[R] Test for equality of complicatedly related average correlations

[Ralph79]

Dear R-Users,

I am currently looking for a way to test the equality of two correlations
that are related in a very special way. Let me describe the situation with
an example.

- There are 100 respondents, and there are 2 points in time, t=1 and t=2. 

- For each of the respondents and at each of the time points, I have
information on 10 X-variables and on 10 Y-variables. 

- Based on this information, I calculate two correlations for each
respondent: cor(X[t=1],X[t=2]) and cor(Y[t=1],Y[t=2]), with X and Y being
the vectors of the corresponding 10 variables.

- Now I get the average correlations over the whole sample using Fishers
Z-transformation, i.e. I have mean(cor(X[t=1],X[t=2])) and
mean(cor(X[t=1],X[t=2])) and want to know if the mean correlations are
significantly different!


I haven't found any test that deals with exactly my situation. Therefore, I
"simply" apply a paired t-test based on the individual z-correlations. From
my point of view this should be ok, because of the z's normality. However, I
am unsure if there is a better way to test the hypothesis that I am
interested in?

I'd be grateful for any comment or hint.

Thank you very much,

Ralph

-----
Ralph Wirth
University Erlangen-Nuremberg, Chair of Statistics
GfK Group, Department of Methods and Product Development

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