I have two conditions: A and B, with around 400 measurement points for each condition.
The most common result for both conditions is around '700', and neither one has a result below '600'.
Condition A has a long tail with results up to 10,000, while condition B has a longer tail with results up to 20,000.
Both the dependent variable and its residuals are not normally distributed (or even close to it).
What I'm trying to do
I want to test whether there is a difference in mean between the group, and whether there is a difference in the distribution, when outliers are taken into account.
Since the dependent variable/residuals are not normally distributed, I thought about using a non-parametric test such as Kruskal Wallis. However, since this test is rank-based, it means that I lose the difference due to outliers, which is crucial to the current analysis. The same happens when I perform a log-transformation (which also doesn't help reach a normal distribution anyway).
What can I do in this situation?