Power Analysis in Two-Level Unbalanced Designs

Previous work on statistical power has discussed mainly single-level designs or 2-level balanced designs with random effects. Although balanced experiments are common, in practice balance cannot always be achieved. Work on class size is one example of unbalanced designs. This study provides methods for power analysis in 2-level unbalanced designs with random effects. Overall, the nesting affects power negatively, the treatment affects power positively, and the Level-2 units affect power more than Level-1 units. Computing power assuming balanced designs provides reasonable estimates only when imbalance is mild or moderate. When imbalance is large or extreme, computing power assuming balanced designs produces larger estimates of power. The use of the harmonic mean provides accurate estimates of power in unbalanced 2-level designs even when imbalance is large.