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There is an intuitive article in wikipedia about the Mann-Whitney U Test with an example of the classic Aesop's fable on the tortoise and the hare.

https://en.wikipedia.org/wiki/Mann–Whitney_U_test

Here is the situation:

I have a set of 10 particles, all distinct from each other, and identifiable. They are moving together but their orders change. I wanted to make a test to check if the order of their movement can be generalized (since I have other observations of them moving too).

I am still trying to formulate the problem, and I don't know where to begin. Please let me know if this is making any sense at all. My question is if I can extend the illustration of Mann-Whitney U Test from the wikipedia article to a case of 10 particles, with 5 independent observations.

And where do I begin?

Thanks for your insights.

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    $\begingroup$ "check if the order of their movement can be generalized" -- I have no clear idea what you intend by this but as phrased it doesn't sound like something you'd use a Mann-Whitney test on. Forget all about the Mann-Whitney test for now and focus on describing (in plain English, without any statistical jargon) the specific question you're trying to answer $\endgroup$ – Glen_b -Reinstate Monica Sep 20 '17 at 14:50
  • $\begingroup$ I wanted to ask if the order of the particles' movements in the data sets I have can be generalized. If this is the observation of the particles' order i have in set A and B, can I say that this is really how the particles behave in general? $\endgroup$ – cgo Sep 20 '17 at 14:57
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Since you only have 5 observations of the set of 10, modeling (let alone significance tests, which would have very low power for conventional $α$s) is unlikely to help. Try making a plot or table of all the data and see how the ranks of each particle change over the observations. If a particle has the same rank all 5 times, you can probably expect it to have that rank in the future most of the time.

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