Table 1.

Computed sample size, estimated power, and simulated power for the ANOVA, approximate ANCOVA, and exact ANCOVA methods when $G=3$, ${\mathrm{\sigma }}_Y^2=10000$, $\mathrm{\rho }=0.1$, ${\mathrm{\sigma }}^2=9900$, $\{{\mathrm{\mu }}_1,{\mathrm{\mu }}_2,{\mathrm{\mu }}_3\}=\{400,450,500\}$, ${\mathrm{\delta }}^2=0.1684$, Type I error $\mathrm{\alpha }=0.05$, and nominal power $1-\mathrm{\beta }=0.80$

P	ANOVA				Approximate ANCOVA				Exact ANCOVA
	$N_{\mathit{TO}}$	Estimated power	Simulated power	Error	$N_{\mathit{TA}}$	Estimated power	Simulated power	Error	$N_{\mathit{TE}}$	Estimated power	Simulated power	Error
1	63	0.8148	0.8169	$-$ 0.0021	63	0.8185	0.8158	0.0027	63	0.8115	0.8123	$-$ 0.0008
2	63	0.8148	0.8062	0.0086	63	0.8181	0.7993	0.0188	63	0.8038	0.7995	0.0043
3	63	0.8148	0.8014	0.0134	63	0.8178	0.7922	0.0256	66	0.8176	0.8216	$-$ 0.0040
4	63	0.8148	0.7913	0.0235	63	0.8174	0.7874	0.0300	66	0.8104	0.8094	0.0010
5	63	0.8148	0.7795	0.0353	63	0.8170	0.7796	0.0374	66	0.8029	0.8026	0.0003
6	63	0.8148	0.7703	0.0445	63	0.8166	0.7773	0.0393	69	0.8166	0.8185	$-$ 0.0019
7	63	0.8148	0.7671	0.0477	63	0.8161	0.7622	0.0539	69	0.8093	0.8080	0.0013
8	63	0.8148	0.7516	0.0632	63	0.8157	0.7522	0.0635	69	0.8018	0.8038	$-$ 0.0020
9	63	0.8148	0.7412	0.0736	63	0.8152	0.7476	0.0676	72	0.8156	0.8210	$-$ 0.0054
10	63	0.8148	0.7355	0.0793	63	0.8147	0.7302	0.0845	72	0.8083	0.8049	0.0034