Using the Bernoulli trial approaches for detecting ordered alternatives

Chang, Chia-Hao; Chin, Chih-Chien; Yu, Weichieh Wayne; Huang, Ying-Yu

doi:10.1186/1471-2288-13-148

BMC Medical Research Methodology

Table 3 Estimated powers and type I error rates of ordered tests under significance level 0.05

From: Using the Bernoulli trial approaches for detecting ordered alternatives

Location parameter	*KTMB*	*KTP*	JT	*MJT*	TM	DP	Location parameter	*KTMB*	*KTP*	JT	*MJT*	TM	DP
n₁=4, n₂=4, n₃=4							n₁=10, n₂=10, n₃=5
Log-F (2,4.5)							Log-F (2,4.5)
(0, 0, 0)	0.0492	0.0496	0.0489	0.0496	0.0494		(0, 0, 0)	0.0494	0.0481	0.0488	0.0494	0.0509
(0, 0.25, 0.5)	0.1176	0.1243	0.1096	0.1243	0.1255	-6.29%	(0, 0.25, 0.5)	0.1491	0.1542	0.1566	0.1554	0.1491	0%
(0.5, 0, 0.25)	0.0295	0.0344	0.0295	0.0344	0.0346	0.00%	(0.25, 0.5, 0)	0.0209	0.022	0.0346	0.0316	0.0217	3.83%
(0.25, 0.75, 0)	0.021	0.029	0.0212	0.029	0.0236	0.95%	(0.5, 0.75, 0)	0.0086	0.0094	0.0167	0.0143	0.0096	9.30%
Log-F (4.5, 4.5)							Log- F (4.5, 4.5
(0, 0, 0)	0.0511	0.0521	0.0518	0.0521	0.0531		(0, 0, 0)	0.0492	0.0478	0.0501	0.0488	0.0512
(0, 0.25, 0.5)	0.1533	0.1612	0.1447	0.1612	0.1604	-4.43%	(0, 0.25, 0.5)	0.2079	0.2118	0.2181	0.217	0.2021	2.87%
(0.5, 0, 0.25)	0.0189	0.0259	0.0212	0.0259	0.0237	12.17%	(0.25, 0.5, 0)	0.0207	0.0217	0.034	0.0303	0.0215	3.86%
(0.25, 0.75, 0)	0.0207	0.0246	0.0213	0.0246	0.0239	2.90%	(0.5, 0.75, 0)	0.0058	0.0058	0.012	0.0093	0.006	0.00%
Log-F (10, 4.5)							Log-F (10, 4.5)
(0, 0, 0)	0.0509	0.0523	0.0519	0.0523	0.0527		(0, 0, 0)	0.0488	0.0494	0.0517	0.0505	0.051
(0, 0.25, 0.5)	0.1802	0.1961	0.1742	0.1961	0.1843	-2.22%	(0, 0.25, 0.5)	0.2522	0.2634	0.27	0.268	0.2446	3.11%
(0.5, 0, 0.25)	0.016	0.021	0.0166	0.021	0.0192	3.75%	(0.25, 0.5, 0)	0.0217	0.0195	0.0353	0.0302	0.024	-10.14%
(0.25, 0.75, 0)	0.0161	0.0196	0.0161	0.0196	0.0198	0.00%	(0.5, 0.75, 0)	0.0064	0.0058	0.0119	0.0093	0.0076	-9.38%
n₁=4, n₂=4,							n₁=8, n₂=8,
n₃=4, n₄=4							n₃=8, n₄=4
Log-F (2,4.5)							Log-F (2,4.5)
(0, 0, 0, 0)	0.0512	0.0519	0.0515	0.0519	0.0514		(0, 0, 0, 0)	0.0505	0.0484	0.0518	0.0507	0.0479
(0, 0.25, 0.5, 0.75)	0.165	0.1806	0.188	0.1806	0.1615	2.17%	(0, 0.25, 0.5, 0.75)	0.2042	0.2313	0.2408	0.2372	0.1915	6.67%
(0.75, 0, 0.25, 0.5)	0.0388	0.0388	0.0417	0.0388	0.0471	0.00%	(0.5, 0.5, 0.5, 0)	0.0121	0.0152	0.0197	0.018	0.013	7.44%
(0.25, 0.75, 1.25, 0)	0.0225	0.0315	0.0313	0.0315	0.0276	22.67%	(0.25, 0.5, 0.75, 0)	0.0258	0.0332	0.0641	0.0575	0.0283	9.69%
Log-F (4.5, 4.5)							Log-F (4.5,4.5)
(0, 0, 0, 0)	0.0507	0.0503	0.0509	0.0503	0.0508		(0, 0, 0, 0)	0.0505	0.0487	0.0508	0.0477	0.048
(0, 0.25, 0.5, 0.75)	0.2242	0.2513	0.2606	0.2513	0.2143	4.62%	(0, 0.25, 0.5, 0.75)	0.2987	0.3358	0.3572	0.3562	0.2795	6.87%
(0.75, 0, 0.25, 0.5)	0.0297	0.0282	0.0304	0.0282	0.0385	-5.05%	(0.5, 0.5, 0.5, 0)	0.0092	0.0086	0.0122	0.0111	0.0111	-6.52%
(0.25, 0.75, 1.25, 0)	0.0237	0.0291	0.0298	0.0291	0.0277	16.88%	(0.25, 0.5, 0.75, 0)	0.025	0.0285	0.0714	0.0592	0.0302	14.00%
Log-F (10, 4.5)							Log-F (10, 4.5)
(0, 0, 0, 0)	0.0527	0.0513	0.0509	0.0513	0.0527		(0, 0, 0, 0)	0.0504	0.0492	0.0493	0.0514	0.0508
(0, 0.25, 0.5, 0.75)	0.2882	0.3179	0.3316	0.3179	0.259	11.27%	(0, 0.25, 0.5, 0.75)	0.3697	0.4268	0.4489	0.4492	0.3458	6.91%
(0.75, 0, 0.25, 0.5)	0.0168	0.0211	0.0204	0.0211	0.0216	21.43%	(0.5, 0.5, 0.5, 0)	0.0049	0.0055	0.01	0.0079	0.0079	12.24%
(0.25, 0.75, 1.25, 0)	0.025	0.0259	0.029	0.0259	0.0317	3.60%	(0.25, 0.5, 0.75, 0)	0.0273	0.027	0.076	0.0568	0.0328	-1.10%

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