Non-Parametric Test controlling for third variable

There are two laboratories measuring identical samples. One of the lab's data is non-normal, therefore I am looking for a non-parametric test.

After comparing overall differences in the dependent variable (continuous) using Wilcoxon Mann-Whitney, I wish to test for differences between labs based on a third variable.

There are a number of third variables that I wish to test for, and some of them are categorical (2 levels, and 3 levels), and another is ordinal (by month).

Which test would be appropriate? I read about the van Elteren test, but the SAS output did not make sense.

• You said "One of the lab's data is non-normal, therefore I am looking for a non-parametric test." -- however, the usual assumptions nonparametric tests tend to make is that the distributions are the same (apart from location shift). If the shapes are all over the shop, nonparametric tests might be affected as much as ANOVA. Even the common bootstrapping-of-residuals (or a number of other resampling approaches) will be screwed up, because they rely on the ability to swap observations across groups. Resampling within groups might be used (one that resamples the rows of $[X|y]$ say). – Glen_b -Reinstate Monica Nov 1 '12 at 21:42