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

Table 5

Power of Test (Ω) values for four single extreme outlier discordancy tests as a function of 𝜀.

𝑛	𝜀	Discordancy tests
		N2		N8			N14			N15
		𝑥N2	(𝑢99)N2	𝑥N8	(𝑢99)N8	Δ𝑥N8	𝑥N14	(𝑢99)N14	Δ𝑥N14	𝑥N15	(𝑢99)N15	Δ𝑥N15
5	±1.1	0.020850	0.0000310	0.020803	0.0000314	−0.227	0.020844	0.0000307	−0.0313	0.020869	0.0000314	0.087
5	±3	0.064711	0.0000419	0.064385	0.0000419	−0.50	0.064691	0.0000425	−0.0304	0.064743	0.0000412	0.050
5	±5	0.154521	0.0000496	0.153274	0.0000481	−0.81	0.154449	0.0000483	−0.046	0.154511	0.0000480	−0.0066
5	±7	0.258413	0.0000570	0.256108	0.0000574	−0.89	0.258284	0.0000555	−0.050	0.258324	0.0000568	−0.0344
5	±10	0.397926	0.0000695	0.394635	0.0000687	−0.83	0.397744	0.0000695	−0.046	0.397724	0.0000691	−0.051
5	±12.9	0.50175	0.0000610	0.49817	0.0000609	−0.71	0.50155	0.0000594	−0.0389	0.50151	0.0000620	−0.047
5	±15	0.560321	0.0000690	0.556782	0.0000652	−0.63	0.560129	0.0000682	−0.0341	0.560080	0.0000690	−0.0429
5	±20	0.660616	0.0000600	0.657405	0.0000600	−0.49	0.660442	0.0000600	−0.0264	0.660386	0.0000588	−0.0347
5	±30	0.771476	0.0000629	0.769007	0.0000655	−0.320	0.771337	0.0000637	−0.0181	0.771296	0.0000644	−0.0233
5	±40	0.822288	0.0000430	0.820357	0.0000442	−0.235	0.822181	0.0000431	−0.0130	0.822138	0.0000428	−0.0182
5	±60	0.881517	0.0000389	0.880180	0.0000385	−0.152	0.881443	0.0000392	−0.0084	0.881408	0.0000394	−0.0124
5	±80	0.911274	0.0000321	0.910263	0.0000327	−0.111	0.911218	0.0000324	−0.0061	0.911195	0.0000311	−0.0087
5	±120	0.941005	0.0000307	0.940328	0.0000307	−0.072	0.940970	0.0000306	−0.00371	0.940951	0.0000306	−0.0058
5	±160	0.955830	0.0000281	0.955330	0.0000269	−0.052	0.955801	0.0000285	−0.00302	0.955792	0.0000281	−0.00395
5	±200	0.964715	0.0000244	0.964312	0.0000248	−0.0417	0.964693	0.0000241	−0.00226	0.964681	0.0000242	−0.00345
10	±1.1	0.023252	0.0000400	0.023052	0.0000335	−0.86	0.023228	0.0000400	−0.106	0.023210	0.0000386	−0.181
10	±3	0.230007	0.0000688	0.215369	0.0000615	−6.4	0.226613	0.0000671	−1.48	0.228723	0.0000691	−0.56
10	±5	0.466178	0.0000675	0.444482	0.0000696	−4.7	0.461346	0.0000693	−1.037	0.464412	0.0000674	−0.379
10	±5.4	0.501202	0.0000668	0.479497	0.0000682	−4.33	0.496385	0.0000629	−0.96	0.499458	0.0000674	−0.348
10	±10	0.609736	0.0000680	0.589504	0.0000642	−3.32	0.605299	0.0000668	−0.73	0.608161	0.0000726	−0.258
10	±10	0.729058	0.0000551	0.712878	0.0000551	−2.22	0.725561	0.0000548	−0.48	0.727835	0.0000575	−0.168
10	±15	0.824592	0.0000517	0.813173	0.0000531	−1.38	0.822123	0.0000498	−0.299	0.823755	0.0000530	−0.101
10	±20	0.872018	0.0000545	0.863336	0.0000533	−1.00	0.870142	0.0000543	−0.215	0.871397	0.0000552	−0.071
10	±30	0.918594	0.0000550	0.912810	0.0000579	−0.63	0.917335	0.0000538	−0.137	0.918194	0.0000540	−0.0435
10	±40	0.934126	0.0000272	0.929776	0.0000294	−0.47	0.933203	0.0000279	−0.099	0.933789	0.0000276	−0.0360
10	±50	0.947611	0.0000234	0.944143	0.0000241	−0.366	0.946875	0.0000242	−0.078	0.947342	0.0000238	−0.0284
10	±100	0.974142	0.0000183	0.972421	0.0000184	−0.177	0.973777	0.0000185	−0.0374	0.974010	0.0000184	−0.0136
10	±150	0.982843	0.0000161	0.981700	0.0000168	−0.116	0.982600	0.0000166	−0.0247	0.982756	0.0000161	−0.0089
10	±200	0.987171	0.0000142	0.986318	0.0000144	−0.086	0.986991	0.0000138	−0.0183	0.987105	0.0000143	−0.0067
15	±1.1	0.024941	0.0000507	0.024516	0.0000434	−1.70	0.024714	0.0000454	−0.91	0.024907	0.0000523	−0.137
15	±3	0.315624	0.0000816	0.285482	0.0000707	−9.6	0.301908	0.0000791	−4.35	0.312616	0.0000768	−0.95
15	±4.4	0.505574	0.0000745	0.470626	0.0000677	−6.9	0.490624	0.0000697	−2.96	0.502393	0.0000705	−0.63
15	±5	0.563420	0.0000689	0.529313	0.0000721	−6.1	0.549047	0.0000748	−2.55	0.560407	0.0000698	−0.53
15	±7	0.692305	0.0000627	0.663682	0.0000610	−4.13	0.680599	0.0000638	−1.69	0.689963	0.0000629	−0.338
15	±10	0.791754	0.0000591	0.770289	0.0000590	−2.71	0.783169	0.0000580	−1.08	0.790166	0.0000564	−0.201
15	±15	0.867777	0.0000506	0.853207	0.0000541	−1.68	0.862030	0.0000516	−0.66	0.866870	0.0000525	−0.105
15	±20	0.904654	0.0000486	0.893754	0.0000511	−1.20	0.900431	0.0000428	−0.47	0.904100	0.0000549	−0.061
15	±30	0.940391	0.0000448	0.933225	0.0000533	−0.76	0.937686	0.0000478	−0.288	0.940194	0.0000497	−0.0209
15	±40	0.950189	0.0000256	0.944782	0.0000263	−0.57	0.948017	0.0000256	−0.229	0.949688	0.0000258	−0.053
15	±60	0.967191	0.0000212	0.963613	0.0000224	−0.370	0.965751	0.0000218	−0.149	0.966859	0.0000207	−0.0343
15	±80	0.975546	0.0000199	0.972878	0.0000213	−0.274	0.974475	0.0000198	−0.110	0.975299	0.0000200	−0.0253
15	±140	0.986132	0.0000140	0.984621	0.0000148	−0.153	0.985524	0.0000143	−0.062	0.985992	0.0000137	−0.0142
15	±200	0.990334	0.0000113	0.989278	0.0000127	−0.107	0.989908	0.0000116	−0.0429	0.990235	0.0000116	−0.0099
20	±1.1	0.025959	0.0000600	0.025296	0.0000570	−2.551	0.025396	0.0000534	−2.17	0.025877	0.0000610	−0.313
20	±3	0.362436	0.0000753	0.321879	0.0000782	−11.2	0.338086	0.0000708	−6.7	0.357843	0.0000754	−1.27
20	±4	0.509029	0.0000677	0.465277	0.0000661	−8.6	0.484093	0.0000691	−4.9	0.504506	0.0000649	−0.89
20	±5	0.609022	0.0000669	0.567957	0.0000706	−6.7	0.586331	0.0000707	−3.73	0.605042	0.0000639	−0.65
20	±7	0.728947	0.0000692	0.695836	0.0000693	−4.5	0.711240	0.0000640	−2.43	0.726084	0.0000696	−0.393
20	±10	0.818758	0.0000462	0.794479	0.0000533	−2.97	0.806135	0.0000486	−1.54	0.816978	0.0000476	−0.217
20	±15	0.886139	0.0000424	0.869861	0.0000430	−1.84	0.877932	0.0000468	−0.93	0.885261	0.0000465	−0.099
20	±20	0.918508	0.0000399	0.906382	0.0000446	−1.32	0.912559	0.0000407	−0.65	0.918085	0.0000427	−0.046
20	±30	0.949667	0.0000432	0.941715	0.0000507	−0.84	0.945966	0.0000481	−0.390	0.949717	0.0000506	0.0053
20	±40	0.956868	0.0000229	0.950924	0.0000258	−0.62	0.953687	0.0000219	−0.332	0.956225	0.0000226	−0.067
20	±60	0.971612	0.0000209	0.967685	0.0000218	−0.404	0.969514	0.0000209	−0.216	0.971191	0.0000210	−0.0434
20	±80	0.978856	0.0000170	0.975928	0.0000185	−0.299	0.977289	0.0000179	−0.160	0.978541	0.0000170	−0.0322
20	±140	0.988015	0.0000127	0.986356	0.0000127	−0.168	0.987127	0.0000139	−0.090	0.987837	0.0000128	−0.0181
20	±200	0.991646	0.0000107	0.990487	0.0000113	−0.117	0.991025	0.0000109	−0.063	0.991520	0.0000113	−0.0126