A systematic approach to designing statistically powerful heteroscedastic 2 × 2 factorial studies while minimizing financial costs

Table 2 Computed sample size, total cost, total size, simulated power, and error for the approaches of the proposed approach and Luh and Guo’s (2016) method, when α = 0.05, 1 – β = 0.8, ψ_I = 2, and {σ ²₁₁ , σ ²₁₂ , σ ²₂₁ , σ ²₂₂ } = (1, 4, 9, 16)

Unit costs	Method	Sample sizes	Total cost	Total sample size	Approximate power^a	Simulated power	Error
{1, 1, 1, 1}	Proposed procedure	{20, 40, 60, 79}	199	199	0.8016	0.8002	0.0014
	Luh and Guo	{20, 40, 60, 80}	200	200	0.8036	0.8029	0.0007
{1, 2, 3, 4}	Proposed procedure	{33, 48, 58, 68}	575	207	0.8000	0.7971	0.0029
	Luh and Guo	{34, 48, 59, 68}	579	209	0.8028	0.8050	–0.0022
{4, 3, 2, 1}	Proposed procedure	{14, 32, 57, 108}	374	211	0.8009	0.7979	0.0030
	Luh and Guo	{14, 32, 58, 109}	377	213	0.8041	0.8047	–0.0006
{1, 1, 2, 5}	Proposed procedure	{32, 63, 68, 58}	521	221	0.8001	0.7928	0.0073
	Luh and Guo	{33, 65, 69, 58}	526	225	0.8038	0.8033	0.0005
{5, 2, 1, 1}	Proposed procedure	{11, 34, 72, 95}	290	212	0.8006	0.8000	0.0006
	Luh and Guo	{11, 34, 73, 97}	293	215	0.8046	0.8089	–0.0043
{1, 3, 3, 1}	Proposed procedure	{27, 32, 47, 107}	371	213	0.8004	0.8030	–0.0026
	Luh and Guo	{28, 32, 48, 109}	377	217	0.8039	0.8067	–0.0028

ISSN: 1471-2288