I have data for two classes A and B for N participants (same group -> dependent) in an experiment. Both classes are described by a feature vector. For each participant i have a certain number of samples (=feature vectors) for each class.
Now, in a first step I am interested in the difference of the average within-class sample-to-sample correlation of A (that is, the sample-to-sample reliability of A) and the average between-class sample-to-sample correlation (r_AB; that is, the similarity of A and B) for each participant separately. I could do the same for B, but for simplicity I focus on A. Thus I subtract z-transformed r_AB (=z_AB) from z-transformed r_A (=z_A) for each participant:
diffz_A = z_A - z_AB
(let's suppose diffz_A has now N values, i.e. one z-transformed correlation difference for each participant)
Now I want to look at two time-points 1 and 2, such that i have two instances of those correlation differences:
diffz_A1 and diffz_A2
How can I test whether the two correlation differences diffz_A1 and diffz_A2 are significantly different?
Upon literature consultation I found that there is a specific test for testing the difference of two dependent non-overlapping correlations (Steiger et al. 1980). However, it's absolutely unclear how to apply this test to differences of correlations, which in turn are partly based on within-class correlations on the participant level..
So my questions are:
do i need a complicated z-test in first place for testing between two differences of correlations? Or can I use a simple t-test?
If no, which test should i use and how?
and somewhat unrelated: if i want to transform a correlation difference back from z-space to r-space (using tanh), can i apply tanh simply to the obtained correlation difference in z-space (i.e. meandiffr = tanh(diffz_A)) or do i have to apply tanh separately to the two terms in the subtraction formulae?