Table 4.

Computed sample size, estimated power, and simulated power for the ANOVA, approximate ANCOVA, and exact ANCOVA methods when $G=3$, ${\mathrm{\sigma }}_Y^2=10000$, $\mathrm{\rho }=0.1$, ${\mathrm{\sigma }}^2=9900$, $\{{\mathrm{\mu }}_1,{\mathrm{\mu }}_2,{\mathrm{\mu }}_3\}=\{410,450,490\}$, ${\mathrm{\delta }}^2=0.1077$, 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	96	0.8119	0.8143	$-$ 0.0024	93	0.8023	0.7987	0.0036	96	0.8114	0.8156	$-$ 0.0042
2	96	0.8119	0.8099	0.0020	93	0.8021	0.7925	0.0096	96	0.8063	0.8141	$-$ 0.0078
3	96	0.8119	0.8016	0.0103	93	0.8019	0.7916	0.0103	96	0.8017	0.8075	$-$ 0.0058
4	96	0.8119	0.7996	0.0123	93	0.8018	0.7863	0.0155	99	0.8109	0.8118	$-$ 0.0009
5	96	0.8119	0.7929	0.0190	93	0.8016	0.7763	0.0253	99	0.8062	0.8090	$-$ 0.0028
6	96	0.8119	0.7857	0.0262	93	0.8014	0.7802	0.0212	99	0.8014	0.7936	0.0078
7	96	0.8119	0.7836	0.0283	93	0.8012	0.7638	0.0374	102	0.8104	0.8122	$-$ 0.0018
8	96	0.8119	0.7688	0.0431	93	0.8010	0.7641	0.0369	102	0.8057	0.8094	$-$ 0.0037
9	96	0.8119	0.7729	0.0390	93	0.8008	0.7570	0.0438	102	0.8009	0.8004	0.0005
10	96	0.8119	0.7677	0.0442	96	0.8144	0.7638	0.0506	105	0.8099	0.8135	$-$ 0.0036