Agreed - it's post hoc. But it would be a method I would then be able to use for future analyses.

So, let's say I have a function that resembles my shape. Indeed, I would have two of them. This brings me back tot he question; how do I compare them?

As of now, this is what I do.

I compare the highest value for column A with the highest value of column B - and note the "winner."

I repeat this for each point, noting the winner each time.

I then use Fisher's Exact to asses the number of winners for Column X (given the number of chances Column X had to be a winner).

And this works just fine when there are the same number of items in each column.

Yes, this approach doesn't take into account the size of the difference between points, but in my data sets, the first point difference will always be extremely large, the second much less so, and after about five points, the differences are very small indeed. So if I do take into account the "size of the difference" then I'm giving too much power to the first point. For this reason, I feel the Fisher's Exact approach has some merit. Some "conservative" merit (and obviously some weaknesses).

I'd appreciate your continued thoughts ...

And I really do appreciate your input.