Dear experts
From a functional connectivity analysis I have r-correlation-maps {r(v,s,t)} and corresponding Fishers-z-maps (for short z*-maps) {z*(v,s,t)} for voxels v={1,...,vsize} ouside a seed-ROI, 8 subjects s={s1,…,s8} and 2 timepoints t={t1,t2). The correlation data are calculated from cross-correlation-coefficients between timeseries of length 251. The correlated timeseries follow bivariate normal-distributions. Therefor the z*-values are (approximatly) normal-distributed N(µ(v,s,t)),1/248) with Estimator(µ(v,s,t)) = z*(v,s,t) . Because of known variance expected differences in FC between the 2 timepoints on subject level can be tested by a z-test with Hypothesis H0 : z*(v,s,t1) = z*{v,s,t2). On group-level differences in FC between the 2 timepoints can NOT be tested by a paired-t-test, because a homogenity-test of equality of the z*(v,s,t) for fixed v and t : z*(v,s1,t= … = z*(v,s8,t) fails for both t1 and t2 and most v.
I want to use the statistic apparatus of SPM, but as shown the obvious way of using the second level model specification design option 'paired-t-test' can not be used.
My idea is now
1. to break up the timeseries of length 251 into shorter timeseries (e.g. each timeseries into 5 timeseries of length 49 (not 50 in order to make the short timeseries disjoint))
2. to perform a first level within subject analysis for each subject with z*-maps calculated from the short timeseries (e.g. 5 z*-maps for each subject and timepoint)
3. to perform a second level between subjects analysis with the within subject analysis results.
I'm aware of the problematic situation of small samples and the loss of information by not using the known variances of the z*-values, which will be estimated by SPM.
My questions are :
1. What speaks in general against my plan ?
2. If the plan in general is okay, what are better or optimal splitting schemas for splitting the timeseries (length, randomized) ?
3. Are their other possibilities to analyse such data by SPM using full information about variances (and therefore using z-tests and not t-tests) ?
4. Which other tools are better suited for analysing such maps with correlation related data ?
