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I have a "source" the claims to return small sets of values (size<10) where each set is uniformly distributed in some range $[n,m]$.

What is the simplest to perform test that would be able to test if this is a reasonable claim?

My first thought was to take the sample standard deviation and compare it to the expected value but how close would be close enough? (and for that matter I don't remember what the expected value is.)

As a sub issue, the small sample size is going to make the results noisy so I will need to run it many time, how should I aggregate the results; Union a bunch of sets? Keep an average of the computed statistics?

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If you think this is a bad question please say why. – BCS Aug 12 '10 at 23:14
This may or may not be a helpful question: why are you thinking of these sets as being uniformly distributed sets, rather than a collection of individual samples from a single unknown distribution? You don't need a statistical test to tell whether you ever get >= 10 numbers from your process, you just notice when that happens. I would draw from your source a large number of times and tally what you see, as a first step. – Eric Tressler Aug 13 '10 at 1:27
You're probably not going to get anything very helpful here. You were voted down because this question isn't research level. Ask at – Eric Tressler Aug 13 '10 at 1:30
I just remembered some more of my stats, and I think you should read, after considering my earlier question. – Eric Tressler Aug 13 '10 at 1:43
@Eric: I'm not trying to find what distribution they are, I'm trying to show that they are in the given distribution. --- Is there a general math/non-research stack exchange? --- IIRC the chi squared test isn't exactly simple. – BCS Aug 13 '10 at 5:18

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