Table 2.

Computed sample size, estimated power, and simulated power for the ANOVA, approximate ANCOVA, and exact ANCOVA methods when $G=3$, ${\mathrm{\sigma }}_Y^2=10000$, $\mathrm{\rho }=0.5$, ${\mathrm{\sigma }}^2=7500$, $\{{\mathrm{\mu }}_1,{\mathrm{\mu }}_2,{\mathrm{\mu }}_3\}=\{400,450,500\}$, ${\mathrm{\delta }}^2=0.2222$, 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	0.9073	$-$ 0.0925	48	0.8136	0.7994	0.0142	48	0.8042	0.8006	0.0036
2	63	0.8148	0.9022	$-$ 0.0874	48	0.8130	0.7993	0.0137	51	0.8217	0.8215	0.0002
3	63	0.8148	0.9006	$-$ 0.0858	48	0.8123	0.7883	0.0240	51	0.8122	0.8062	0.0060
4	63	0.8148	0.8945	$-$ 0.0797	48	0.8115	0.7705	0.0410	51	0.8022	0.8053	$-$ 0.0031
5	63	0.8148	0.8926	$-$ 0.0778	48	0.8108	0.7592	0.0516	54	0.8201	0.8271	$-$ 0.0070
6	63	0.8148	0.8799	$-$ 0.0651	48	0.8099	0.7528	0.0571	54	0.8104	0.8177	$-$ 0.0073
7	63	0.8148	0.8737	$-$ 0.0589	48	0.8091	0.7366	0.0725	54	0.8004	0.7976	0.0028
8	63	0.8148	0.8653	$-$ 0.0505	48	0.8082	0.7196	0.0886	57	0.8185	0.8291	$-$ 0.0106
9	63	0.8148	0.8539	$-$ 0.0391	48	0.8072	0.7087	0.0985	57	0.8088	0.8157	$-$ 0.0069
10	63	0.8148	0.8526	$-$ 0.0378	48	0.8062	0.6957	0.1105	60	0.8263	0.8259	0.0004