What non-parametric test do I use?

I am analyzing environmental data and am pretty new to it. Data does not satisfy the normal distribution condition. It also does not satisfy the normal distribution condition for residuals. I tried transforming it and it didn't work. I am forced to use the non-parametric tests. So, I wonder what the best non-parametric test is because I have been using Wilcoxon's test. I am currently analyzing multiple plots and I am not sure whether to keep using the Wilcoxon's test or not, since I am not really clear with the assumptions made for this test. Thank you all!


Not a robit
Can you tell us more about your data. Also do you just have a continuous DV and categorical IV. Feel free to post your residuals plots.