If I run a group-level analysis (e.g., 3dANOVA) on a subject-wise statistic (e.g., a pair of betas), which I assume are independent identically distributed normal random variables, should I ever expect to see fewer than 5% of the voxels exceeding the p < .05 threshold?
I'm using the Kriegeskorte method of passing a sphere through the brain, looking at the correlation between a local area and a psychological dissimilarity matrix, and then assigning the correlation coefficient to the center voxel. I was hoping to then just pass those statistics back out to AFNI, and let 3dANOVA do the group-level analysis. I get beautiful, noise-free brain maps at ridiculously low t values (e.g., t=1), but none of the t values exceed t=3. Doing some investigating, I've found that only 2% of my voxels exceed what AFNI thinks should be the .05 level.
Am I right that under either the null or alternative hypothesis, this should not happen (for large N, such as 60,000 voxels)? This must mean that I have violated the assumptions of the ANOVA, correct?
Is there any way to correct the p values? I'd like to use AlphaSim or 3dFDR to determine whether these clusters are significant, but the abnormally low t-values make this difficult. If 2% of my voxels exceed a given threshold, can I use that value as the p-threshold in AlphaSim to determine the cluster size threshold? Intuitively, if 2% of my voxels exceed a particular threshold, isn't 2% the upper limit my "true" p-value?
Thanks for the stats help,
cdm
