The question is relatively simple, but trivial.
I have data divided by one fixed effect (Emotion, with 2 conditions: A and B), and I have a covariate, for each of my 20 subjects.
My aim is to
1) evaluate correlation between data and covariate;
2) know if there is a significantly bigger correlation between data in A condition and A covariate, than between data in B condition and B covariate (or viceversa). That means, analitically, to compare regression slopes.
I evaluated five different strategies:
a) use of Cohens'q. That gives no probability of a significance (no p-value), but an 'effect size' (small/medium/large) based on the difference between r values (transformed in z values using Fisher's procedure).
b) use of Fisher's method. That takes in account sample size, other than transformed r values.
c) use of ANCOVA. In particular, an analysis of covariance that doesn't force the slope to be the same. MatLab's 'aoctool' can do that work. To be clear:
y = (a1 + a2) + (b1 + b2)*X + e
In this case, not only sample sizes are taken in account, but also variability in each group.
d) Bootstrap procedure, followed by an effect size measure (Cohens'd).
e) Linear Mixed Effect model. It is usually indicated as a method which provides better estimates by using both group-level and population-level information (Thanks to @mzunhammer).
Cohens'q is just about correlations. Instead, Fishers' method takes also in account the sample size, and ANCOVA/LME methods also account for variability; but the latter two methods, with a small sample size, will tend to reject a difference between slopes. Actually, in neuroimaging studies, it is common to have 15-25 subjects. Therefore it appears to be useful to use Cohens'q, to have an estimate of the difference between correlations.
What would you recommend to solve the point 2)?
Does the bootstrapapproach seem reasonable?