"Jeff Miller" wrote in message news:email@example.com...
The confidence interval approach is much more informative in most such situations, because they allow conclusions of the form "Ho is not wrong by more than X units". CIs are not easily adapted to your original question of checking for normality, though, AFAIK.
CIs are "easy" to apply here, in one of two ways. CIs are just things that contain the set of all null hypotheses that are not rejected based on the data. So either:
(i) form a discrete collection of possible families of distributions, test each of these as the null hypothesis and form a list of all those that are not rejected. This list would indicate how much non-normality is not excluded by the data available.... but it clearly requires both wide-ranging behaviours in the original list and an understanding of these behaviours if the CI s to be useful.
(ii) embed the normal distribution in a 3 or 4 parameter family of distributions, with the extra parameters representing departure from normality. Then an "ordinary" confidence region can in indicate how much non-normality is not excluded by the data available.