Independent, non-normal, unbalanced, analysis of an interaction effect


New Member
I have previously used straightforward two-way ANOVAs for comparing bone density across sport disciplines.
I have males (M) and females (F) across low impact (LI) and high impact (HI) sports (N = 92).
I have 24 males and females in in the LI group, 19 females in the HI group, but 39 males in the HI group.
Variance is similar in the groups, but the data are skewed, and as such a testing of medians would be more appropriate.

I know there are several ways to deal with unbalanced design or with non-normal distributions, but generally this would result in sacrificing analysis of the interaction effect as it involves ranking bone density scores. The only reasonable suggestion I've come across is the Friedman test, but it is not applicable here as these are not repeated measures, but completely independent observations.
Could anyone suggest a good way of approaching the interaction between sex and sport, while accounting for skewness and unequal group sizes?

Your help is much appreciated. Thank you!


Less is more. Stay pure. Stay poor.
The imbalance usually isn't much of an issue, unless it is extreme resulting in sparsity in subgroups and power issues.

Look into quantile regression.