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

Table 6

Test Performance Criterion P5 (𝜋_𝐷∣𝐶) 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	0.011106	0.0000274	0.011080	0.0000273	−0.237	0.011101	0.0000274	−0.0425	0.011115	0.0000280	0.076
5	±3	0.056787	0.0000393	0.056474	0.0000387	−0.55	0.056768	0.0000397	−0.0321	0.056810	0.0000382	0.0408
5	±5	0.146913	0.0000462	0.145680	0.0000452	−0.84	0.146842	0.0000447	−0.048	0.146893	0.0000452	−0.0131
5	±7	0.250890	0.0000523	0.248598	0.0000537	−0.91	0.250762	0.0000512	−0.051	0.250790	0.0000524	−0.0397
5	±10	0.390462	0.0000624	0.387183	0.0000608	−0.84	0.390280	0.0000627	−0.047	0.390249	0.0000624	−0.055
5	±13.1	0.50043	0.0000544	0.49686	0.0000559	−0.71	0.50023	0.0000544	−0.0406	0.50018	0.0000553	−0.050
5	±15	0.552883	0.0000554	0.549351	0.0000535	−0.64	0.552692	0.0000547	−0.0346	0.552630	0.0000551	−0.046
5	±20	0.653179	0.0000491	0.649982	0.0000501	−0.49	0.653009	0.0000491	−0.0262	0.652941	0.0000480	−0.0365
5	±30	0.764071	0.0000476	0.761610	0.0000464	−0.322	0.763935	0.0000480	−0.0178	0.763882	0.0000487	−0.0248
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	0.013593	0.0000385	0.013418	0.0000340	−1.29	0.013562	0.0000384	−0.227	0.013564	0.0000378	−0.209
10	±3	0.222304	0.0000659	0.207623	0.0000591	−6.6	0.218930	0.0000661	−1.52	0.220981	0.0000656	−0.60
10	±5	0.458753	0.0000661	0.437008	0.0000668	−4.7	0.453946	0.0000689	−1.05	0.456939	0.0000667	−0.395
10	±5.41	0.499554	0.0000668	0.477805	0.0000682	−4.35	0.494764	0.0000629	−0.96	0.49776	0.0000674	−0.359
10	±7	0.602388	0.0000651	0.582111	0.0000625	−3.37	0.597979	0.0000649	−0.73	0.600766	0.0000684	−0.269
10	±10	0.721760	0.0000501	0.705530	0.0000527	−2.25	0.718290	0.0000492	−0.48	0.720482	0.0000517	−0.177
10	±15	0.817312	0.0000418	0.805848	0.0000426	−1.40	0.814868	0.0000429	−0.299	0.816420	0.0000412	−0.109
10	±20	0.864739	0.0000433	0.856024	0.0000408	−1.01	0.862890	0.0000426	−0.214	0.864058	0.0000439	−0.079
10	±30	0.911335	0.0000299	0.905514	0.0000319	−0.64	0.910096	0.0000294	−0.136	0.910883	0.0000309	−0.050
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	0.015232	0.0000509	0.014804	0.0000414	−2.81	0.014971	0.0000442	−1.71	0.015180	0.0000518	−0.340
15	±3	0.307670	0.0000774	0.277454	0.0000694	−9.8	0.293796	0.0000758	−4.5	0.304363	0.0000734	−1.08
15	±4.5	0.508306	0.0000693	0.473352	0.0000627	−6.9	0.493247	0.0000686	−2.96	0.504762	0.0000674	−0.70
15	±5	0.555712	0.0000644	0.521524	0.0000708	−6.2	0.541147	0.0000721	−2.62	0.552297	0.0000664	−0.61
15	±7	0.684663	0.0000590	0.655963	0.0000589	−4.19	0.672765	0.0000603	−1.74	0.681886	0.0000602	−0.406
15	±10	0.784156	0.0000518	0.762607	0.0000574	−2.75	0.775363	0.0000548	−1.12	0.782114	0.0000522	−0.260
15	±15	0.860198	0.0000416	0.845545	0.0000444	−1.70	0.854249	0.0000423	−0.69	0.858831	0.0000422	−0.159
15	±20	0.897091	0.0000348	0.886105	0.0000350	−1.22	0.892656	0.0000352	−0.49	0.896063	0.0000350	−0.115
15	±30	0.932834	0.0000271	0.925572	0.0000285	−0.78	0.929908	0.0000291	−0.314	0.932159	0.0000271	−0.072
15	±40	0.950189	0.0000256	0.944782	0.0000263	−0.57	0.948017	0.0000256	−0.228	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	0.016228	0.0000577	0.015531	0.0000546	−4.29	0.015647	0.0000516	−3.58	0.016119	0.0000580	−0.67
20	±3	0.354224	0.0000726	0.313612	0.0000769	−11.5	0.329474	0.0000698	−7.0	0.349056	0.0000732	−1.46
20	±4	0.500954	0.0000639	0.457154	0.0000653	−8.7	0.475548	0.0000651	−5.1	0.495727	0.0000620	−1.04
20	±5	0.601015	0.0000617	0.559904	0.0000661	−6.8	0.577809	0.0000665	−3.86	0.596262	0.0000581	−0.79
20	±7	0.721004	0.0000628	0.687842	0.0000622	−4.6	0.702741	0.0000577	−2.53	0.717289	0.0000637	−0.52
20	±10	0.810844	0.0000448	0.786525	0.0000468	−3.0	0.797652	0.0000469	−1.63	0.808171	0.0000433	−0.330
20	±15	0.878244	0.0000370	0.861918	0.0000398	−1.86	0.869456	0.0000419	−1.00	0.876461	0.0000382	−0.203
20	±20	0.910617	0.0000332	0.898443	0.0000353	−1.34	0.904086	0.0000333	−0.72	0.909299	0.0000325	−0.145
20	±30	0.941779	0.0000246	0.933781	0.0000270	−0.85	0.937486	0.0000248	−0.46	0.940911	0.0000255	−0.092
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