This is a simple question, yet, the more I think/read about it the more confused I get 
If I have 2 groups, and a simple design of 1 for the control and 0 for the experimental group
e.g.
1 0
1 0
0 1
0 1
and a contrast of 1 -1. Then, let’s say, the FC_fwe corrected output would represent an increase or a decrease in the FC for the control group?
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Hi Milly,
Sorry for taking forever to get back on here; I’ve got a long list ahead of me…
With that design matrix, beta0 is the mean value of FC (or more likely log(FC)) for the control group, and beta1 is the mean value of that parameter for the experimental group.
Your contrast vector performs the inner product:
(1 x beta0) + (-1 x beta1) = beta0 - beta1
This gets scaled appropriately to form a t-value.
So if you are getting p-values less than 1, which can only happen for positive t-values, this means that:
beta0 > beta1
, or equivalently, the value of FC (or log(FC)) is greater in controls than in the experimental group.
It is also worth bearing in mind that FC is not an “absolute fibre bundle cross-sectional area”, but a change in cross-sectional area as image data are warped from subject space to template space. Thankfully this correction in interpretation does not induce a sign flip:
The determinant of the Jacobian reflects local volumetric differences, where values less than one reflect shrinkage and values greater than one reflect expansion (with respect to the template).
So if the value of the FC (or log(FC)) metric is greater in the control group than the experimental group, this indicates a greater fibre bundle cross-sectional area in the control group than in the experimental group.
Often when one questions these things it’s helpful to write out the individual underlying steps, even if each step on its own seems trivial.
Rob
This makes perfect sense!
Thank you so much!