Table 6.

Computed sample size, estimated power, and simulated power for the ANOVA, approximate ANCOVA, and exact ANCOVA methods when $G=3$, ${\mathrm{\sigma }}_Y^2=10000$, $\mathrm{\rho }=0.9$, ${\mathrm{\sigma }}^2=1900$, $\{{\mathrm{\mu }}_1,{\mathrm{\mu }}_2,{\mathrm{\mu }}_3\}=\{410,450,490\}$, ${\mathrm{\delta }}^2=0.5614$, 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	1.0000	$-$ 0.1881	21	0.8084	0.7851	0.0233	24	0.8516	0.8516	0.0000
2	96	0.8119	1.0000	$-$ 0.1881	21	0.8035	0.7568	0.0467	24	0.8281	0.8296	$-$ 0.0015
3	96	0.8119	1.0000	$-$ 0.1881	24	0.8637	0.8023	0.0614	24	0.8022	0.8034	$-$ 0.0012
4	96	0.8119	1.0000	$-$ 0.1881	24	0.8600	0.7777	0.0823	27	0.8437	0.8500	$-$ 0.0063
5	96	0.8119	1.0000	$-$ 0.1881	24	0.8557	0.7548	0.1009	27	0.8203	0.8162	0.0041
6	96	0.8119	1.0000	$-$ 0.1881	24	0.8508	0.7160	0.1348	30	0.8586	0.8577	0.0009
7	96	0.8119	1.0000	$-$ 0.1881	24	0.8450	0.6800	0.1650	30	0.8375	0.8354	0.0021
8	96	0.8119	1.0000	$-$ 0.1881	24	0.8382	0.6346	0.2036	30	0.8141	0.8208	$-$ 0.0067
9	96	0.8119	1.0000	$-$ 0.1881	24	0.8301	0.6029	0.2272	33	0.8537	0.8593	$-$ 0.0056
10	96	0.8119	1.0000	$-$ 0.1881	24	0.8203	0.5493	0.2710	33	0.8325	0.8390	$-$ 0.0065