Confidence intervals construction for difference of two means with incomplete correlated data

Li, Hui-Qiong; Tang, Nian-Sheng; Yi, Jie-Yi

doi:10.1186/s12874-016-0125-3

BMC Medical Research Methodology

Table 9 ECPs of various confidence intervals with different ρ and δ, μ ₁, μ ₂, (n,n ₁,n ₂)=(5,5,2), when \({\sigma _{1}^{2}}={\sigma _{2}^{2}}=4\)

From: Confidence intervals construction for difference of two means with incomplete correlated data

Bivariate normal distribution
ρ	δ	μ ₁	μ ₂	T ₃	T ₄	T ₅	W _s	W _a	B ₁	B ₂	B ₃	B ₄
-0.9	-0.25	0	0.25	0.935	0.960	0.906	0.920	0.880	0.952	0.954	0.947	0.954
	0	1	1	0.944	0.956	0.894	0.920	0.869	0.946	0.947	0.933	0.947
	0.5	2	1.5	0.944	0.967	0.902	0.931	0.883	0.951	0.953	0.942	0.951
-0.5	-0.25	0	0.25	0.941	0.961	0.903	0.910	0.861	0.942	0.943	0.939	0.943
	0	1	1	0.937	0.958	0.900	0.915	0.862	0.950	0.952	0.949	0.951
	0.5	2	1.5	0.941	0.962	0.898	0.925	0.882	0.952	0.957	0.952	0.957
-0.1	-0.25	0	0.25	0.933	0.958	0.900	0.903	0.838	0.944	0.945	0.945	0.946
	0	1	1	0.939	0.966	0.907	0.912	0.853	0.952	0.951	0.954	0.953
	0.5	2	1.5	0.943	0.975	0.924	0.943	0.892	0.961	0.959	0.960	0.959
0	-0.25	0	0.25	0.936	0.964	0.914	0.913	0.860	0.949	0.949	0.950	0.950
	0	1	1	0.925	0.959	0.906	0.908	0.861	0.941	0.941	0.940	0.940
	0.5	2	1.5	0.932	0.968	0.913	0.924	0.887	0.952	0.952	0.951	0.951
0.1	-0.25	0	0.25	0.922	0.960	0.918	0.911	0.858	0.948	0.948	0.948	0.947
	0	1	1	0.923	0.963	0.909	0.906	0.859	0.944	0.946	0.944	0.944
	0.5	2	1.5	0.928	0.969	0.913	0.935	0.889	0.946	0.947	0.947	0.946
0.5	-0.25	0	0.25	0.927	0.968	0.923	0.904	0.843	0.950	0.947	0.934	0.947
	0	1	1	0.928	0.964	0.923	0.913	0.857	0.942	0.944	0.935	0.947
	0.5	2	1.5	0.924	0.978	0.933	0.947	0.901	0.960	0.958	0.943	0.960
0.9	-0.25	0	0.25	0.913	0.947	0.974	0.929	0.880	0.951	0.951	0.777	0.951
	0	1	1	0.908	0.952	0.976	0.930	0.883	0.947	0.955	0.781	0.951
	0.5	2	1.5	0.913	0.942	0.974	0.974	0.944	0.946	0.953	0.778	0.954
Bivariate t-distribution
-0.9	-0.25	0	0.25	0.922	0.972	0.908	0.929	0.870	0.952	0.953	0.946	0.956
	0	1	1	0.915	0.973	0.914	0.935	0.868	0.948	0.943	0.937	0.948
	0.5	2	1.5	0.930	0.978	0.914	0.937	0.873	0.948	0.950	0.941	0.951
-0.5	-0.25	0	0.25	0.929	0.976	0.921	0.939	0.869	0.942	0.941	0.940	0.945
	0	1	1	0.931	0.975	0.925	0.935	0.872	0.943	0.942	0.943	0.946
	0.5	2	1.5	0.922	0.971	0.910	0.924	0.868	0.953	0.951	0.950	0.955
-0.1	-0.25	0	0.25	0.932	0.973	0.922	0.925	0.856	0.951	0.951	0.955	0.954
	0	1	1	0.926	0.971	0.924	0.923	0.859	0.941	0.942	0.946	0.947
	0.5	2	1.5	0.924	0.972	0.918	0.921	0.859	0.950	0.948	0.954	0.955
0	-0.25	0	0.25	0.919	0.973	0.921	0.918	0.852	0.944	0.944	0.949	0.949
	0	1	1	0.925	0.972	0.923	0.925	0.864	0.940	0.940	0.947	0.947
	0.5	2	1.5	0.939	0.977	0.924	0.926	0.857	0.950	0.950	0.954	0.954
0.1	-0.25	0	0.25	0.930	0.971	0.929	0.928	0.857	0.954	0.954	0.956	0.956
	0	1	1	0.929	0.982	0.927	0.928	0.857	0.949	0.949	0.950	0.951
	0.5	2	1.5	0.934	0.979	0.924	0.930	0.859	0.952	0.953	0.957	0.957
0.5	-0.25	0	0.25	0.929	0.973	0.947	0.940	0.864	0.944	0.950	0.942	0.951
	0	1	1	0.920	0.976	0.937	0.928	0.861	0.943	0.944	0.936	0.946
	0.5	2	1.5	0.939	0.970	0.942	0.930	0.868	0.945	0.947	0.942	0.951
0.9	-0.25	0	0.25	0.923	0.969	0.978	0.943	0.880	0.939	0.938	0.797	0.939
	0	1	1	0.920	0.966	0.977	0.952	0.887	0.939	0.942	0.795	0.949
	0.5	2	1.5	0.931	0.965	0.979	0.944	0.878	0.953	0.944	0.804	0.947

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ISSN: 1471-2288

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