Counterbalancing

50xp

Suppose you have three levels of an independent variable A (i.e. A1, A2, A3) and a blocked design. You want to use full counterbalancing to take into account order effects.

What are all the possible orders that you need to use? In other words, what are the order conditions?

Possible Answers

(A1, A2, A3), (A2, A3, A1), (A3, A1, A2)
1
(A1, A2, A3), (A1, A3, A2) , (A2, A1, A3), (A2, A3, A1)
2
(A1, A2, A3), (A1, A3, A2) , (A2, A1, A3), (A2, A3, A1) , (A1, A2, A3), (A3, A1, A2)
3
(A1, A2, A3), (A1, A3, A2) , (A2, A1, A3), (A2, A3, A1) , (A3, A2, A1), (A3, A1, A2)
4
(A1, A1, A1), (A1, A1, A2), (A1, A1, A3), (A1, A2, A3), (A2, A2, A2), (A2, A2, A1), (A2, A2, A3), (A3, A3, A3), (A3, A3, A1), (A3, A3, A2)
5

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