I am trying to adjust a hierarchical multiple regression model and no matter which transformations I use (z-transformation, sqrt, cuberoot, inv, inv sqrt ...), I do not manage to get the residuals normally distributed. What can I do? Does anyone have any suggestions? I also checked out a related thread, the transformations suggested there did not help me. My residuals are normal according to D'Agostino Normality Test, but not according to Shapiro-Wilk (which is the crucial one according to my supervisor). I cannot use a non-parametric model. I would appreciate your help a lot! Thanks, brobdingnag!
Why can't you use non-parametric tests? Depending on what you are trying to learn there is probably a meaningful permutation test that would give meaningful results without needing the normality assumption (and is more meaningful that rank based tests).
Also note that the normality tests are really answering the wrong question. If you residuals are near normal (how near depends on sample size and other factors) then the normal based tests may give results that are close enough even though the normality tests may reject the "exact normality" hypothesis.