Hi,
We are interested in conducting a 1 between 1 within two-way ANOVA on our
fMRI data. The between group factor has 5 levels corresponding to five
groups and the within group factor has three levels corresponding to three
experimental conditions (negative words, positive words, and neutral
words). In our analyses we have 36 participants with 7 in group 1, 8 in
group 2, 8 in group 3, 7 in group 4 and 6 in group 5. In the first level
analyses we generate cope maps representing the negative, positive and
neutral word conditions for each subject. We would like to use the copes as
inputs to a higher-level analysis in such a way that we can implement the
ANOVA, examining the main effect of emotion condition (positive, neutral or
negative), the main effect of group (1-5), the interaction between the two
main effects, and an omnibus test of the significance of the overall
model. Our goal follows a traditional ANOVA design, in that we’re
interested in finding those voxels/clusters whose activity significantly
varies as a function of each of our factors (e.g. not just asking the
question of whether one group or valence is significant).
Our question: will the following model give use the ANOVA outputs looking
for? Given that we have cope maps as inputs for each subject for each
condition, here’s what the EV design matrix might look. Each row in the
design matrix represents a single cope map (pos, neu and neg represent
positive, neutral and negative word conditions respectively). For
illustration, we’re pretending that there are only 3 subject per group.
EV’s
Input map grp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
pos_grp1_sub1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
pos_grp1_sub2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
pos_grp1_sub3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
pos_grp2_sub1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
pos_grp2_sub2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
pos_grp2_sub3 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
pos_grp3_sub1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
pos_grp3_sub2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
pos_grp3_sub3 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
pos_grp4_sub1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
pos_grp4_sub2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
pos_grp4_sub3 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
pos_grp5_sub1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
pos_grp5_sub2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
pos_grp5_sub3 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
neu_grp1_sub1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
neu_grp1_sub2 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
neu_grp1_sub3 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
neu_grp2_sub1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
neu_grp2_sub2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
neu_grp2_sub3 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
neu_grp3_sub1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
neu_grp3_sub2 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
neu_grp3_sub3 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
neu_grp4_sub1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
neu_grp4_sub2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
neu_grp4_sub3 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
neu_grp5_sub1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
neu_grp5_sub2 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
neu_grp5_sub3 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
neg_grp1_sub1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
neg_grp1_sub2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
neg_grp1_sub3 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
neg_grp2_sub1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
neg_grp2_sub2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
neg_grp2_sub3 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
neg_grp3_sub1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
neg_grp3_sub2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
neg_grp3_sub3 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
neg_grp4_sub1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
neg_grp4_sub2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
neg_grp4_sub3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
neg_grp5_sub1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
neg_grp5_sub2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
neg_grp5_sub3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
And here is the contrast matrix and f-tests we’re thinking would give us
the ANOVA outputs we’re interested in. The first four contrasts represent
the main effect of group, the next two represent the main effect of
valence, and the next 8 represent the interaction (this set of contrasts
follows a cell-means model):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 F1 F2 F3 F4
C1 1 -1 0 0 0 1 -1 0 0 0 1 -1 0 0 0 on on off off
C2 1 1 -2 0 0 1 1 -2 0 0 1 1 -2 0 0 on on off off
C3 1 1 1 -3 0 1 1 1 -3 0 1 1 1 -3 0 on on off off
C4 1 1 1 1 -4 1 1 1 1 -4 1 1 1 1 -4 on on off off
C5 1 1 1 1 1 -1 -1 -1 -1 -1 0 0 0 0 0 on off on off
C6 1 1 1 1 1 1 1 1 1 1 -2 -2 -2 -2 -2 on off on off
C7 1 -1 0 0 0 -1 1 0 0 0 0 0 0 0 0 on off off on
C8 1 1 -2 0 0 -1 -1 2 0 0 0 0 0 0 0 on off off on
C9 1 1 1 -3 0 -1 -1 -1 3 0 0 0 0 0 0 on off off on
C10 1 1 1 1 -4 -1 -1 -1 -1 4 0 0 0 0 0 on off off on
C11 1 -1 0 0 0 1 -1 0 0 0 -2 2 0 0 0 on off off on
C12 1 1 -2 0 0 1 1 -2 0 0 -2 -2 4 0 0 on off off on
C13 1 1 1 -3 0 1 1 1 -3 0 -2 -2 -2 6 0 on off off on
C14 1 1 1 1 -4 1 1 1 1 -4 -2 -2 -2 -2 8 on off off on
So, my question: Will the four f-tests represent the omnibus test (F1), the
main effect for group (F2), the main effect for emotion condition (F3), and
the interaction (F4), given how the design and contrast matrices are set up?
I can also send the fsf file as an attachment if it is more helpful.
Thanks
Appu
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