Quantifi the homogeneity

#1
Hello
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.
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Are you looking to compare all regions to one, or perform pairwise comparisons amongst them all?

This reply may show my ignorance, but I am assuming the test provides a test statistic and p-value. Is it possible to use the test statistic to contrast the comparison homogeneity?
 
#3
I am looking to "quantify" the homogeneity of a given region i.e. to calculate a measurement that can be interpreted as homogeneity index. I agree with you that the value of statistic of test can compare two region but it does not have any sence. For that i'm looking for a measurement between 0 and 1.