A couple of points, I hope not too muddled: I find probability difficult to understand, but I sometimes get concerned when a small p value is taken as proof-positive. I know that the .05 level used in psychology is arbitrary (though it probably makes sense) and Cohen points out that research in psychology has traditionally lacked statistical power, making nonsense of the .05 level when used in such studies. When a researcher says that 'compared to chance' their results are significant, I'm starting to wonder what they mean. You hear things like '50 people score above chance on a card-guess study which is evidence for psi'; what exactly are we comparing the guesses to? I know if there are 5 cards in the deck, they have a 1 in 5 chance... or do they? I've heard that a random number generator may throw up non-random sequences, so how predictable is chance?