Testing whether two separate distributions systematically vary typically involves a t-test or ksmirnov test. These two popular GOF tests involve comparing two distributions' means (t-test) or a hypothesized equal distribution (ksmirnov). A recently-released user-written command in Stata, distcomp, moves the needle a bit for GOF testing by assessing the equality of the distribution functions point-by-point. That is, instead of a single rejection (or non-rejection), the distcomp test generates ranges of values in which the two distributions' difference may achieve statistical significance.
To locate and download distcomp use the "findit" or "ssc install" functions in Stata. For a much more thorough explanation and description of the distcomp command click here.
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