Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations

Table 2

NonSpurious type II error probability (𝜋_𝐷𝐶) parameter for four single extreme outlier discordancy tests.

𝑛	𝛿	Discordancy tests
		N2		N8			N14			N15
		𝑥N2	(𝑢99)N2	𝑥N8	(𝑢99)N8	Δ𝑥N8	𝑥N14	(𝑢99)N14	Δ𝑥N14	𝑥N15	(𝑢99)N15	Δ𝑥N15
5	0	0.990003	0.0000057	0.990026	0.0000058	0.0023	0.990005	0.0000057	0.0002	0.989994	0.0000058	−0.0009
5	±0.1	0.989948	0.0000139	0.989975	0.0000140	0.0027	0.989950	0.0000140	0.0002	0.989940	0.0000144	−0.0009
5	±2	0.977285	0.0000113	0.977358	0.0000125	0.0075	0.977290	0.0000111	0.0005	0.977267	0.0000116	−0.0018
5	±3	0.961486	0.0000148	0.961632	0.0000142	0.0152	0.961497	0.0000146	0.0012	0.961459	0.0000146	−0.0028
5	±5	0.891864	0.0000205	0.892491	0.0000194	0.070	0.891901	0.0000200	0.0043	0.891823	0.0000208	−0.0046
5	±6	0.834635	0.0000222	0.835779	0.0000231	0.137	0.834704	0.0000226	0.0084	0.834602	0.0000225	−0.0038
5	±7	0.764660	0.0000240	0.766559	0.0000257	0.248	0.764766	0.0000250	0.0139	0.764661	0.0000237	0.0002
5	±8	0.685336	0.0000253	0.688202	0.0000255	0.418	0.685496	0.0000249	0.0234	0.685401	0.0000247	0.0095
5	±10	0.514122	0.0000280	0.519336	0.0000282	1.01	0.514407	0.0000292	0.056	0.514394	0.0000287	0.053
5	±12	0.351103	0.0000258	0.358468	0.0000275	2.10	0.351500	0.0000257	0.113	0.351629	0.0000258	0.150
5	±15	0.165615	0.0000194	0.174053	0.0000215	5.1	0.166070	0.0000196	0.275	0.166367	0.0000196	0.45
5	±18	0.062959	0.0000126	0.069566	0.0000148	10.5	0.063321	0.0000127	0.58	0.063618	0.0000134	1.05
5	±20	0.029322	0.0000082	0.033997	0.0000089	15.9	0.029577	0.0000084	0.87	0.029815	0.0000081	1.68
10	0	0.990008	0.0000057	0.990041	0.0000057	0.0034	0.990003	0.0000054	−0.0006	0.990025	0.0000059	0.0017
10	±0.1	0.989851	0.0000197	0.989888	0.0000173	0.0037	0.989844	0.0000207	−0.0006	0.989869	0.0000195	0.0019
10	±1	0.978810	0.0000183	0.979321	0.0000174	0.052	0.978911	0.0000179	0.0103	0.978879	0.0000188	0.0070
10	±2	0.949169	0.0000168	0.951501	0.0000163	0.246	0.949704	0.0000165	0.056	0.949433	0.0000175	0.0279
10	±3	0.878974	0.0000199	0.886717	0.0000192	0.88	0.880804	0.0000197	0.208	0.879762	0.0000202	0.090
10	±4	0.736953	0.0000241	0.756911	0.0000242	2.71	0.741679	0.0000266	0.64	0.738849	0.0000253	0.257
10	±5	0.523889	0.0000273	0.561084	0.0000257	7.1	0.532523	0.0000263	1.65	0.527197	0.0000266	0.63
10	±6	0.300940	0.0000248	0.349468	0.0000258	16.1	0.311799	0.0000260	3.61	0.304921	0.0000249	1.32
10	±7	0.136560	0.0000182	0.181585	0.0000226	33.0	0.146058	0.0000174	7.0	0.139899	0.0000185	2.44
10	±8	0.048488	0.0000122	0.079155	0.0000144	63	0.054422	0.0000118	12.2	0.050495	0.0000130	4.14
10	±9	0.013431	0.0000074	0.029234	0.0000092	118	0.016139	0.0000075	20.2	0.014300	0.0000074	6.5
10	±10	0.002900	0.0000031	0.009248	0.0000056	219	0.003821	0.0000036	31.8	0.003180	0.0000030	9.6
10	±11	0.000489	0.0000013	0.002529	0.0000029	418	0.000726	0.0000016	49	0.000556	0.0000014	13.8
15	0	0.989998	0.000006	0.990015	0.0000062	0.0017	0.98998	0.0000061	−0.0018	0.989989	0.000006	−0.0010
15	±0.1	0.989768	0.0000204	0.989811	0.0000210	0.0044	0.989766	0.0000209	−0.0002	0.989759	0.0000200	−0.0009
15	±0.5	0.985307	0.0000236	0.985665	0.0000202	0.0364	0.985507	0.0000249	0.0204	0.985345	0.0000240	0.0039
15	±2	0.974943	0.0000225	0.976229	0.0000186	0.132	0.975702	0.0000241	0.078	0.975113	0.0000236	0.0174
15	±5	0.932551	0.0000202	0.938851	0.0000184	0.68	0.936096	0.0000207	0.380	0.933417	0.0000206	0.093
15	±4	0.827672	0.0000245	0.848433	0.0000236	2.51	0.838586	0.0000251	1.32	0.830350	0.0000236	0.324
15	±4.5	0.621647	0.0000288	0.669717	0.0000270	7.7	0.644852	0.0000332	3.73	0.627283	0.0000285	0.91
15	±5	0.487591	0.0000276	0.550018	0.0000319	12.8	0.516243	0.0000322	5.9	0.494476	0.0000290	1.41
15	±5	0.351577	0.0000269	0.423601	0.0000266	20.5	0.382834	0.0000290	8.9	0.358972	0.0000287	2.10
15	±6	0.137443	0.0000198	0.204194	0.0000211	49	0.162735	0.0000196	18.4	0.143150	0.0000201	4.15
15	±7	0.035757	0.0000093	0.074779	0.0000144	109	0.048090	0.0000112	34.5	0.038352	0.0000098	7.3
15	±8	0.006107	0.0000043	0.021184	0.0000094	249	0.009822	0.0000054	61	0.006819	0.0000042	11.7
15	±9	0.000682	0.0000015	0.004748	0.0000039	600	0.001393	0.0000019	104	0.000802	0.0000017	17.6
15	±10	0.000049	0.0000004	0.000858	0.0000017	1640	0.000138	0.0000007	180	0.000062	0.0000005	25.7
20	0	0.990017	0.0000057	0.990004	0.000006	−0.0014	0.990026	0.000006	0.0009	0.990004	0.0000059	−0.0014
20	±0.1	0.989743	0.0000259	0.989771	0.0000248	0.0028	0.989786	0.0000243	0.0043	0.989734	0.0000277	−0.0009
20	±0.5	0.984600	0.0000243	0.985127	0.0000258	0.054	0.985093	0.0000265	0.050	0.984682	0.0000246	0.0083
20	±1	0.972754	0.0000237	0.974729	0.0000256	0.203	0.974439	0.0000213	0.173	0.973084	0.0000225	0.0339
20	±2	0.922859	0.0000259	0.932611	0.0000219	1.06	0.930457	0.0000234	0.82	0.924463	0.0000266	0.174
20	±3	0.798422	0.0000265	0.829677	0.0000230	3.91	0.820494	0.0000248	2.76	0.803167	0.0000283	0.59
20	±4	0.561409	0.0000283	0.628839	0.0000267	12.0	0.604043	0.0000273	7.6	0.570474	0.0000288	1.61
20	±4.5	0.415514	0.0000280	0.498225	0.0000261	19.9	0.464616	0.0000262	11.8	0.425784	0.0000285	2.47
20	±5	0.276626	0.0000244	0.365289	0.0000265	32.1	0.325675	0.0000297	17.7	0.286659	0.0000245	3.63
20	±6	0.085535	0.0000163	0.152881	0.0000198	79	0.116833	0.0000185	36.6	0.091506	0.0000175	7.0
20	±7	0.015809	0.0000070	0.046048	0.0000127	191	0.026842	0.0000087	70	0.017699	0.0000079	12.0
20	±8	0.001716	0.0000021	0.010242	0.0000053	500	0.003921	0.0000036	128	0.002041	0.0000025	18.9
20	±9	0.000109	0.0000006	0.001733	0.0000024	1500	0.000366	0.0000011	237	0.000139	0.0000007	28.5
20	±10	0.000004	0.0000001	0.000229	0.0000010	5600	0.000022	0.0000002	450	0.000006	0.0000001	41.3