# Small samples: test for uniform distribution

I have ~500 of (experimental) samples of data from a range [0,1], and I would like to see if the overall distribution is uniform or whether there is some clustering going on. I would have used Chi-Squared test as recommended here (https://math.stackexchange.com/questions/2435/is-there-a-simple-test-for-uniform-distributions), but there are two problems

1. Each sample is small (3-10 datapoints), which is probably too small for a Chi-squared test
2. The particular interval in which clustering may occur varies, e.g. for one samples it may be at ~0.2 and for another at ~0.5 etc
3. I see some clustering using visualisations, but there is a small number of outliers so I can't rescale each sample based on the value of the first datapoint.

Is there a statistical test / some other approach that I could use?

• If you have a particular alternative model in mind, then fit the two and compare loglikelihoods. Aug 4, 2017 at 16:44
• @kjetilbhalvorsen Thanks! The problem is I don't! I just expect that there'll be some clustering. Also even if I try something like Normal, do you think that I can get results with 3-10 points per sample? Aug 4, 2017 at 16:47
• Is there any reason you can't combine all your samples into one big sample? The range is the same for all of them, so... Aug 4, 2017 at 16:58
• @jbowman Unfortunately, no, as I suspect that the interval where clustering occurs is different for each sample (point 2 in the question), so I'm afraid that if I combine everything together, any clustering will be evened out. Aug 4, 2017 at 17:25
• you could calculate the correlations with order statistics and the expected order statistics from a uniform sample same size, and find p-values by simulation. Then plot the p-values (which should be uniform if all he nulls are true). Aug 4, 2017 at 17:48