Thank you CowboyBear for the reply.

I thought statistics was a math...

I was meaning "prove" in terms of a given level of significance.

A hypothesis that beauty contests are decided purely by random chance would imply that the rankings in different beauty contests are independent. So if you took a sample of women each of which were both contestants in two or more pageants, their rankings across pageants should be uncorrelated.

That is where I am not sure how one would do any kind of statistical analysis to show they are uncorrelated. Contestants rarely compete in the same pageant multiple years. Or, I should say, at the Miss USA level, the contestants were selected at lower pageants, and although they may compete in those year after year, rarely does one come up from those multiple years. Only two this year competed previously.

What if we were to ignore the actual contestants and just focus on the state? For instance, Alabama has placed for the fourth consecutive year, three other states for their third consecutive year, and three for their second consecutive. Connecticut, who won this year has never previously won.

Buutttt to be pragmatic I think it's best to spend time on testing hypotheses that are plausible. Beauty pageant prizes are not allocated randomly.

I am actually trying to be pragmatic and learn how to do a statistical analysis of rankings. There are many things that are ranked - the best songs, the greatest movies, the top cars, the best jobs, the prettiest woman in the world... How would a statistician show that a certain ranking system is (possibly) not random?

On this site, there are many threads of rankings where the population is set. Such as, of these 10 items, rank them from least to worst, or of these 10 items give it a value from 1 to 5. For these studies, the majority of experts suggest using Kruskal-Wallis, and I see how that would work.

However, I have not found anything where the population is quite large and one is selecting a limited number to rank. For instance, given 50 contestants, select the top 10 (and ignore the rest). If I have 5 people complete the ranking, I might have 5 completely different rankings. I'm stuck.

As a math teacher and someone who enjoys statistics, this is something that really has me intrigued and searching for answers. There must be some way that statistics can be used to show that any of these types of rankings are more than just chance.

Again thank you very much for your reply.