Excellent answer--the polymodal distribution for the residuals almost surely indicate an important factor that is not being included in the model.  The other distribution problem that I get worried about is a severely platykurtotic distribution, which isn't as amenable to transformation as even a severe skew. Besides normality testing being nearly useless, another test prior to ANOVA that I find done over and over are tests for homogeneity of variance. I offer the quote from George Box: "To make a preliminary test on variances is rather like putting to sea    in a row boat to find out whether conditions are sufficiently calm    for an ocean liner to leave port!" - [Box, "Non-normality and tests    on variances", 1953, Biometrika 40, pp. 318-335] Almost all of the tests for homogeneity that I know about, including that in PROC GLIMMIX based on change in the log likelihood or the various HOVTEST options in PROC GLM, are sensitive to the assumption of normality for the residuals, so the whole vicious circle becomes a problem. Some approachs I like: never trust p values completely, always treat variances as heterogeneous, learn how to do permutation tests.  Someday, I'll follow my own advice. Steve Denham ... View more