Lecture 13

We demonstrated how to conduct a multivariate response test of whether the multivariate mean vector is zero or not using the bone density data below.

These examples are taken from Johnson and Wichern: Applied Multivariate Statistical Analysis. The first set of data consists of measurements of body size in male and female Cophosaurus texanus lizards. The data were provided by Kevin E, Bonine. The second set of data consists of bone mineral content before and after treatment for bone loss and were provided by Everett Smith.

Sex	weight(grams)	Snout-Vent-Length(mm)	Hind-Limb-Span(mm)
f	5.526	59.0	111.5
m	10.401	75.0	142.0
f	9.213	69.0	124.0
f	8.953	67.5	125.0
m	7.063	62.0	129.5
f	6.610	62.0	123.0
m	11.273	74.0	140.0
f	2.445	47.0	97.0
m	15.493	86.5	162.0
f	9.004	69.0	126.5
m	8.199	70.5	136.0
f	6.601	64.5	116.0
m	7.622	67.5	135.0
m	10.067	73.0	136.5
m	10.091	73.0	135.5
m	10.888	77.0	139.0
f	7.610	61.5	118.0
m	7.733	66.5	133.5
m	12.015	79.5	150.0
m	10.049	74.0	137.0
f	5.149	59.5	116.0
f	9.158	68.0	123.0
m	12.132	75.0	141.0
f	6.978	66.5	117.0
f	6.890	63.0	117.0
subject	Dradius	radius	Dhumerus	humerus	Dulna	ulna	1yrDradius	1yrradius	1yrDhumerus	1yrhumerus	1yrDulna	1yrulna	DR	r	Dh	h	DU	u
1	1.103	1.052	2.139	2.238	0.873	0.872	1.027	1.051	2.268	2.246	0.869	0.964	-0.076	-0.001	0.129	0.008	-0.004	0.092
2	0.842	0.859	1.873	1.741	0.590	0.744	0.857	0.817	1.718	1.710	0.602	0.689	0.015	-0.042	-0.155	-0.031	0.012	-0.055
3	0.925	0.873	1.887	1.809	0.767	0.713	0.875	0.880	1.953	1.756	0.765	0.738	-0.050	0.007	0.066	-0.053	-0.002	0.025
4	0.857	0.744	1.739	1.547	0.706	0.674	0.873	0.698	1.668	1.443	0.761	0.698	0.016	-0.046	-0.071	-0.104	0.055	0.024
5	0.795	0.809	1.734	1.715	0.549	0.654	0.811	0.813	1.643	1.661	0.551	0.619	0.016	0.004	-0.091	-0.054	0.002	-0.035
6	0.787	0.779	1.509	1.474	0.782	0.571	0.640	0.734	1.396	1.378	0.753	0.515	-0.147	-0.045	-0.113	-0.096	-0.029	-0.056
7	0.933	0.880	1.695	1.656	0.737	0.803	0.947	0.865	1.851	1.686	0.708	0.787	0.014	-0.015	0.156	0.030	-0.029	-0.016
8	0.799	0.851	1.740	1.777	0.618	0.682	0.886	0.806	1.742	1.815	0.687	0.715	0.087	-0.045	0.002	0.038	0.069	0.033
9	0.945	0.876	1.811	1.759	0.853	0.777	0.991	0.923	1.931	1.776	0.844	0.656	0.046	0.047	0.120	0.017	-0.009	-0.121
10	0.921	0.906	1.954	2.009	0.823	0.765	0.977	0.925	1.933	2.106	0.869	0.789	0.056	0.019	-0.021	0.097	0.046	0.024
11	0.792	0.825	1.624	1.657	0.686	0.668	0.825	0.826	1.609	1.651	0.654	0.726	0.033	0.001	-0.015	-0.006	-0.032	0.058
12	0.815	0.751	2.204	1.846	0.678	0.546	0.851	0.765	2.352	1.980	0.692	0.526	0.036	0.014	0.148	0.134	0.014	-0.020
13	0.755	0.724	1.508	1.458	0.662	0.595	0.770	0.730	1.470	1.420	0.670	0.580	0.015	0.006	-0.038	-0.038	0.008	-0.015
14	0.880	0.866	1.786	1.811	0.810	0.819	0.912	0.875	1.846	1.809	0.823	0.773	0.032	0.009	0.060	-0.002	0.013	-0.046
15	0.900	0.838	1.902	1.606	0.723	0.677	0.905	0.826	1.842	1.579	0.746	0.729	0.005	-0.012	-0.060	-0.027	0.023	0.052
16	0.764	0.757	1.743	1.794	0.586	0.541	0.756	0.727	1.747	1.860	0.656	0.506	-0.008	-0.030	0.004	0.066	0.070	-0.035
17	0.733	0.748	1.863	1.869	0.672	0.752	0.765	0.764	1.923	1.941	0.693	0.740	0.032	0.016	0.060	0.072	0.021	-0.012
18	0.932	0.898	2.028	2.032	0.836	0.805	0.932	0.914	2.190	1.997	0.883	0.785	0.000	0.016	0.162	-0.035	0.047	-0.020
19	0.856	0.786	1.390	1.324	0.578	0.610	0.843	0.782	1.242	1.228	0.577	0.627	-0.013	-0.004	-0.148	-0.096	-0.001	0.017
20	0.890	0.950	2.187	2.087	0.758	0.718	0.879	0.906	2.164	1.999	0.802	0.769	-0.011	-0.044	-0.023	-0.088	0.044	0.051
21	0.688	0.532	1.650	1.378	0.533	0.482	0.673	0.537	1.573	1.330	0.540	0.498	-0.015	0.005	-0.077	-0.048	0.007	0.016
22	0.940	0.850	2.334	2.225	0.757	0.731	0.949	0.900	2.130	2.159	0.804	0.779	0.009	0.050	-0.204	-0.066	0.047	0.048
23	0.493	0.616	1.037	1.268	0.546	0.615	0.463	0.637	1.041	1.265	0.570	0.634	-0.030	0.021	0.004	-0.003	0.024	0.019
24	0.835	0.752	1.509	1.422	0.618	0.664	0.776	0.743	1.442	1.411	0.585	0.640	-0.059	-0.009	-0.067	-0.011	-0.033	-0.024
25	0.915	0.936	1.971	1.869	0.869	0.868	*	*	*	*	*	*	*	*	*	*	*	*