Table 3.

Estimated required number of clusters for the covariate-adjusted ATE test based on the proposed formula, empirical type I error (Emp. size), empirical power (Emp. power), as well as predicted power (Pred. power) for the covariate-adjusted ATE test when randomization is at the cluster level. For studying power, the ATE size is fixed at

Design parameters							Performance characteristics
							Emp. size	Emp. power	Pred. power
20	4	0.015	0.010	0.150	0.100	22	0.051	0.824	0.828
20	4	0.015	0.010	0.300	0.150	22	0.052	0.821	0.828
20	4	0.015	0.010	0.500	0.300	22	0.054	0.821	0.828
20	4	0.100	0.050	0.150	0.100	60	0.052	0.798	0.801
20	4	0.100	0.050	0.300	0.150	60	0.053	0.797	0.801
20	4	0.100	0.050	0.500	0.300	60	0.053	0.796	0.801
20	8	0.015	0.010	0.150	0.100	16	0.048	0.820	0.819
20	8	0.015	0.010	0.300	0.150	16	0.048	0.818	0.819
20	8	0.015	0.010	0.500	0.300	16	0.051	0.814	0.819
20	8	0.100	0.050	0.150	0.100	52	0.048	0.815	0.811
20	8	0.100	0.050	0.300	0.150	52	0.048	0.815	0.811
20	8	0.100	0.050	0.500	0.300	52	0.049	0.813	0.811
50	4	0.015	0.010	0.150	0.100	16	0.051	0.839	0.832
50	4	0.015	0.010	0.300	0.150	16	0.053	0.840	0.832
50	4	0.015	0.010	0.500	0.300	16	0.055	0.837	0.832
50	4	0.100	0.050	0.150	0.100	56	0.050	0.812	0.810
50	4	0.100	0.050	0.300	0.150	56	0.050	0.814	0.810
50	4	0.100	0.050	0.500	0.300	56	0.050	0.813	0.810
50	8	0.015	0.010	0.150	0.100	14	0.054	0.851	0.851
50	8	0.015	0.010	0.300	0.150	14	0.056	0.850	0.851
50	8	0.015	0.010	0.500	0.300	14	0.059	0.842	0.851
50	8	0.100	0.050	0.150	0.100	48	0.051	0.805	0.801
50	8	0.100	0.050	0.300	0.150	48	0.052	0.802	0.801
50	8	0.100	0.050	0.500	0.300	48	0.054	0.802	0.801