Sorting and testing multiple distributions

Hi,

I have 10 sample distributions of (benchmarking) values and want to sort
them and determine significance of differences. They are not normally
distributed and consist of the identical numbers of samples.

I was now thinking about different approaches to determine the order of the distributions and how to determine the significance of the differences:

(1) sort the distributions by their means (they are not normally
distributed, however) and test distributions that are subsequent in the
ordered list by e.g. Kendall's tau to determine significance.

(2) first test for homogeneity with H-test (Kruskal, Wallis) and then use
one of the approaches for multiple pairwise comparisons of mean ranks
(chi^2; Harter, 1960; Tukey-Kramer) that are proposed by my statistics book of choice (Sachs, Angewandte Statistik, [395]).

(3) test all pairs of distributions and use some multiple testing correction (Bonferroni, Benjamini, or similar).

For (1) I am not even sure if it is a sound approach at all. (2) and (3)
appear to be correct solutions, but I am not absolutely sure. If they are both correct which would be the best choice?

Does somebody have an advice? I would appreciate for any help. Thanks!

Philip

.

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