help > RE: three factor ANOVA - or simplify design?
Sep 8, 2020  06:09 PM | Andrew Zalesky
RE: three factor ANOVA - or simplify design?
Hi Preini

I would suggest the following design matrix, where S1 and S2 are in the treatment group and S3 and S4 are placebo:

S1T1  1  0  0  1  0  0  0
S1T2  1  1  1  1  0  0  0
S2T1  1  0  0  0  1  0  0
S2T2  1  1  1  0  1  0  0
S3T1  0  0  0  0  0  1  0
S3T2  0  1  0  0  0  1  0
S4T1  0  0  0  0  0  0  1
S4T2  0  1  0  0  0  0  1

The first column is group (active/placebo), the second is time (baseline - T1 and follow up - T2), the third is the group x time interaction and the final four columns model the within subject mean.

Important: you will need to remove the first column, otherwise the design will be rank deficient. I have only shown the first column to convey how the interaction terms was computed.

Once the first column is removed, you will have 6 columns and the contrast for testing the interaction would be:
[ 0 1 0 0 0 0]
or
[0 -1 0 0 0 0]

Andrew

Originally posted by preini:
Dear Andrew,

thanks for your help in this forum here, I appreciate it very much.

I'm working on a project with 2 groups (medication group, placebo group) with 2 fMRI sessions, where one session is medication/placebo, and one is a baseline scan.
That means I have subjects from the Placebo group that have one placebo and one baseline scan and vice versa with the medication group.
So, every subject has 2 scans, baseline + placebo or medication.

- I have read that you sometimes advice to simplify the design. Would you advise to just use medication vs. placebo sessions? This would be okay, but my sample size is not that high so I don't want to lose data

- I am not sure if my Design Matrix is correct, as I struggled a bit to put this design into a the DM.

I tried it and tried out several types of DM, but I am not sure if I have done it correctly. Say I have 2 subjects:
M_subj2_post, M_subj1_pre, P_subj4_post, P_subj3_pre

I would code it this way:

1 0 1 1
0 1 0 1
1 0 1 -1
0 1 0 -1

where the last 2 columns are: timepoint (0 for pre, 1 for post) and group (modafanil and placebo group).