 How do you get the p-value? You make a little toy model, a mathematical model, of what the world looks like when the null hypothesis is true. We never examine any other world. We just look at that one. Figure out how that world works, and that's where the hard work is, that's what those calculations are all about. They're all about figuring out that null hypothesis world to answer what is the probability that that world that you just imagined coughs up evidence, data, at least as extreme, at least as damning to the null hypothesis as what we just got. That number that you get that way, that is the p-value. And that is a punchline that tells you what decision you should make because statistics is all about making decisions under uncertainty. So what's a p-value? Probability of seeing something at least as bad as what we saw in that toy world that is the null hypothesis. And it is therefore a summary of how ridiculous we feel entertaining the null hypothesis. The lower it is, the more surprising the evidence, the more ridiculous we would feel persisting in acting as if we live in the null hypothesis world.