ANOVA vs Kruskal-Wallis for combined normal and non-normal data

#1
I have a number of distributions that I need to determine significant differences. However, some distributions are normal and some are not. In order to properly compare the p values/significance between these distributions, should I use only the Kruskal-Wallis test on all distributions or just on the non-normal distributions? Is there a reason I wouldn't be able to use a Kruskal-Wallis on normally distributed data?
 

Karabiner

TS Contributor
#2
The distribution of a dependent variable is irrelevant. Sometimes, the distribution within groups / the distribution of the model residuals is relevant, especially if you total sample is small (n < 30 or so). You did not mention sample size, which is nearly the most important information if statistical problems are described, but if your sample size is large enough, you can use ANOVA throughout (assumed that all of your variables are interval scaled).

With kind regards

Karabiner