in an analysis of survey data, I have to deal with multilevel/three-dimensional data. Now, I need to aggregate correlation coefficients found on the individual level (between individual rank-orders) and then compare these coefficients.
The original data looks like this: For each individual, 3 series á 15 items (agendas of public issues) have been measured. For a single individual, this could look like:
i A B C 1 1 2 1 2 15 7 12 3 2 15 6 4 3 1 11 5 9 6 2 .. ... 15 4 5 4
These are ranks, so I can compute the rank-correlations A~B and B~C on the individual level. Doing that, I result in a series of two correlations coefficients per case/individual.
CASE rAB rBC 1 .213 .114 2 .951 .524 3 -.101 .022 4 .607 1.0 ... 999 .549 -.661
Now I need to compare these coefficients to tell if A~B is larger then B~C (i.e., if the rank-order A is systematically more similar to B, than B is to C).
Of course, I could do simple t-tests over the two pairs. Yet, I doubt that correlation coefficients are scaled in such a way that adding/averaging them is allowed?
I have read about Fisher's z-transformation for correlation coefficients, but in this data set, it it likely to have single cases with r=1 in the data - and a their z-value would be ∞ (Fisher's z-value is undefined for r=1), which makes averaging senseless.
I could (not really) square the correlation coefficients to work with the explained variance r², but this would obviously conceil that some individual correlation are positive, while others are negative.
RQ: Are the agendas A and B more similar then the agendas B and C (systematically over 1000 individuals)? An agenda is a series of ranks or absolute values for each individual.
Update: Distribution of the correlations coefficients