Can you perform an ANOVA on r-values (correlation values)?

#1
Hi all:

This may be a simple question but...
I'm doing neuroimaging research and long story short, I am doing what is essentially a correlational analysis wherein my output is a brain's-worth of r-values (so like 15000 voxels worth of r-values). In this particular study I had 3 groups and I want to take these brains worth of r-values and see if they differ across the 3 groups. In normal situations in neuroimaging when you have beta weights you just do a 3-way ANOVA on the beta weights to get an F-value (or a t-value for more specific comparisons) so my default was just to assume I could do the same thing here - a 3 way ANOVA with group as the fixed factor. However I realized I'm not sure performing an ANOVA on r-values is appropriate. Can someone speak to this? If it IS inappropriate, can someone recommend how I could go about testing for differences using these values?

Follow-up question: I also have Z-scored brain maps and ultimately I'd like for the comparisons to be made using the Z-scores. I suppose if using an ANOVA on r-values is inappropriate then using one on the Z'd r-values is also inappropriate but if using an ANOVA is okay with correlation values, I'd assume it's okay with Z'd correlation values as well?

Thanks for any help you can provide.

Lauren
 

CB

Super Moderator
#2
Couple of questions:

How many people in each group?
How are the r-values obtained?

Correlation coefficients will not have a normal sampling distribution with constant variance within each group, so technically you have a distribuitonal violation (though depending on the sample size this may not really matter). You could perform a Fisher z transformation on the r values to obtain z values that have a normal sampling distribution with constant variance.
 
#3
How many people in each group?
There are 17 people in each group (51 total) which is on the higher end for an MRI study.

How are the r-values obtained?
After preprocessing, each voxel in the brain has an activation value for however many timepoints in the MRI scan. So for example, if the scan was 240 TRs (TRs = a unit of time in scanning) then each voxel will have 240 activation values.

We then defined an area of interest consisting of 300(ish) voxels representing a brain area and average those voxels' activation values together to get an ROI activation value. That ROI value at each timepoint is correlated with the activation values of all other voxels in the brain so essentially we're looking at the correlation of the activation patterns across time. Hopefully this is clear enough?

A Fisher's Z is easy enough to perform in this situation so as long as an ANOVA can be performed on these values, that is likely the way I will proceed.