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pcm comments on Open thread, 24-30 March 2014 - Less Wrong Discussion
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Am I confused about frequentism?
I'm currently learning about hypothesis testing in my statistics class. The idea is that you perform some test and you use the results of that test to calculate:
P(data at least as extreme as your data | Null hypothesis)
This is the p-value. If the p-value is below a certain threshold then you can reject the null hypothesis (which is the complement of the hypothesis that you are trying to test).
Put another way:
P(data | hypothesis) = 1 - p-value
and if 1 - p-value is high enough then you accept the hypothesis. (My use of "data" is handwaving and not quite correct but it doesn't matter.)
But it seems more useful to me to calculate P(hypothesis | data). And that's not quite the same thing.
So what I'm wondering is whether under frequentism P(hypothesis | data) is actually meaningless. The hypothesis is either true or false and depending on whether its true or not the data has a certain propensity of turning out one way or the other. Its meaningless to ask what the probability of the hypothesis is, you can only ask what the probability of obtaining your data is under certain assumptions.
That may be true if you have little influence over what data is available.
Frequentists are mainly interested in situations where they can create experiments that cause P(hypothesis) to approach 0 or 1. The p-value is intended to be good at deciding whether the hypothesis has been adequately tested, not at deciding whether to believe the hypothesis given crappy data.