Multiple comparisons of mean vectors with large dimension under general conditions

Figures & data

Table 1. Estimated size of pairwise comparisons for g = 3: all distributions.

			ND				UD				ED
${\mathbf{\Sigma }}_i$	$n_1,n_2,n_3$	p	$T_{12}$	$T_{13}$	$T_{23}$	$T_{max}$	$T_{12}$	$T_{13}$	$T_{23}$	$T_{max}$	$T_{12}$	$T_{13}$	$T_{23}$	$T_{max}$
CS,AR,AR	10,15,20	50	0.945	0.939	0.945	0.934	0.942	0.939	0.954	0.921	0.944	0.945	0.953	0.923
		300	0.957	0.956	0.946	0.952	0.954	0.942	0.945	0.940	0.946	0.939	0.945	0.927
		500	0.946	0.940	0.948	0.933	0.945	0.938	0.942	0.928	0.940	0.945	0.944	0.939
		1000	0.940	0.951	0.947	0.947	0.942	0.939	0.944	0.931	0.938	0.945	0.947	0.925
	20,30,40	50	0.945	0.944	0.951	0.920	0.943	0.949	0.948	0.930	0.946	0.949	0.951	0.927
		300	0.953	0.954	0.959	0.945	0.962	0.960	0.958	0.954	0.950	0.949	0.955	0.933
		500	0.953	0.947	0.955	0.953	0.945	0.944	0.949	0.944	0.955	0.957	0.950	0.956
		1000	0.943	0.948	0.954	0.951	0.947	0.951	0.956	0.940	0.951	0.954	0.943	0.940
	10,30,60	50	0.950	0.945	0.955	0.915	0.946	0.946	0.951	0.929	0.943	0.938	0.941	0.908
		300	0.941	0.945	0.947	0.937	0.948	0.947	0.941	0.935	0.944	0.947	0.942	0.918
		500	0.949	0.951	0.948	0.942	0.953	0.943	0.947	0.943	0.944	0.942	0.958	0.931
		1000	0.953	0.945	0.948	0.937	0.955	0.949	0.946	0.938	0.959	0.953	0.944	0.912
	50,75,100	50	0.949	0.944	0.948	0.925	0.950	0.952	0.954	0.928	0.943	0.944	0.947	0.926
		300	0.942	0.948	0.951	0.932	0.958	0.954	0.945	0.949	0.947	0.952	0.962	0.949
		500	0.940	0.944	0.957	0.952	0.952	0.948	0.943	0.951	0.947	0.949	0.941	0.926
		1000	0.953	0.945	0.947	0.937	0.945	0.948	0.950	0.942	0.949	0.952	0.940	0.930
AR,AR,UN	10,15,20	50	0.959	0.940	0.941	0.921	0.948	0.944	0.949	0.920	0.946	0.935	0.940	0.917
		300	0.944	0.948	0.943	0.928	0.947	0.940	0.949	0.932	0.948	0.943	0.953	0.935
		500	0.943	0.941	0.946	0.927	0.950	0.940	0.960	0.939	0.938	0.940	0.944	0.925
		1000	0.948	0.949	0.953	0.925	0.941	0.956	0.954	0.936	0.940	0.942	0.951	0.938
	20,30,40	50	0.953	0.946	0.944	0.920	0.950	0.960	0.943	0.937	0.949	0.945	0.956	0.943
		300	0.947	0.942	0.941	0.932	0.940	0.956	0.949	0.943	0.946	0.961	0.944	0.958
		500	0.954	0.952	0.950	0.943	0.942	0.944	0.951	0.937	0.943	0.962	0.951	0.943
		1000	0.951	0.950	0.947	0.940	0.944	0.940	0.953	0.939	0.945	0.955	0.946	0.941
	10,30,60	50	0.940	0.941	,.947	0.922	0.944	0.940	0.951	0.924	0.953	0.944	0.942	0.923
		300	0.951	0.946	0.946	0.948	0.940	0.939	0.942	0.933	0.948	0.951	0.958	0.943
		500	0.945	0.951	0.954	0.944	0.946	0.951	0.954	0.946	0.945	0.953	0.957	0.943
		1000	0.950	0.956	0.948	0.947	0.945	0.942	0.956	0.936	0.951	0.947	0.960	0.941
	50,75,100	50	0.942	0.945	0.948	0.924	0.951	0.957	0.946	0.936	0.947	0.957	0.956	0.942
		300	0.950	0.963	0.956	0.952	0.948	0.953	0.944	0.943	0.944	0.951	0.953	0.926
		500	0.957	0.945	0.947	0.948	0.956	0.948	0.947	0.933	0.952	0.942	0.945	0.938
		1000	0.955	0.949	0.946	0.940	0.951	0.941	0.944	0.938	0.943	0.947	0.950	0.941

Table 2. Estimated size of comparisons with a control for g=6: All distributions.

			${\mathbf{\Sigma }}_i$: CS, AR, AR						${\mathbf{\Sigma }}_i$: AR, AR, UN
$\mathcal{F}$	$n_1,\dots ,n_6$	p	$T_{12}$	$T_{13}$	$T_{14}$	$T_{15}$	$T_{16}$	$T_{max}$	$T_{12}$	$T_{13}$	$T_{14}$	$T_{15}$	$T_{16}$	$T_{max}$
ND	(10,10,10	50	0.939	0.947	0.946	0.935	0.946	0.945	0.941	0.942	0.952	0.942	0.944	0.960
	20,20,20)	300	0.938	0.936	0.945	0.941	0.947	0.966	0.947	0.941	0.940	0.944	0.942	0.963
		500	0.941	0.943	0.957	0.944	0.946	0.974	0.953	0.940	0.944	0.940	0.945	0.971
		1000	0.946	0.954	0.952	0.953	0.948	0.965	0.940	0.949	0.950	0.954	0.944	0.970
	(30,40,50	50	0.944	0.943	0.943	0.939	0.946	0.947	0.940	0.943	0.942	0.946	0.947	0.953
	30,40,50)	300	0.946	0.940	0.942	0.942	0.946	0.965	0.945	0.943	0.959	0.947	0.944	0.975
		500	0.944	0.950	0.945	0.952	0.945	0.980	0.945	0.947	0.951	0.947	0.948	0.981
		1000	0.951	0.946	0.953	0.949	0.941	0.961	0.947	0.949	0.950	0.961	0.945	0.973
	(30,40,50	50	0.960	0.944	0.951	0.949	0.948	0.953	0.946	0.947	0.946	0.942	0.943	0.957
	60,70,80)	300	0.953	0.954	0.955	0.940	0.943	0.981	0.954	0.948	0.963	0.948	0.940	0.975
		500	0.940	0.944	0.942	0.948	0.945	0.976	0.941	0.944	0.946	0.942	0.946	0.965
		100	0.947	0.948	0.958	0.951	0.944	0.948	0.945	0.951	0.941	0.949	0.947	0.941
UD	(10,10,10	50	0.938	0.942	0.941	0.940	0.945	0.940	0.943	0.937	0.943	0.945	0.952	0.953
	20,20,20)	300	0.943	0.944	0.942	0.952	0.945	0.974	0.943	0.940	0.946	0.943	0.950	0.981
		500	0.941	0.944	0.942	0.943	0.942	0.962	0.941	0.947	0.944	0.949	0.940	0.973
		1000	0.944	0.944	0.950	0.959	0.945	0.972	0.942	0.948	0.951	0.960	0.941	0.975
	(30,40,50	50	0.952	0.946	0.947	0.944	0.949	0.963	0.961	0.947	0.941	0.948	0.948	0.971
	30,40,50)	300	0.949	0.943	0.946	0.950	0.950	0.974	0.949	0.954	0.949	0.941	0.951	0.977
		500	0.950	0.946	0.953	0.940	0.944	0.975	0.951	0.951	0.942	0.958	0.955	0.978
		1000	0.948	0.959	0.952	0.944	0.941	0.991	0.942	0.950	0.956	0.942	0.955	0.988
	(30,40,50	50	0.928	0.943	0.951	0.960	0.941	0.968	0.949	0.959	0.940	0.956	0.948	0.969
	60,70,80)	300	0.953	0.942	0.949	0.945	0.950	0.982	0.940	0.956	0.954	0.949	0.944	0.973
		500	0.953	0.950	0.950	0.948	0.944	0.973	0.948	0.940	0.952	0.940	0.946	0.985
		1000	0.957	0.958	0.949	0.951	0.948	0.938	0.955	0.952	0.941	0.943	0.940	0.939
ED	(10,10,10	50	0.943	0.945	0.931	0.936	0.938	0.958	0.950	0.956	0.949	0.960	0.958	0.957
	20,20,20)	300	0.954	0.946	0.941	0.942	0.950	0.968	0.948	0.945	0.947	0.949	0.946	0.964
		500	0.947	0.950	0.956	0.946	0.961	0.977	0.947	0.948	0.949	0.945	0.954	0.975
		1000	0.953	0.946	0.953	0.959	0.955	0.972	0.950	0.948	0.958	0.958	0.946	0.977
	(30,40,50	50	0.948	0.951	0.960	0.947	0.948	0.965	0.945	0.950	0.952	0.947	0.955	0.965
	30,40,50)	300	0.943	0.943	0.945	0.946	0.951	0.972	0.946	0.963	0.942	0.956	0.946	0.974
		500	0.956	0.950	0.955	0.947	0.956	0.980	0.949	0.946	0.941	0.948	0.945	0.973
		1000	0.942	0.0.935	0.942	0.949	0.943	0.975	0.944	0.938	0.946	0.945	0.952	0.981
	(30,40,50	50	0.951	0.946	0.945	0.949	0.952	0.963	0.952	0.946	0.945	0.941	0.945	0.958
	60,70,80)	300	0.946	0.941	0.946	0.955	0.943	0.968	0.941	0.962	0.945	0.953	0.954	0.956
		500	0.948	0.941	0.945	0.944	0.951	0.978	0.946	0.952	0.949	0.947	0.954	0.978
		1000	0.956	0.948	0.961	0.953	0.950	0.985	0.954	0.951	0.953	0.947	0.944	0.982

Table 3. Estimated power of pairwise comparisons for g=3: All distributions.

				ND			UD			ED
${\mathbf{\Sigma }}_i$	$n_1,n_2,n_3$	p	ϑ	$T_{12}$	$T_{13}$	$T_{max}$	$T_{12}$	$T_{13}$	$T_{max}$	$T_{12}$	$T_{13}$	$T_{max}$
CS,AR,AR	10,15,20	50	0.2	0.149	0.141	0.173	0.134	0.139	0.134	0.143	0.137	0.158
			0.4	0.493	0.511	0.532	0.490	0.505	0.537	0.474	0.505	0.514
			0.6	0.905	0.947	0.949	0.900	0.928	0.943	0.902	0.943	0.963
			0.8	0.997	1.000	0.999	0.995	0.998	1.000	0.997	1.000	1.000
			1.0	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		100	0.2	0.167	0.175	0.165	0.162	0.190	0.196	0.149	0.175	0.167
			0.4	0.679	0.742	0.745	0.658	0.726	0.755	0.668	0.711	0.742
			0.6	0.991	0.998	0.999	0.955	0.986	0.997	0.992	0.998	1.000
			0.8	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		300	0.2	0.262	0.288	0.272	0.260	0.283	0.263	0.258	0.279	0.270
			0.4	0.961	0.982	0.981	0.962	0.981	0.976	0.959	0.980	0.983
			0.6	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
	10,30,60	50	0.2	0.138	0.179	0.165	0.157	0.168	0.155	0.132	0.168	0.162
			0.4	0.596	0.675	0.617	0.614	0.670	0.619	0.587	0.648	0.613
			0.6	0.968	0.975	0.970	0.967	0.990	0.984	0.970	0.974	0.992
			0.8	0.999	1.000	1.000	0.998	0.999	0.999	0.999	0.998	1.000
			1.0	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		100	0.2	0.195	0.212	0.179	0.185	0.215	0.186	0.178	0.208	0.203
			0.4	0.811	0.875	0.835	0.809	0.879	0.848	0.800	0.896	0.816
			0.6	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		300	0.2	0.339	0.406	0.367	0.335	0.409	0.371	0.337	0.410	0.368
			0.4	0.996	0.996	0.999	0.995	0.997	0.998	0.996	0.998	0.999
			0.6	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
	50,75,100	50	0.2	0.570	0.667	0.657	0.568	0.664	0.671	0.576	0.647	0.656
			0.4	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		100	0.2	0.812	0.863	0.884	0.808	0.868	0.863	0.812	0.876	0.869
			0.4	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000

Table 4. Estimated power of comparisons with a control for g=6: All distributions.

				${\mathbf{\Sigma }}_i$: CS, AR, AR						${\mathbf{\Sigma }}_i$: AR, AR, UN
$\mathcal{F}$	$n_1,\dots ,n_6$	p	ϑ	$T_{12}$	$T_{13}$	$T_{14}$	$T_{15}$	$T_{16}$	$T_{max}$	$T_{12}$	$T_{13}$	$T_{14}$	$T_{15}$	$T_{16}$	$T_{max}$
ND	(10,10,10	50	0.2	0.134	0.149	0.145	0.157	0.167	0.127	0.118	0.122	0.149	0.157	0.155	0.128
	20,20,20)		0.4	0.425	0.416	0.536	0.571	0.545	0.538	0.396	0.420	0.533	0.542	0.540	0.521
			0.6	0.844	0.848	0.936	0.950	0.932	0.955	0.815	0.837	0.947	0.943	0.950	0.952
			0.8	0.989	0.989	0.999	1.000	0.999	1.000	0.993	0.991	1.000	0.999	0.999	1.000
			1.0	0.999	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		100	0.2	0.144	0.144	0.182	0.213	0.183	0.123	0.145	0.161	0.184	0.187	0.198	0.132
			0.4	0.581	0.567	0.759	0.765	0.758	0.750	0.573	0.565	0.720	0.738	0.743	0.730
			0.6	0.974	0.972	0.999	0.997	0.996	0.998	0.969	0.966	0.997	0.997	0.998	0.995
			0.8	1.000	0.999	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		300	0.2	0.24	0.248	0.289	0.305	0.312	0.217	0.221	0.224	0.315	0.334	0.301	0.226
			0.4	0.913	0.909	0.990	0.989	0.991	0.990	0.899	0.909	0.984	0.988	0.989	0.989
			0.6	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
	(30,40,50	50	0.2	0.340	0.383	0.303	0.327	0.360	0.341	0.340	0.381	0.308	0.342	0.367	0.341
	30,40,50)		0.4	0.981	0.986	0.949	0.973	0.984	0.995	0.960	0.984	0.945	0.976	0.982	0.988
			0.6	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		100	0.2	0.473	0.546	0.400	0.496	0.527	0.502	0.496	0.543	0.425	0.494	0.562	0.519
			0.4	1.000	1.000	0.998	1.000	1.000	1.000	0.998	1.000	0.999	1.000	1.000	1.000
ED	(10,10,10	50	0.2	0.126	0.116	0.140	0.132	0.124	0.103	0.121	0.130	0.140	0.144	0.132	0.095
	20,20,20)		0.4	0.404	0.373	0.521	0.535	0.540	0.496	0.399	0.403	0.536	0.512	0.513	0.512
			0.6	0.851	0.826	0.951	0.945	0.941	0.974	0.823	0.815	0.942	0.950	0.956	0.974
			0.8	0.989	0.985	1.000	1.000	0.999	1.000	0.989	0.990	1.000	0.999	1.000	1.000
			1.0	0.999	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		100	0.2	0.141	0.149	0.189	0.172	0.155	0.119	0.151	0.148	0.166	0.169	0.195	0.113
			0.4	0.557	0.562	0.746	0.742	0.744	0.729	0.558	0.585	0.736	0.746	0.747	0.755
			0.6	0.965	0.976	0.997	0.998	1.000	0.999	0.961	0.965	0.998	0.998	0.999	0.999
			0.8	0.999	1.000	1.000	1.000	1.000	1.000	0.999	0.999	1.000	1.000	1.000	1.000
		300	0.2	0.220	0.222	0.287	0.287	0.322	0.218	0.210	0.204	0.304	0.289	0.283	0.202
			0.4	0.902	0.906	0.986	0.985	0.988	0.991	0.913	0.907	0.992	0.986	0.991	0.996
			0.6	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	v	1.000	1.000	1.000
	(30,40,50	50	0.2	0.339	0.366	0.310	0.335	0.339	0.344	0.351	0.365	0.275	0.331	0.369	0.334
	30,40,50)		0.4	0.975	0.987	0.954	0.977	0.995	0.999	0.977	0.979	0.935	0.978	0.987	0.989
			0.6	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
		100	0.2	0.453	0.545	0.402	0.502	0.528	0.500	0.489	0.541	0.413	0.516	0.511	0.494
			0.4	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.994	1.000	1.000	1.000