> For that matter, due to the Central Limit Theorem, neither do analytic approximations like a t-test for comparing different group means. Actually, it doesn't

> For that matter, due to the Central Limit Theorem, neither do analytic approximations like a t-test for comparing different group means. Actually, it doesn't. You need a confidence interval, and central limit theorem doesn't give you a confidence interval. It just says that the distribution is close enough to normal at some point. In some cases, it might take a very large n before it become close to normal.