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, letâ€™s say, the FC_fwe corrected output would represent an increase or a decrease in the FC for the control group?

Hi Milly,

Sorry for taking forever to get back on here; Iâ€™ve got a *long* list ahead of meâ€¦

With that design matrix, *beta _{0}* is the mean value of

*FC*(or more likely

*log(FC)*) for the control group, and

*beta*is the mean value of that parameter for the experimental group.

_{1}Your contrast vector performs the inner product:

(1 x

*beta*) + (-1 x

_{0}*beta*) =

_{1}*beta*-

_{0}*beta*

_{1}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:

*beta _{0}* >

*beta*

_{1}, 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 â€śabsolute fibre bundle cross-sectional areaâ€ť, 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 itâ€™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!