Great little demo. > It is only when the statistical evidence against the null is overwhelming — “six sigma” overwhelming or more —that you’re also getting tig

Great little demo. > It is only when the statistical evidence against the null is overwhelming — “six sigma” overwhelming or more —that you’re also getting tight confidence intervals in relative terms. Among other things, this highlights that if you need to use your estimates quantitatively, rather than just to reject the null, default power analysis is going to be overoptimistic. This I think will be a real head-scratcher for a lot of students, who are often taught to construct confidence intervals by no method apart from "inverting" an hypothesis test. It illustrates one of the many challenges (and dangers!) of teaching statistics.