Hi all,
Does anyone here have experience generating balanced latin square designs in JMP, or know is that's even possible? (e.g. Bradley, J. Complete counterbalancing of immediate sequential effects in a Latin square design. J. Amer. Statist. Ass.,.1958, 53, 525-528.). In my own research I've just created these designs manually, but I've had a few researchers ask me lately if there is something automated we can do in JMP.
Specifically, I'm looking for one of our DOE platforms to provide a table of runs for each subject (these designs apply to repeated measures designs, and each subject will experience all treatment in some order) such that 1) across all subjects each treatment condition appears only once in each ordinal position (thus controlling for order effects), and 2) each treatment condition follows every other condition an equal number of times (thus controlling for carryover effects).
For example, here's one possible balanced latin square for a study where there are 4 treatment conditions (each row is a subject, and the columns list the order of treatments A - 
1. A B D C
2. B C A D
3. C D B A
4. D A C B
here's one for 6 treatments:
1. A B F C E D
2. B C A D F E
3. C D B E A F
4. D E C F B A
5. E F D A C B
6. F A E B D C
Odd numbers of treatments actually require two latin squares to meet the listed criteria, but back to the point at hand. In JMP, as far as I know, I can randomize treatment orders within blocks (or plots, or anything hard to change), but I can't specifically counterbalance (or use a latin square, the next best thing to a full counterbalance). Have I missed this somewhere?
Thanks!
Julian
