mistake you did not talk about is one done in many meta-analyses: one aggregates the data of several studies without checking if the data are logically independent.
Regarding the stopping rule issue, it really depends how you decide the stopping. I believe sequential inference lets you do that without any problem but it’s not the same as saying that the p-value is within the wanted bounds. But basically all of this derives from working with p-values instead of workable values like log-odds. The other problem of p-values is that it only lets you work with binary hypotheses and makes you believe that writing things like P(H0) actually carry a meaning, when in reality you can’t test an hypothesis in a vacuum, you have to test it against an other hypothesis (unless once again it’s binary of course).
An other common mistake you did not talk about is one done in many meta-analyses: one aggregates the data of several studies without checking if the data are logically independent.