Well I would start with a standard linear models analysis for a replicated random block design. maybe you don't need nonparametric statistical methods at all. I don't see any reference to time in the question. What is there to detrend? Best, David

An aligned ranks approach allows for rank-based tests on more complex designs. See http://depts.washington.edu/madlab/proj/art/ .

There is also a Scheirer–Ray–Hare test which handles 2-way designs, though it doesn't seem to be particularly well-respected.

Thank you both for the recommendations. In regard to David Booth's question about my use of the word "detrend", I meant using a general linear model to check the block effects [e.g. glm(response~block)]. If I find the block coefficient to be significant, could I use the deviations of this model, instead of the real measurements, to test differences amongst treatments? The way I see this would be a way of getting rid of block effects, allowing me to use the simpler (response~treatment) model. I would like to remark that I'm using glm instead of stantard linear models because both my variables present skewed distributions, and also one is a counting variable and glm allows me to choose a "poisson" distribution of errors.

I don't understand the question about generalized linear models.... If you have ideas about appropriate glm's for your data, why not just use them for the full analysis?

Because I'm interested in differences between my different treatments. What I mean is that, since I have 4 treatments, I can have 6 contrasts between means. Using a glm only tells me if the difference amongst all treatments is significant. When I read about the usual non parametric post hoc tests for multiple comparisons most tests, and most functions already coded in R, consider only the model without blocks (response~treatment).

You can use the emmeans package for post-hoc test with complex models. It will take into account both the main effects and the blocks, and you can get separations on interaction terms.

See library(emmeans); ?models for a discussion of how glm is handled.

The code in the example at the following link should be applicable to your situation. lsmeans is an older version of emmeans. You should be able to simply use emmeans in place of lsmeans. http://rcompanion.org/handbook/I_06.html

Thank you once again. I've read the lsmeans specifications before and didn't know there was a newer version. I'm going to check it.