I have a numerical response variable A which depends on a categorical explanatory variable B. I also have another variable C that I'd like to check for confounding effects. So far I've been using ANOVA, but I've realised my response variable A is not normally distributed, so I need a non-parametric test. Thus I thought about Kruskal-Wallis, but I am not aware it's possible to perform such test (I'm an R user). Do you know if there's any equivalent to ANOVA but non-parametric for such task?
First, the response variable does not have to be normally distributed to use ANOVA. The errors (as estimated by the residuals) do.
Second, if you want a method that does not require the assumption that the residuals are normally distributed, you can use robust regression or quantile regression.