I am trying to analyze the data from a field experiment I ran in 2015. I have 4 fixed factors with various levels (we'll call them a,b,c, and d). Factor c is nested in b. I have 1 random factor (blocking - randomized complete block design). My response variable is % growth in length (mm) ranging from -25% (some shrunk) to 70% and my n is 304. I used the fit-model platform to general a linear mixed model that came out pretty much as I expected - with factors a,b, c, and axb having significant effects.
My problem is that when I go to check the residuals for the assumptions of normality, the data are not normally distributed. Looking at the quantil plot reveals an s curve that just strays a little bit from the normal line. In my search I have seen these type of curves called fat tailed, and some have instructed that all %change data are actually Cauchy distributed rather than Gaussian (normal) and should not be analysed with ANOVA. That's great, but I have no idea what to do with that information. I understand how to do ANOVA and ANCOVA, but beyond that, I'm a little lost. I have tried the standard transforms (log, sqrt) with no luck.
I know that using a generalized linear mixed model allows you to work with data that are not normally distributed, but I don't have JMP pro (which I think is the only way to use glmm). Any tips or advice would be greatly appreciated. Thanks for your time.