# Split-split-split plot cross-over design… is this even possible?

I'm doing statistical analysis on a psychology study I ran a short while ago, and I'm starting to think that I've designed myself into a corner.

In the study, we measured participants' pointing responses after traveling in a virtual environment. There were three factors, each nested within another:

Physical rotation: 2 levels Visuals: 3 levels Turning angle: 10 levels

Each participant was subjected to all variations of these treatments, so they ran 60 trials each. However, due to this large number of factors, we restricted the randomization of the order of treatments for each participant. In picture form, our design looks like this:

M represents the physical rotation condition, V is the visual condition, and A is the turning angle condition. Each table represents one full session of 60 trials for a participant assigned to that group. The numbers in the cells represent the order in which participants assigned to that group perform trials. We ran 36 participants in total, and assigned each randomly to a group so that each of the four groups had 9 participants.

This is a bit complex, so please let me know if I can explain something better. The groups represent the four different permutations of the 60 conditions we decided on, to make the best out of our limited number of participants.

Group 1:

1. M1|V1
2. M2|V1
3. M1|V2
4. M2|V2
5. M1|V3
6. M2|V3

Group 2:

1. M1|V3
2. M2|V3
3. M1|V2
4. M2|V2
5. M1|V1
6. M2|V1

Group 3:

1. M2|V1
2. M1|V1
3. M2|V2
4. M1|V2
5. M2|V3
6. M1|V3

Group 4:

1. M2|V3
2. M1|V3
3. M2|V2
4. M1|V2
5. M2|V1
6. M1|V1

Within each of the six blocks, participants completed all ten turning angle conditions, in random order.

So, we have one factor that is randomized (turning angle), one that is alternated (movement condition) and one that is ordered (visual condition). Each of these is nested within another, making for a split-split-split plot design.

Now, what we are analyzing is how the pointing responses differ between conditions, and between participants. I have read everything I could find on split-plots, and even found some references to split-split-split plots, but I am still very unsure of how to actually crunch the numbers in R or SPSS.

I would be very grateful for any advice, hints or references to useful reading material that could help me in this. Please ask if you have any questions, or if I can explain something more clearly.