The problem isn't with the use of p-values, per se: the problem is that the human brain tends to distort probabilities on either end of the spectrum. People s

The problem isn't with the use of p-values, per se: the problem is that the human brain tends to distort probabilities on either end of the spectrum. People see that there's only a 5% chance that something could have happened by chance, and they put that in the "Not possible" bucket. It's a fundamental weakness of the human brain. There's not a whole lot we can do about it.