Dear Rajeev and all,
Maybe you could address the problem by removing from your matrix --
beforehand -- those correlations which results you know -- beforehand, again
-- are clearly spuriously correlated and possibly of no interest (i.e., all
the brain-and-brain and behaviour-with-behaviour correlations).
Note that this is not anything like "p-surfing" or "inference-based
inference". This is equivalent to draw ROIs in neuroimaging studies, or even
removing non-brain voxels before applying any statistical test.
However, if you cannot get rid of these "correlated correlations", then I'd
use a possibly safer, but more conservative approach: Bonferroni.
Hope it helps!
Best regards,
Anderson
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