Check to see if sample data could be uniformly distributed

Question

I have data and I want to see if it is plausible that it comes from some uniform distribution. Is it uniformly distributed?

Answer 1

You can't tell that a population is uniform from a set of data, but sometimes you can see that it isn't.

I'll assume for the moment that you mean continuous uniform with known endpoints.

1. The most common approach is to apply goodness of fit tests.

   A number of such tests exist; these include the Kolmogorov-Smirnov, Cramer-von Mises Anderson-Darling (but there are a host of other such tests).

   Which you might use depends on which alternatives are most important to you. The Anderson-Darling is often a good default choice; it's most sensitive near the ends of the interval which is usually where the alternatives most often of interest will tend to clearly show differences. However, at moderate sample sizes it can have very low power against some shorter-tailed alternatives.

   Depending on your circumstances (which you don't describe) some other test might be a better choice but absent any other information, that would be a reasonable default choice.

2. While often used, whether a goodness of fit test suits your needs is unclear from your question. These tests are very frequently used in circumstances where they're not actually much use (such as testing distributional assumptions of some other procedure).

   It's important to consider why you're applying a test here and whether the actual problem this is supposed to solve might not be better solved in a different way. You say so little that at present it's hard to judge.