You can choose among different alternative in my opinion the most elegant is to build a correlation matrix Made by all the pairwise Spearman correlations between elements this summetric matrix is the input (once transformed into a distancematrix by d(ab) = 1 - r(ab) with r(ab) Spearman correlation between generic a b elements..in the case of strongly negative correlations use 2 - r ad metrica otherwise is preferable approximate negative to Zero correlations) This distance matrix is the input of a multidimensional scaling procedure (eg Kruskal scaling) that sul file rise to two explicit quantitative coordinates for such element reflecting orderin similarities compare the two Group e coordinate value by t test and you got it !

In addition by plotting the coordinates you will have an immediate appreciation of the separation of the two Group of participants

Alessandro Giuliani Alessandro, thank you for the quick advise - I'll need some time to digest this, and I'll post an update how it goes..

Cheers!

I am looking forward....Remember to set the 'self distances' (i.e. d(AA)) to zero. This is automatic when in presence of the metrics d(i,j) = 1 - r instead it must be forced to zero when the metrics is d (i,j) = 2 - r.

Here below a website with a lot of multidimensinal scaling procedures described and made available:

http://ordination.okstate.edu/

Ciao

Alessandro

Alessandro Giuliani, I think that I should describe the problem more precisely - hopefully an example would work the best.

Say, I am conducting and experiment that compares the consonance levels of 5 tone intervals: A, B, C, D and E. I have two groups of participants, and the goal is to test if the ratings of intervals' consonance considerably differ between the two groups.

The participants are comparing pairs of intervals (each by each), and the interval "votes" increase when it is chosen as more consonant than the one it is compared to. That is how we end up with the following table (the numbers are the total number of votes that each interval got by each group):

Interval: A B C D E

Group 1: 10 30 20 40 50

Group 2: 10 30 26 39 48

The null hypothesis would be that there is no significant difference between the ranks of the elements between the two groups.

The alternative hypothesis would be that there will be a significant difference in the ranks.

The two groups could be, say, musically educated and non-educated; or, North Americans and Europeans...

The problem I have with the Spearman correlation is that it is only sensitive to the rank, so the following two cases will be rated very differently, since for the first case the ranks are the same (perfect correlation), but for the second the correlation drastically goes down (and i need it to be near to the previous). So, the change of only 1 vote for the intervals B and C in group 2 swaps B's and C's ranks, causing big jump in the calculated Spearman correlation.

Interval: A B C D E

Group 1: 10 20 30 40 50

Group 2: 10 26 27 40 50

Interval: A B C D E

Group 1: 10 20 30 40 50

Group 2: 10 27 26 40 50

Any ideas how to make the correlation result a bit less dependent on the rank, and somewhat dependent on the actual values of the votes, or I am asking for impossible?

Go to direct distances between partecipants by computing euclidean distances on the dove intervals space. IF you sant to eliminate the possible bias due to the entity of the value of merit you can standardize by rows vedere computing distances

Alessandro Giuliani thank you for all your advises!

Let me know IF multidimensionali scaling on euclidean distances worked