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

Table 1 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, and {σ ²₁₁ , σ ²₁₂ , σ ²₂₁ , σ ²₂₂ } = (0.6889, 0.5184, 0.1156, 0.5929)

ψ^a	Unit costs^b	Method	Sample sizes	Total cost	Total sample size	Approximate power^c	Simulated power	Error
ψ_I	C_U	Proposed procedure	{11, 16, 13, 19}	18604.08	59	0.8005	0.7964	0.0041
		Luh and Guo	{12, 17, 14, 19}	19739.72	62	0.8254	0.8169	0.0085
	C_E	Proposed procedure	{16, 14, 7, 15}	52	52	0.8038	0.8053	–0.0015
		Luh and Guo	{17, 14, 7, 15}	53	53	0.8113	0.8077	0.0036
ψ_A	C_U	Proposed procedure	{10, 13, 12, 16}	16205.20	51	0.8004	0.7906	0.0098
		Luh and Guo	{10, 15, 13, 17}	17066.50	55	0.8208	0.8157	0.0051
	C_E	Proposed procedure	{14, 12, 6, 13}	45	45	0.8014	0.8012	0.0002
		Luh and Guo	{15, 13, 6, 14}	48	48	0.8273	0.8304	–0.0031
ψ_B	C_U	Proposed procedure	{38, 56, 48, 62}	63838.28	204	0.8000	0.7889	0.0111
		Luh and Guo	{38, 57, 48, 64}	64591.12	207	0.8046	0.8019	0.0027
	C_E	Proposed procedure	{56, 49, 23, 52}	180	180	0.8021	0.7969	0.0052
		Luh and Guo	{56, 49, 23, 52}	180	180	0.8021	0.8008	0.0013

Note: ^aThe contrast effects are ψ_I = 1.06, ψ_R = 1.14, and ψ_C = 0.56. ^bThe cost coefficients are C_U = {784.74, 267.96, 82.94, 242.44} and C_E = {1, 1, 1, 1}. ^cThe attained power computed by the suggested approximate power function

ISSN: 1471-2288