# Two-way robust ANOVA

My struggle with non-parametric methods continues... I'd like to apply a median polish instead of two-way ANOVA (normality and homoscedascity assumptions are violated, and $n_{ij}$ are small, so I can't use CLT as an excuse). I've never used median polish so far, and our course in statistics taught us to worship ANOVA and forget about robust methods if basic assumptions are not met. I saw this post and it seems that median polish can be applied for two-way factorial design. Which technique do you find appropriate in case of violation of ANOVA assumptions?

Now, what are the basic data considerations for median polish (or any other technique you find appropriate in this case)? Same shape, homoscedascity? Any resource (link/reference) is appreciated.

P.S.

Note that I'm aware of medpolish function in R.

• John Tukey describes median polish, with many examples and exercises, in his EDA book. It's easily carried out by hand (although a spreadsheet helps for doing the subtractions correctly :-). It's important that there not be too many missing data (empty cells) in the array, for then median polish can fail to converge and can be pretty biased. Otherwise, there are no other requirements. The proof of the pudding is in the analysis of the residuals. Tukey describes several very clever ways to extract additional information (e.g., interactions, transformations) from them. – whuber Mar 28 '11 at 22:57
• You should provide this as an answer instead of a comment. – aL3xa Mar 28 '11 at 23:02

• Well... AFAICT homoscedascity is not so problematic, but normality is. I used shapiro.test, lillie.test and ad.test, and $p < 0.01$. Density plot shows clear bi/multimodality and positive skewness. – aL3xa Mar 28 '11 at 16:36