I have two groups of data (not distributed under a normal distribution): I would like to test the hypothesis that the first group has a lower (or narrower) standard deviation than the other.

An alternative explanation to this is that I would like to tell whether the first group is less 'variable', 'heterogeneous', than the first.

A kruskal-wallis won't do it because it compares the medians of two or more groups, and I am not interested in that.

A Levene or a Brown-Forsynth test compare the variance between the two groups and tell whether they have the same variance. This is better, but I would also like to tell if the variance in the first group is lower than in the other(s) group(s).

A simple Chi-Square test would tell me whether the standard deviation of a group is equal to a certain value, and the one-tailed version can tell me whether it is higher/lower.

An additional difficulty is that I would have to do this test as a two-way, because I have two grouping variables, but I would like to ask you if you can point me to any direction or give me some hint, I have not many ideas on where to search :-)

What is your non-normality assumption based on? Have you thought about transforming the data (with log transformation, for example) to be more normal?

You might also want to ask that question on stats.stackexchange.com. It's populated by lots of true-blooded statisticians who eat this stuff for breakfast.

Hi Giovanni, how did you end up solving this? I ran into a very similar problem.