>>13194076Hm, that is harder to explain. But I will give it a try.
The p-value is not the same thing as the probability of a particular theory being true, for two main reasons.
The p-value is the probability of a particular experiment being non-misleading in a particular way. But the probability of the theory you are studying is not the same thing as the probability of the sensibleness of the individual experiment. The probability of the theory as a whole, after having done the experiment, is a combination of the results of that experiment, any other experiments that have been done, the prior probability of the theory (Occam's razor plays a role here), and other non-experimental evidence you have on the theory (known gaps, consistency with other understanding and historical data, etc). The p-value is a measure of the evidential weight of a *particular experiment*, but the overall probability of a theory is a summation of a bunch of such things. This is why items 1-4 in the table are out.
Item 5 is close. But the p-value measures only the probability of an experiment giving misleading results *due to noise in the data being mistaken for a signal due to chance*. There are a thousand other ways you can fuck up an experiment that are unrelated to noisy data: bad procedures, biased interpretations, equipment errors, the list goes on and on and on. If your experiment has a low p-value, that means that *one particular* mistake -- noise being interpreted as signal -- is not being made in your analysis. But the other 999 might still apply. A low p-value means the first 0.1% of sanity checks on your experiment give a green light, but the other 99.9% still remain, and they are not covered by this number. Item 6 is out for the same reason.
A low p-value is one quality sanity-check piece out of many. Misinterpreting it as something much broader is the central error in OP's picture.
