In article <[EMAIL PROTECTED]>, Robert J. MacG. Dawson <[EMAIL PROTECTED]> wrote: > The problem with *any* hypothesis test for normality (or any other >"gatekeeper test", such as the infamous "F before t") is that it >answers the wrong question.
> What you *want* to know (or should) is "do these data give me reason to >be confident that the population distribution is close enough to normal >[or whatever] for purpose X?" This is ALWAYS the question in ANY testing situation. It is a decision problem which cannot be adequately treated by looking at the probability of rejecting the special null under the essentially impossible assumption that it is true. > What these tests tell you is "do these data give me reason to be sure >that the distribution is NOT perfectly normal [or whatever]?" It is rare that I need such a reason. > Mistaking one of these for the other (and acting on a rejection by not >doing whatever you were planning to) yields all sorts of ironies, for >instance: > For most purposes, as N -> infinity, you need to worry less about >normality. As N -> infinity, the K-S is _more_ likely to tell you to >start worrying. It is not clear that you need to worry less; it depends on the possible actions. > For very small N, distributional asumptions are most important. For >such samples, the K-S will notice nothing. Better, it is unlikely to notice anything. However, it is not clear that this is the case. Tolerance regions depend on the distribution of the residuals, but this may be ameliorated by the inaccuracy of the estimates for smaller samples. Robust prior Bayes, with the use of simple priors only when one can prove that they are not bad for more reasonable situations, seems to be the only way out in general. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Deptartment of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
