Comparison of alternative approaches for difference, noninferiority, and equivalence testing of normal percentiles

Table 2 The error between simulated alpha and nominal alpha for the non-inferiority tests of percentile H0: θ ≤ θ₀ versus H1: θ > θ₀ with μ₀ = 0, σ₀ = 1, σ = 1, and α = 0.05

μ	p	Exact approach		Chakraborti-Li method		Bland-Altman method
μ	p	N	Error	N	Error	N	Error
0.4	0.1	85	0.0047	77	0.0124	75	0.0168
	0.2	63	0.0017	57	0.0155	56	0.0175
	0.3	51	−0.0011	48	0.0123	47	0.0141
	0.4	44	0.0033	43	0.0046	42	0.0070
	0.5	41	−0.0010	41	0.0004	41	0.0003
	0.6	39	−0.0017	41	−0.0048	41	−0.0077
	0.7	40	−0.0004	44	−0.0112	45	−0.0120
	0.8	46	0.0001	51	−0.0154	52	−0.0183
	0.9	60	−0.0019	68	−0.0170	69	−0.0182
0.6	0.1	42	−0.0027	36	0.0197	35	0.0274
	0.2	31	−0.0042	27	0.0192	26	0.0278
	0.3	25	0.0010	23	0.0119	22	0.0215
	0.4	21	−0.0002	20	0.0052	20	0.0072
	0.5	19	−0.0006	19	−0.0008	19	−0.0014
	0.6	18	−0.0008	19	−0.0086	19	−0.0092
	0.7	18	−0.0013	20	−0.0154	21	−0.0195
	0.8	20	−0.0026	23	−0.0220	24	−0.0252
	0.9	25	−0.0016	31	−0.0258	31	−0.0260

ISSN: 1471-2288