. Author manuscript; available in PMC: 2018 Feb 1.

Published in final edited form as: Stat Methods Med Res. 2016 Jul 11;26(1):399–413. doi: 10.1177/0962280214547381

Table 2.

Comparison of theoretical power and simulation-based empirical power when group sizes are equal in a two-level model: Determinations of K with given J.

Δ₍₂₎	ρ	Experimental arm: N_E = JK		Control arm: N_C = J′	N_E + N_C	φ⁽²⁾	φ̃⁽²⁾
Δ₍₂₎	ρ	J	K	J′ = JK	N_E + N_C	φ⁽²⁾	φ̃⁽²⁾
0.4	0.025	5	26	130	260	0.807	0.776
	0.050	5	37	185	370	0.802	0.749
	0.075	5	69	345	690	0.800	0.725
0.5	0.025	5	15	75	150	0.811	0.790
	0.050	5	18	90	180	0.809	0.767
	0.075	5	22	110	220	0.800	0.742
0.6	0.025	5	10	50	100	0.816	0.767
	0.050	5	11	55	110	0.811	0.786
	0.075	5	12	60	120	0.800	0.764
Mean						0.806	0.763

Note: Δ₍₂₎ is a standardized effects size for two-level models; ρ (2) is the intra-class correlation coefficient of outcome Y within groups in the experimental arm; J is the given number of groups in the experimental arm; K is the number of subjects per group determined based on equation (7); φ⁽²⁾ is the theoretical power based on equation (5); and φ̃⁽²⁾ is the empirical power estimated based on 1000 simulations for each combination of design parameters.