Permutations are my Samples

kretchmar

New Member
I have a question matching samples to a known distribution where my samples are actually permutations.

Let's suppose I have 100 people (p1, p2, ... p100) competing in a race. I get a single sample which is the top 15 finishers in order, maybe something like:
(p67, p34, p12, p90, ..., p2) <- finishing order for the top 15 people.

Let's suppose I re-run this race 20 times or so and get 20 different top-15 finishing orders. These are my 20 samples.

Now I can also analytically compute the probability of any 15-person permutation based on knowledge I have about the ability for each of the 100 people in the race. So I can theoretically compute a probability distribution over all possible 15-permutations (though there are too many to compute in practice).

I am looking for a goodness of fit type test where I can compare the likelihood of my 20 samples against the probability distribution of potential finishing orders. I suspect the race is "rigged", and the results I am observing do not match the known probability distribution over all permutations, i.e. I am "observing" a lot of very unlikely finishing orders. I have looked at trying some basics such as Chi-square and K-S testing. Anyone seen something like this before where the samples are permutations? Any help is very much appreciated.

fed2

Member
I think it is 'rank ordered logits' for this, with 'partial rankings'. unfortunately for you, i have not looked at this type of data in recent memory, so is as far as i can take you on your journey. id bet some of the social science types around here would know.

fed2

Member
glad you like, well if you ever figure out how'd to do this id be interested to hear it.