Dear FSL experts
We have come across a problem with our design matrix and analysis with randomise.
We have two groups (controls and patients) with diffusion data and cognitive scores. We wanted to test correlations between FA and cognitive score for each group separately, and also test whether the correlations are different between the two groups. To set up our design matrix, we followed the example we found in chapter 8 of the book “Diffusion MRI” by H Johansen-Berg and TEJ Behrens (1st edition 2009; page 160; chapter authors SM Smith and G Kindlmann).
design1:
1 0 -2 0
1 0 -7 0
1 0 4 0
1 0 5 0
0 1 0 3
0 1 0 2
0 1 0 0
0 1 0 -5
contrasts
c1 [1 -1 0 0] to test group 1 > group 2
c2 [ -1 1 0 0] to test group 1 < group 1
c3 [0 0 1 0] to test positive correlation in group 1
c4 [0 0 0 1] to test positive correlation in group 2
c5 [0 0 1 -1] to test correlation group 1 > correlation group 2
c6 [0 0 -1 1] to test correlation group 1 < correlation group 2
These are the contrast from the diffusion book. We added
c7 [0 0 -1 0] to test negative correlation in group 1
c8 [0 0 0 -1] to test negative correlation in group 2
In addition, we tested the groups in separate designs, i.e. for control group
design2
1 -2
1 -7
1 4
1 5
contrasts
c1 [0 1] to test for positive correlation
c2 [0 -1] to test for negative correlation
To our surprise, the results for the correlations were different depending on whether we put both groups in the same design or look at them separately. We were expecting c3 of design1 to give the same result as c1 of design2. However this was not the case.
When setting up the design to include only one group, significant clusters were less extended, or no significant results were found (although significant results were found when both groups were in the same design). To get approximately the same regions showing as significant, we have to decrease the p-value to 0.01 for the design that includes both groups, to match the results from the design that includes only a single group.
What is the reason for this discrepancy? And which result is correct?
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