I want to statistically test the mean difference of a continuous variable (let's call this variable 1) between four groups (nominal) in my sample. Variable 1 has a very skewed distribution. This test also needs to be corrected for three other continuous variables that are certainly confounding variables when it comes to explaining the "variable 1" differences between the four groups. Many thanks!
First, regular regression does not assume that the dependent variable is normally distributed, but that the error (as estimated by the residuals) is. SO first test that. If they are skewed, there are a number of options; the two that come to mind first are :
1) Transform the dependent variable, then perform regular regression. For highly right-skew variables try either log or square-root, or look up Box-Cox
2) Perform some variation of robust regression - there are a variety of them out there. Which one is right depends on various things.