Brad Klingbenberg has an insightful article on false discovery rate:

A good frequentist would never interpret a p-value as the probability that the null hypothesis is true. But it can be enormously tempting. And despite all your efforts to the contrary it is likely that many of your colleagues don’t appreciate the distinction.

So, really, how wrong is it to treat a p-value as (one minus) the posterior probability that the null hypothesis is true? In general, it’s bad. But in some cases a p-value is a very good approximation to a posterior probability. Here we examine that approximation in a common testing scenario.

Check it out for sure.