How to analyze non-normal DVs from 4x4 repeated-measures design

#1
Hello all

I am struggling to find the right technique for analyzing my data. 20 subjects experienced all levels of both factors. Both factors had four levels. The residuals for most DVs were not normally distributed as would be assumed for a two-way repeated-measures ANOVA. I am not aware of a corresponding non-parametric test. How should I proceed? I am told removing outliers is unwise with small sample size. I have encountered the Box-Cox method of finding ideal transformations for data. Is there a way to find the optimum transformation to use when there are many combinations of factor levels (4x4=16) as with my data? Do I need residuals of DVs for all 16 combinations of factors to be normally distributed or can I proceed if I find a transformation that normalizes the data for most of the factor level combinations? Thanks for any advice, suggested techniques, reading materials, etc.

Z. Redding
 
#2
Since you have only 20 subjects, the normality assumption is essential for the plain vanilla repeated measures ANOVA. You would need to find one transformation which makes the distribution normal at each stage in each group. This is unlikely to happen. So another approach to look at is a very general method, good for many non-parametric situations: randomization test. It is closely related to the idea of bootstrap. You would have to perform some programming of your own.