Hi Gang,

I'm working with Christy on the project that you've been discussing (and also with Kyle Simmons). Much thanks for your help! If possible we'd greatly appreciate your further feedback on a different approach to this issue.

Image that we have the following design, with Variables A and B, each having 2 levels:

Variable B
Level 1 Level 2
Variable A
Level 1 A1B1 A1B2
Level 2 A2B1 A2B2

Further imagine that we have two groups of subjects, with each group receiving only 2 cells of this design, as follows:

Group 1: A1B1, A2B2
Group 2: A1B2, A2B1

Such a design is necessary because this is a learning experiment, and a given level of Variable A (an emotion, such as fear) can only be learned once in 1 of 2 chronic situational contexts that constitute Variable B (physical danger vs. social threat). For example, Level 1 of Variable A (fear) can only be learned in Level 1 of Variable B (physical danger) or in Level 2 (social danger). If fear is learned in one of the contexts (e.g., physical threat), then the other level of Variable A, anger, must be learned in the other context (i.e., social threat). The learning associated with each emotion (which takes place outside the scanner) can only occur in one of the two chronic situations, not both, so that the chronic effect of a particular situation on a specific emotion can be assessed.

This is the kind of design that we would like to be able to analyze. As just described, we would like to assess the effect of chronic situational context on emotion. For example, do the neural activations for fear differ following chronic exposure to physical fear vs. social threat situations? Similarly, does the representation of anger differ after chronic exposure to physical danger vs. social threat? We realize that no existing AFNI anova program will handle this design exactly.

Here's our current question. Could we analyze this experiment using 3dAnova, ignoring the repeated measures within groups, acting instead as if the four conditions were all between subjects? We realize that the assumption of independence is violated to some extent, but the violation does not strike me, at least, as serious, although I could be wrong. Furthermore, it would also be the case that such an approach would be relatively conservative, given that the within-subject variance that exists within groups is not being modeled.

Specifically, here's a sketch of a 3dAnova script that could be used to analyze this experiment. Assume that the 4 conditions in the 2x2 design above constitute 4 levels as follows:

Level 1: A1B1
Level 2: A1B2
Level 3: A2B1
Level 4: A2B2

Here's a partial script

3dAnova
-levels 4
-dset 1 subject-1_A1B1
-dset 4 subject-1_A2B2
-dset 1 subject-3_A1B1
-dset 4 subject-3_A2B2
-dset 1 subject-5_A1B1
-dset 4 subject-5_A2B2
...(additional subjects from Group 1)
-dset 2 subject-2_A1B2
-dset 3 subject-2_A2B1
-dset 2 subject-4_A1B2
-dset 3 subject-4_A2B1
-dset 2 subject-6_A1B2
-dset 3 subject-6_A2B1
...(additional subjects from Group 2)
-contr 1.0 -1.0 0.0 0.0 fear_situation_effect
-contr 0.0 0.0 1.0 -1.0 anger_situation_effect
-contr 1.0 1.0 -1.0 -1.0 A_main_effect
-contr 1.0 -1.0 1.0 -1.0 B_main_effect

Again, our question is whether this would be an appropriate and effective way to analyze data from this design?

Also do you have any suggestions for other possible approaches?

Much thanks for your help!

Larry Barsalou