I have an odd problem; I'm computing the axis lengths of ellipsoids, these are sorted based on their length (i.e. longest axis and shortest axis).
The problem is that I want to say the long axes are longer than the short ones, how can I properly do that? The 'long axis' group would be expected to have larger values purely due to the sorting. I imagine there must be a shuffle I can do to test if the difference I see between long and short axes are greater than chance but I can't work out what the shuffle should be...
Should I take random pairs of axis lengths from a shuffled population, rank them and compute the difference and then compare this shuffled difference to the one I observed?
Thanks for any help,