Concatenate run/session or not?
We have a design with 2 independent variables (IV1 and IV2), each with 3
levels. IV1 is manipulated across blocks within a run and IV2 is
manipulated across runs. There are two approaches I can think of to anaylze
the data for the main effects and interaction for this design. What is the
advantage and disadvantage of each approach, from the conceptual and
practical perspectives? Is one more valid than the other from the
statistics point of view? Thanks very much.
Approach 1:
Concatenate all the runs together and model each of the 9 conditions as EVs
(ev11, ev12, ev13 ... ev31, ev32, ev33, the first number denotes the levels
of IV1 and the second number denotes the levels of IV2). Then the main
effects and interaction contrasts can be set up as below.
Contrast ev11 ev12 ev13 ev21 ev22 ev23 ev31 ev32 ev33
IV1 (1) 1 1 1 -1 -1 -1 0 0 0
(2) 1 1 1 0 0 0 -1 -1 -1
(3) 0 0 0 1 1 1 -1 -1 -1
IV2 (4) 1 -1 0 1 -1 0 1 -1 0
(5) 1 0 -1 1 0 -1 1 0 -1
(6) 0 1 -1 0 1 -1 0 1 -1
Int (7) 1 -1 0 -1 1 0 0 0 0
......
And then proceed to the group analysis with just one EV/contrast for group
mean.
Approach 2:
Analyze each run separately and model just the 3 conditions/levels of IV1
(ev1, ev2, ev3). Then the main effects of IV1 can be set up as below.
Contrast ev1 ev2 ev3
mean (1) 1 1 1
IV1 (2) 1 -1 0
(3) 1 0 -1
(4) 0 1 -1
And then proceed to the group analysis with the EVs/contrasts setup as
below for the three levels of IV2 (say for 5 subjects)
Group ev1 ev2 ev3 ev4 ev5 ev6 ev7 ev8
1 1 1 1 1 0 0 0 0
1 1 1 1 0 1 0 0 0
1 1 1 1 0 0 1 0 0
1 1 1 1 0 0 0 1 0
1 1 1 1 0 0 0 0 1
1 1 -1 0 1 0 0 0 0
1 1 -1 0 0 1 0 0 0
1 1 -1 0 0 0 1 0 0
1 1 -1 0 0 0 0 1 0
1 1 -1 0 0 0 0 0 1
1 1 0 -1 1 0 0 0 0
1 1 0 -1 0 1 0 0 0
1 1 0 -1 0 0 1 0 0
1 1 0 -1 0 0 0 1 0
1 1 0 -1 0 0 0 0 1
Contrast ev1 ev2 ev3 ev4 ev5 ev6 ev7 ev8
c1 1 0 0 0 0 0 0 0
c2 0 1 0 0 0 0 0 0
c3 0 0 1 0 0 0 0 0
c4 0 1 -1 0 0 0 0 0
Then the .gfeat folder should include 4 cope#.feat subfolders, one for each
of the contrasts from the first level. zstat2 to zstat4 of cope1.feat will
assess the main effect of IV2 (zstat1 is the overall grand mean of both IVs
again baseline). zstat1 of cope2.feat to cope4.feat will assess the main
effect of IV1. zstat2 to zstat4 of cope2.feat to cope4.feat will assess the
interactions.
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