Dear SPMers,
I have a couple of questions regarding the flexible factorial design in SPM12 to perform two-way repeated measures ANOVA.
Our fMRI data were collected from 22 subjects and each subject was subjected to each of two conditions (i.e., conditions A and B) on a separate day. In each day, two fMRI runs (with a similar experimental paradigm and a single fMRI run was collected two times) were acquired before (i.e. pre-condition) and after (post-condition) the condition A or B.
Now, I think our data fit to the 2x2 repeated measures ANOVA (i.e., two conditions A and B are the first factor; pre-condition and post-condition are the second factor). There are eight fMRI runs for each subject (i.e., 2 fMRI runs per pre- or post-condition x 2 pre-/post-conditions x 2 conditions A/B = 8) and I used the flexible factorial design in SPM12 to analyse these 8 fMRI runs across 22 subjects.
I set three factors including the subject factor (with independence 'yes'; variance 'unequal'; unequal variance of the subject factor is based on the research in this email list, in which this variance of within-subject factor is actually unequal, since this unequal variance option resulted in a covariance matrix that is deviated from an identity matrix; i.e. if the variance of within-subject factor is actually equal, then the covariance matrix would be close to an identity matrix even with the ‘unequal’ variance option), the condition A/B factor (with independence 'no'; variance 'unequal'), and the pre-/post-condition factor (with independence 'no'; variance 'unequal'). Then, to specify all 8 scans/runs of each subject, I used the numbers as follows:
[1 1;
1 1;
1 2;
1 2;
2 1;
2 1;
2 2;
2 2]
The model was estimated and the contrasts to find the main effects and interaction were specified as follows:
Main effect of condition A/B: [1 -1 0 0 0.5 0.5 -0.5 -0.5]
Main effect of pre-/post-condition: [0 0 1 -1 0.5 -0.5 0.5 -0.5]
Interaction: [0 0 0 0 1 -1 -1 1]
Then, I can observe some significant clusters from the above contrasts.
My questions are:
(1) Is there any issue regarding above my specification of the analysis given my experimental setting/data?
(2) How I can draw/present the activity from input data (i.e., 8 input volumes of the analysis corresponding to the 8 runs per subject) to show the significant main effect and/or interaction of the survived clusters?
This may not be straightforward because the variance option to 'unequal' for each factor did additional correction to address the non-sphericity (due to the unequal variance across the voxels within a volume)?
When I draw the activity from each condition A/B and pre-/post-condition simply using the input data (without any processing related to the non-sphericity correction of the flexible factorial design analysis), the levels of the activity in the significant cluster seem not that significantly different compared to the significance level of the corresponding cluster from the flexible factorial design analysis.
(3) Is there any way/process to reflect/obtain the non-sphericity corrected values of the input data? (related to (2)). This would not be a simple normalization step across the voxels within a volume such as a pseudo z-scoring (i.e. zero mean and unit variance), right?
Any thoughts/help would be very much appreciated!
Please let me know for any questions/comments.
Best,
JH
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