Non normal and unequal variance

[#1]

Hello everyone,

I am analyzing a dataset with three treatment factors. The data satisfy the normality assumption but violate the assumption of homogeneity of variance. I understand that Welch’s ANOVA may not be appropriate because I want to evaluate the main effects of each factor as well as their interactions.

In another scenario, the data violate both the normality and homogeneity of variance assumptions.

What statistical approaches would you recommend for analyzing these two scenarios while accounting for the three-factor experimental design?

Thank you.

[#2]

ANOVA is actually reasonably robust to the situations you describe. It is more important the residuals are normally distributed with constant variance.