I know the central limit theorem says the distribution of the sample average must converge to the mean as n->infinity, but that's just "theory" and in real life I feel even with 100 million trials 32% is hardly impressive. I'd only feel the results to be significant if they have 90%+. Another article I read was about precognition by Daryl Bem, he got 55% with thousands of trials and it was published in a reputable journal (50% is theoretical chance). I mean 55% with 50% chance is enough to conclude ANYTHING AT ALL seriously!? It must be close to 100% to conclude anything.

This made me question a thing I never thought about before: are statistical methods really legit in determining whether A has an effect on B? My questions are

(1) has there been any experiments (of anything) where A gives a result a bit different from chance (like 32% with real chance 25%), and removal of A gives a result very close to chance (e.g. 25.3% with real chance 25%), and they flipped A on and off a lot of times and each time same things happen?

(2) are there any experiments with a different-from-chance result such that later people put B under the microscope and confirmed A really does have an effect on B?

I'm sorry if this question sounds stupid and confusing, but I've always felt stats is only useful for surveys, or pattern recognition at best. It seems to me many if not most results in psychology rely on these statistical methods where the deviation from chance is not impressive at all.