# How do i normalize residuals?

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!

qq plot of residual

• See this.
– Stat
Mar 14 '14 at 21:11
• Hover your mouse over your normalization tag, in order that you see that "normalize" doesn't mean 'transform to normality'. There are many, many posts here discussing the issues with explicit tests of normality assumptions. Failure to reject doesn't mean your residuals are normal (that is D'Agostino test does NOT say your residuals are normal). On the other hand, a Shapiro-Wilk rejection on this data may be of no consequence whatever. Mar 15 '14 at 0:09
• (ctd) (When did real - i.e. non-simulated -- data ever actually have a normal distribution?) ... With that QQ plot at that sample size, your inference should not be substantively impacted by the very mild non-normality that seems to be present. Mar 15 '14 at 0:11
• See discussion here and here and here. Note that even a graphical diagnostic check or approximate normality (your QQ plot) only makes sense if the other assumptions aren't violated. Mar 15 '14 at 0:24