This paper (http://psycnet.apa.org/journals/med/6/4/147/) states that departures from normality can be tolerated for one-way ANOVA.
"The results give strong support for the robustness of the ANOVA under application of non-normally distributed data."
I have a factorial design and some of my data is not normal distributed. Although it is only a minor fraction of the total data set (28 out of 340 samples) I wonder if it is legitimate to proceed with a factorial design ANOVA.
My dependant variable is the relative absorption in an IR range (defined by DRIFT analysis) and my independent variables are timepoint, treatment, exposition, depth. Per sampling condition (example: timepoint=0, treatment=x, exposition=north, depth= 0-5cm) I have 3 replicates.
I have 4 treatment, 3 timepoints, 2 exposition and 2 depth. As some replicates are missing, my design is unbalanced and I used type III Anova (from car package) in R . I assumed a linear model with interactions. (linear Model = Absorption ~ Treatment * Timepoint * Depth * Exposition)