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 :-)