[stdbrouw]

An example from Leonard Mlodinow: imagine a friend doesn't pick up the phone when you call. Now, you might think that maybe they're upset at you, because if they are indeed upset, the the probability that they wouldn't pick up the phone is very high. On the other hand, there might be many other reasons your friend doesn't pick up the phone – battery's dead, they went on an impromptu holiday, they're having a bad day, they didn't hear it ring. Frequentist statistics deals in the first kind of probabilities (the probability of seeing what you saw given a particular hypothesis) whereas Bayesian statistics is the other way around (the probability of a particular hypothesis given what you saw).

[xapata]

Except the Frequentist would test the null hypothesis: what's the probability the friend doesn't answer if the friend is not upset?

[stdbrouw]

Given that the alternative hypothesis is usually defined as the complement of the null hypothesis (HA = 1 - H0) this doesn't make much of a difference, though.

[xapata]

Frequentist:

    H1: answer ~ upset + error
    H0: answer ~ error

I find many people have trouble expressing a reasonable hypothesis / null-hypothesis pair. In fact, I'd bet that a good chunk of folks would try to make "upset" be the dependent variable in the phone call scenario.