i am hydrologe and i search to find a solution for the following problem:

Suppose that i have k samples of observations (region) of the same variable ( e.g., annual peak flow) at different measuring sites are available (each sample i=1,..k have a record length ni).

The homogeneity test (e.g., Ksample Anderson-Darling test) answers the question: is the region homogeneous? As a null hypothesis test, there are only two possibilities of answer i.e. the region is homogeneous (F1=F2=...=Fk=F) or is heterogeneous.This binary answer is not flexible and do not allow me to compare homogeneity among several regions to point out the most homogeneous of them.

So i am looking for a measure that overcomes this limitation. By analogy, this measure would be the same as the Akaike Information Criterion (AIC) for linear models. Indeed, the AIC compares different models in order to determine which one is the better to fit to data. Thus, this measure would compare different region and measure of how much sampling sites are alike within regions.

Thanks in advance.