Hi all,

Merry Christmas!

I have a three-part question about how to correctly set up contrasts. I apologize in advance for the length of this question.

I've been studying the wiki pages describing group statistics for FEAT:
http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FEAT/UserGuide#Group_Statistics

Suppose I have 3 subjects (S1,S2,S3), each subject has been scanned under 4 conditions (A1,A2, B1,B2).  The data for these conditions are the result of a fixed effects analysis for each subject.  I am not sure if this fact is important for my question so I'll describe this at the end.

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PART 1:
I want to look at the contrast between (A1+A2) v (B1+B2).
Can I do this contrast in one step?  Or do I need to run another fixed effects model for each subject?  For example, let A = A1 + A2.  Do I need to run fixed effects to get A for each subject combining A1 + A2?

I was trying to follow the "paired t-test" example to see if I can do this contrast all in one step:
http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FEAT/UserGuide#Paired_Two-Group_Difference_.28Two-Sample_Paired_T-Test.29

In this example, I understand that EVs 2-9 remove each subject's mean effect.  In my example that would be 4 repeats of this matrix (one repeat for each condition A1,A2, B1,B2):

each subj's mean effect:
S1 = 1 0 0 
S2 = 0 1 0
S3 = 0 0 1

I will not include this sub-matrix in further discussion here but will include it in my final design matrix.

Can I treat contrast (A1+A2) v (B1+B2) as if it were a paired t-test where
EV1 =  1 for A1 or A2;
EV1 = -1 for B1 or B2

In the contrast definition, the weights for EV1 would be:
A > B:  0.5  0 0 0 ....
B > A: -0.5  0 0 0 ....

where the 0.5 takes care of A = (A1+A2) and B = (B1+B2)?  (Perhaps this really does not matter.)  I think I need to do this:
A > B: (0.5*A1 + 0.5*A2) - (0.5*B1 + 0.5*B2)

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PART 2:
I want to look at the contrast between (A1) v (A2+B1+B2).
Can I treat contrast (A1) v (A2+B1+B2) as if it were a paired t-test where EV1 =  3 for A1;
EV1 = -1 for A2 or B1 or B2

And contrasts weights:
A1 > (A2+B1+B2):  1
(A2+B1+B2) > A1: -1

I am trying to do this:
A1 > (A2+B1+B2): (1*A1) - (0.33*A2 + 0.33*B1 + 0.33*B2)

I suppose an ANOVA might handle this, but I'm not confident with that yet.

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PART 3:
How would I add age as a covariate of no interest for Part 1 and Part 2?  I would demean the age and define it as the last EV, EVn.  Do I need to repeat the sub-vector of demeaned age four times, once for each condition in EVn:

each subj's demeaned age:
S1 = 9.67
S2  -0.33
S3  -9.33

For the contrast in Part 1, do I need to weight the ages by 1/2 or it doesn't matter here?

For the contrast in Part 2, do I need to weight the age sub-vector by 1/3 for (A2+B1+B2)?

Sorry for the length of this email. I realize you all are on holiday.  But I believe in Santa ... there were two Santas who helped me last week.

Happy holidays and all the best in the new year.

Thanks for all the help I've received this year,
- BettyAnn


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Fixed effects logic:
Each condition (A1,A2, B1,B2) is the subject mean from 4 scans.  That is:
A1 for S1 = fixed effects( S1:a11, S1:a12, S1:a13, S1:a14)

where:
a11 = condition A1 from scan 1;
a12 = condition A1 from scan 2;
a13 = condition A1 from scan 3;
a14 = condition A1 from scan 4;

So 
Condition A3 for subject S2 = 
  fixed effects( S2:a31, S2:a32, S2:a33, S2:a34)