Robust regression or ANOVA for non-normal dependent variable I have a data set with a dependent variable on a scale from 0 to 100 (n=198). The problem is that many subjects (25) scored exactly 100 but below 100 every score is achieved only once. 
This distorts the histogram as you can see on the following link:

I'm trying to run an ANOVA (regression with two contrast coded predictors) and an interaction.
The interaction comes out non-significant, but I was wondering that maybe it is caused by the non-normality of the dependent variable.
Are there any robust methods to avoid this problem? 
 A: First a comment: "robust" usually refers to approaches guarding against outliers and violations of distributional assumptions. In your case, the problem is obviously a violation of distributional assumption, but it seems to depend on your DV (sorry for the pun).
What method to use depends on whether 100 is "truely" the highest possible value of your DV or if your DV measures an unobserved variable that has a latent distribution with possibly infinite values.
For illustration of the "latent variable" concept: On a cognitive test, you want to measure "intelligence", but you only observe if someone solves a question. So if some people solve all the questions, you do not know if these people all have the same intelligence or if there is still some variance in their intelligence scores.
If your DV is of the second kind, you could use tobit regression.
It's more difficult if your DV is really of the first kind, that is, if 100 is truely the highest score that could ever be measured. 
And BTW, even with the "right" kind of approach you might still end up with a non-significant interaction.
A: Rank based tests work by transforming the data to a uniform distribution then relying on the central limit theorem to justify approximate normality (the clt kicks in for the uniform around n=5 or 6), this helps counter the effects of skewness or outliers.  Your data has the opposite problem and the rank transform is unlikely to help (the 100's will still all be ties in the ranks).  For your sample size and the restrictions on the data, the normal theory tests are probably fine due to the clt.  I would be more concerned about unequal variances if some combinations have only 100's or mostly 100's.
If you really want to you could do a permutation test, but I doubt that it will tell you much more than what you have already done, possibly using some statistic based on medians rather than the F-stat may help.
A: Without knowing that the data are really about it's hard to say.  One potential very general solution is to consider that 100 isn't really 100 (sometimes).  What to do with that is what you need to work out.  You need to come up with a model about what other values 100 is.  Would some people have wanted to pick 1000? 110? 99.9? or was it just a garbage answer?  If you can work that out then you can either throw data away or jitter it in log or linear space.  You could add random noise to the 100s and do it repeatedly and see if outcomes are still relatively consistent across your conditions.
But without much more information it's hard to help.  I hope that I've given you some things to think about.
