Table 1.

Sample size N₃ theoretical power φ and empirical power $\tilde{\phi }$ for testing intervention group by time interaction effect in a three level mixed-effects linear regression analysis, based on 1000 simulations.

			Δδ Tend = 0.3			Δδ Tend = 0.4			Δδ Tend = 0.5
N2	N1	ρ 1	N3	φ	$\tilde{\phi }$	N3	φ	$\tilde{\phi }$	N3	φ	$\tilde{\phi }$
5	3	0.4	42	0.801	0.798	24	0.807	0.787	16	0.823	0.838
		0.5	35	0.801	0.804	20	0.807	0.810	13	0.813	0.806
		0.6	28	0.801	0.818	16	0.807	0.810	11	0.834	0.839
	6	0.4	30	0.801	0.803	17	0.804	0.807	11	0.808	0.836
		0.5	25	0.801	0.775	15	0.826	0.835	9	0.801	0.798
		0.6	20	0.801	0.810	12	0.826	0.802	8	0.841	0.847
	12	0.4	18	0.806	0.831	10	0.801	0.800	7	0.835	0.832
		0.5	15	0.806	0.821	9	0.831	0.829	6	0.845	0.837
		0.6	12	0.806	0.794	7	0.820	0.817	5	0.860	0.855
10	3	0.4	21	0.801	0.801	12	0.807	0.788	8	0.823	0.829
		0.5	18	0.812	0.811	10	0.807	0.804	7	0.841	0.852
		0.6	14	0.801	0.791	8	0.807	0.802	6	0.865	0.865
	6	0.4	15	0.801	0.809	9	0.826	0.845	6	0.841	0.843
		0.5	13	0.816	0.809	8	0.849	0.855	5	0.841	0.846
		0.6	10	0.801	0.795	6	0.826	0.822	4	0.841	0.829
	12	0.4	9	0.806	0.788	5	0.801	0.814	4	0.881	0.875
		0.5	8	0.831	0.822	5	0.868	0.869	3	0.845	0.834
		0.6	6	0.806	0.784	4	0.868	0.878	3	0.914	0.912
20	3	0.4	11	0.819	0.825	6	0.807	0.793	4	0.823	0.826
		0.5	9	0.812	0.809	5	0.807	0.793	4	0.885	0.878
		0.6	7	0.801	0.784	4	0.807	0.805	3	0.865	0.863
	6	0.4	8	0.826	0.816	5	0.863	0.862	3	0.841	0.853
		0.5	7	0.844	0.822	4	0.849	0.826	3	0.900	0.903
		0.6	5	0.801	0.800	3	0.826	0.838	2	0.841	0.839
	12	0.4	5	0.845	0.850	3	0.868	0.857	2	0.881	0.866
		0.5	4	0.831	0.842	3	0.920	0.919	2	0.930	0.927
		0.6	3	0.806	0.800	2	0.868	0.871	2	0.970	0.964
30	3	0.4	7	0.801	0.823	4	0.807	0.800	3	0.865	0.863
		0.5	6	0.812	0.806	4	0.873	0.867	3	0.918	0.901
		0.6	5	0.828	0.824	3	0.851	0.846	2	0.865	0.851
	6	0.4	5	0.801	0.801	3	0.826	0.829	2	0.841	0.839
		0.5	5	0.867	0.867	3	0.888	0.887	2	0.900	0.900
		0.6	4	0.867	0.868	2	0.826	0.828	2	0.952	0.956
	12	0.4	3	0.806	0.819	2	0.868	0.857	2	0.970	0.964
		0.5	3	0.872	0.871	2	0.920	0.929	1	0.845	0.847
		0.6	2	0.806	0.801	2	0.965	0.964	1	0.914	0.916
Mean				0.815	0.814		0.840	0.837		0.866	0.865

N₁ = the number of level one units (repeated measures) per subjects; N₂ = the number of level two units (subjects) per clinic; N₃ = the number of level three units (clinics) per group, i.e., the sample size obtained from equation (15); T_endd = N₁ - 1; ρ₁ = correlation among level one data (5); φ = theoretical power based on the formula (13); $\tilde{\phi }$ = empirical power based on equation (18); Δ_δ = standardized effect size of the slope difference that yields an intervention efect Δ_δ T_end at the end of a study.