If we had a factorial experiment with different levels of treatment, this would still be considered a factorial design. For instance, in Lesson 7C, there is a factorial example (Pesticide Example) where we have two treatments: the pesticide and the variety. The pesticide has 4 levels, and the variety has 3 three levels. The Pesticide experiment is balanced because each treatment combination is assigned to the same # of EUs. An unbalanced factorial design could happen if: (1) if the treatment-combination was not assigned to the same # of EU (maybe due to missing data), or (2) some treatment-combination are missing (this is common when certain treatment combinations would be dangerous or unreasonable). Hope this helps!
