We discussed how to conduct a test of equal multivariate means in two populations without the assumption of equal variance and covariances using large sample size theory. The data below are measurements on two species of biting flies, Leptoconops torrens and Leptoconops carteri. The data are in Johnson and Wichern: Applied Multivariate Statistical Analysis and are originally from William Atchley.
species wing_length wing_width third_palp_length third_palp_width fourth_palp_length length_antennal_12 length_antennal_13 0 85 41 31 13 25 9 8 0 87 38 32 14 22 13 13 0 94 44 36 15 27 8 9 0 92 43 32 17 28 9 9 0 96 43 35 14 26 10 10 0 91 44 36 12 24 9 9 0 90 42 36 16 26 9 9 0 92 43 36 17 26 9 9 0 91 41 36 14 23 9 9 0 87 38 35 11 24 9 10 0 97 45 39 17 27 9 10 0 89 38 36 13 22 9 9 0 94 45 37 13 26 9 9 0 96 44 37 14 24 9 10 0 104 49 35 14 21 10 10 0 94 41 31 17 26 10 9 0 99 44 31 18 28 10 9 0 94 38 32 13 22 9 9 0 94 43 37 16 26 9 10 0 93 43 38 14 28 10 10 0 95 44 37 18 27 10 10 0 95 45 39 13 27 10 10 0 96 39 37 12 26 8 8 0 103 46 34 18 26 10 10 0 108 44 37 14 25 11 11 0 106 47 38 15 26 10 10 0 105 46 34 14 31 10 11 0 103 44 34 15 23 10 10 0 100 41 35 14 24 10 10 0 109 44 36 13 27 11 10 0 104 45 36 15 30 10 10 0 95 40 35 14 23 9 10 0 104 44 34 15 29 9 10 0 90 40 37 12 22 9 10 0 104 46 37 14 30 10 10 1 86 19 37 11 25 9 9 1 94 40 38 14 31 6 7 1 103 48 39 14 33 10 10 1 82 41 35 12 25 9 8 1 103 43 42 15 32 9 9 1 101 43 40 15 25 9 9 1 103 45 44 14 29 11 11 1 100 43 40 18 31 11 10 1 99 41 42 15 31 10 10 1 100 44 43 16 34 10 10 1 112 47 44 16 38 12 11 1 99 48 37 14 32 10 9 1 98 45 41 19 31 9 8 1 101 46 42 14 24 11 10 1 99 45 37 13 28 10 9 1 103 47 44 15 20 8 9 1 98 40 38 12 32 9 8 1 101 46 36 14 28 10 10 1 101 46 40 17 32 9 9 1 98 47 39 15 33 10 10 1 99 45 42 15 32 10 9 1 102 45 44 15 30 10 10 1 97 45 37 15 32 10 9 1 96 39 40 14 20 9 9 1 89 39 33 12 20 9 8 1 99 42 38 14 33 9 9 1 110 45 41 17 36 9 10 1 99 44 35 16 31 10 10 1 103 43 38 14 32 10 10 1 95 46 36 15 31 8 8 1 101 47 38 14 37 11 11 1 103 47 40 15 32 11 11 1 99 43 37 14 23 11 10 1 105 50 40 16 33 12 11 1 99 47 39 14 34 7 7