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

Shieh, Gwowen

doi:10.1186/s12874-020-00933-z

Table 1 The error between simulated alpha and nominal alpha for the difference tests of percentile H₀: θ = θ₀ versus H1: θ ≠ θ₀ with μ₀ = 0, σ₀ = 1, σ = 1, and α = 0.05

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

μ	p	Exact approach				Chakraborti-Li method				Bland-Altman method
μ	p	N	Lower-tail error	Upper-tail error	Two-tail error	N	Lower-tail error	Upper-tail error	Two-tail error	N	Lower-tail error	Upper-tail error	Two-tail error
0.4	0.1	109	−0.0020	0.0009	− 0.0011	97	− 0.0101	0.0108	0.0007	95	−0.0108	0.0118	0.0010
	0.2	80	−0.0042	−0.0019	− 0.0061	72	− 0.0113	0.0060	− 0.0053	71	− 0.0121	0.0082	− 0.0039
	0.3	65	−0.0030	−0.0020	− 0.0050	60	− 0.0086	0.0045	− 0.0041	60	− 0.0091	0.0058	− 0.0033
	0.4	57	0.0009	0.0012	0.0021	54	−0.0026	0.0040	0.0014	54	−0.0031	0.0046	0.0015
	0.5	52	0.0024	0.0010	0.0034	52	0.0024	0.0010	0.0034	52	0.0024	0.0010	0.0034
	0.6	50	0.0019	0.0005	0.0024	52	0.0056	−0.0029	0.0027	52	0.0056	−0.0032	0.0024
	0.7	51	0.0020	−0.0004	0.0016	56	0.0093	−0.0083	0.0010	57	0.0101	−0.0088	0.0013
	0.8	58	0.0014	−0.0012	0.0002	66	0.0124	−0.0119	0.0005	66	0.0147	−0.0127	0.0020
	0.9	75	−0.0024	−0.0025	− 0.0049	87	0.0106	−0.0133	− 0.0027	88	0.0133	−0.0138	− 0.0005
0.6	0.1	54	0.0004	0.0012	0.0016	46	−0.0137	0.0155	0.0018	44	−0.0148	0.0181	0.0033
	0.2	40	0.0014	−0.0009	0.0005	34	−0.0105	0.0137	0.0032	33	−0.0111	0.0158	0.0047
	0.3	32	−0.0001	−0.0022	− 0.0023	29	− 0.0094	0.0087	− 0.0007	28	− 0.0103	0.0104	0.0001
	0.4	27	0.0005	−0.0002	0.0003	26	−0.0048	0.0044	−0.0004	25	−0.0053	0.0052	−0.0001
	0.5	24	0.0016	0.0005	0.0021	24	0.0016	0.0005	0.0021	24	0.0016	0.0005	0.0021
	0.6	23	0.0037	0.0017	0.0054	24	0.0105	−0.0037	0.0068	25	0.0117	−0.0041	0.0076
	0.7	22	0.0028	0.0001	0.0029	26	0.0150	−0.0094	0.0056	26	0.0173	−0.0107	0.0066
	0.8	24	0.0014	−0.0012	0.0002	30	0.0183	−0.0155	0.0028	30	0.0209	−0.0159	0.0050
	0.9	31	0.0009	−0.0015	−0.0006	39	0.0201	−0.0174	0.0027	40	0.0248	−0.0182	0.0066

Back to article page

ISSN: 1471-2288

Contact us

General enquiries: journalsubmissions@springernature.com

BMC Medical Research Methodology

Contact us