# Linear regression on non-normal response with categorical predictors

I am trying to define a model for an experiment comparing 3 groups of samples, with 8 observations in each group. The purpose is to assess if observations in groups 2 and 3 are smaller than in group 1, and if so, how much.

From the biological background of the experiment the response is supposed to be log-normally distributed (log10). However one cannot assume as much with this few observations.

As one can see on group 2, the response is significantly non-normal (shapiro.test in R reports p=0.01519093).

These are the histograms for the log10-transformed responses on groups 1:3.

For this reason, I opted not to do a one-way ANOVA (or Kruskal-Wallis) test. Instead I am modelling as log10 (y) ~ Group in R.

As I understand it, the important assumption of regression is in the residuals and not the response. Below is the residuals plots from R, where there seems to be such an issue with group 2.

What would be a sound regression strategy here?

• Should I do another transformation on the data to try to address the non-normality of residuals in group 2? If so, would it change the interpretation of coefficients?
• Should I use ANOVA instead of regression in this situation, maybe with some other considerations applicable?
• Anova and regression are the same second option will not be helpful – Deep North Oct 3 '17 at 20:39
• Thanks for your comment. What second option do you refer to? – philsf Oct 3 '17 at 20:40