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 * * * * * * * * * * * *