I'm using Kruskal-Wallis to as a non-parametric ANOVA of a non-normal distribution. My understanding is that it assumes each group of the independent variable has the same shape. As it turns out, three of my four groups have approximately the same shape, however the fourth does not. The fourth is roughly the inverse of the first two.
Does this invalidate significance? Are there any steps I should take to mitigate its impact?
Update based on comment and further steps taken:
@Miroslav Sabo pointed me to a similar question he asked about using Mann-Whitney when certain assumptions are not met. That answer suggested welch's correction.