I have measured Gaussian curvature data of 3D objects from two different groups, A and B. I would like to find out whether the objects differ in curvature.
The distribution of data values for each subject looks like an extreme value distribution:
(This is expected since Gaussian curvature is computed as the product of the 2 principal curvature k1 and k2, which are the maximum and the minimum over all possible curvature lines.)
If the data were normally distributed, I would take the mean of the data for each subject and fit a linear model to the data, then look at the main effect of the group variable.
However, taking the mean of such a distribution does not seem to make much sense. What would be a suitable approach here?
Note that one could model positive and negative values separately, I guess. Would it be valid to apply a Box-Cox transformation (to the positive and negative parts separately) and then check for mean differences of the resulting distributions? (I somehow doubt it.) Or should I use a GAM?