Table 5.

Computed sample size, estimated power, and simulated power for the ANOVA, approximate ANCOVA, and exact ANCOVA methods when $G=3$, ${\mathrm{\sigma }}_Y^2=10000$, $\mathrm{\rho }=0.5$, ${\mathrm{\sigma }}^2=7500$, $\{{\mathrm{\mu }}_1,{\mathrm{\mu }}_2,{\mathrm{\mu }}_3\}=\{410,450,490\}$, ${\mathrm{\delta }}^2=0.1422$, 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	0.9125	$-$ 0.1006	72	0.8069	0.8032	0.0037	72	0.8007	0.7979	0.0028
2	96	0.8119	0.9072	$-$ 0.0953	72	0.8066	0.7901	0.0165	75	0.8122	0.8151	$-$ 0.0029
3	96	0.8119	0.9057	$-$ 0.0938	72	0.8063	0.7850	0.0213	75	0.8062	0.8072	$-$ 0.0010
4	96	0.8119	0.9057	$-$ 0.0938	72	0.8060	0.7835	0.0225	78	0.8177	0.8215	$-$ 0.0038
5	96	0.8119	0.8916	$-$ 0.0797	72	0.8057	0.7736	0.0321	78	0.8117	0.8011	0.0106
6	96	0.8119	0.8948	$-$ 0.0829	72	0.8054	0.7681	0.0373	78	0.8054	0.8039	0.0015
7	96	0.8119	0.8922	$-$ 0.0803	72	0.8051	0.7577	0.0474	81	0.8170	0.8215	$-$ 0.0045
8	96	0.8119	0.8818	$-$ 0.0699	72	0.8048	0.7561	0.0487	81	0.8109	0.8185	$-$ 0.0076
9	96	0.8119	0.8829	$-$ 0.0710	72	0.8044	0.7306	0.0738	81	0.8047	0.8041	0.0006
10	96	0.8119	0.8770	$-$ 0.0651	75	0.8218	0.7570	0.0628	84	0.8163	0.8204	$-$ 0.0041