We will discuss two-way and higher MANOVA modeling using the following data sets. The first involves rice varieties and come from http://www.stat.psu.edu/~rathbun/stat505/ The second involves cholesterol and diet and comes from D. Johnson: Applied Multivariate Methods for Data Analysis.
block variety height tillers 1 a 58 4 1 b 49 7 1 c 54 6 1 d 58 4 2 a 62 6 2 b 55 6 2 c 52 6 2 d 55 4 3 a 60 7 3 b 48 4 3 c 51 7 3 d 51 5 4 a 54 6 4 b 52 4 4 c 58 5 4 d 49 6 5 a 58 6 5 b 49 7 5 c 61 6 5 d 52 4
Rat CHOL FIBER Block Total_Liver_Lipids Total_Liver_Cholesterol Plasma_Cholesterol HDL Percent_Dry_Matter A1 1 1 1 53.54 1.16 56.49 48.41 79.6782 A2 1 1 2 47.01 2.12 66.06 28.52 74.6070 A3 1 1 3 48.35 2.52 62.92 24.91 73.6120 A4 1 1 4 41.30 1.65 76.91 59.80 83.0698 A5 1 1 5 43.70 0.94 73.54 54.09 87.6766 A6 1 1 6 51.09 1.44 66.03 54.45 65.5570 A7 1 1 7 42.90 1.96 102.13 28.06 89.0863 A8 1 1 8 44.02 0.96 79.22 19.64 88.1979 A9 1 1 9 48.37 2.18 67.86 20.15 83.9571 B1 2 1 1 59.52 5.10 79.04 24.99 67.8646 B2 2 1 2 61.96 8.63 92.72 29.92 85.1869 B3 2 1 3 53.26 5.75 65.72 35.02 86.6071 B4 2 1 4 74.73 7.25 67.50 41.65 83.0164 B5 2 1 5 68.48 6.30 103.91 63.16 83.1006 B6 2 1 6 49.19 3.37 69.10 38.04 88.5445 B7 2 1 7 73.93 7.21 93.43 26.61 88.6631 B8 2 1 8 53.81 3.18 78.51 20.70 80.9957 B9 2 1 9 78.81 6.90 73.18 13.22 78.5185 C1 1 2 1 44.57 1.28 73.54 50.37 83.3915 C2 1 2 2 44.84 2.03 39.43 16.02 80.5000 C3 1 2 3 45.11 1.02 59.51 32.94 85.7453 C4 1 2 4 44.03 1.94 49.05 23.29 79.7797 C5 1 2 5 39.40 1.83 70.69 57.08 79.3296 C6 1 2 6 42.94 1.20 58.08 37.23 80.8010 C7 1 2 7 35.13 1.56 76.38 18.75 81.9524 C8 1 2 8 60.33 1.79 81.89 16.75 56.2547 C9 1 2 9 44.02 1.87 72.83 20.53 73.8789 D1 2 2 1 41.31 2.47 80.64 35.74 73.8142 D2 2 2 2 39.40 0.95 47.07 14.28 87.7888 D3 2 2 3 38.32 1.90 63.77 33.37 76.5250 D4 2 2 4 42.07 1.25 65.37 51.34 76.8590 D5 2 2 5 41.03 2.22 55.06 46.28 83.4076 D6 2 2 6 39.40 2.31 57.73 45.39 76.6460 D7 2 2 7 39.68 2.50 49.92 26.48 75.8586 D8 2 2 8 53.81 1.51 89.70 22.87 74.0351 D9 2 2 9 46.47 2.62 65.90 17.89 82.2788 E1 1 3 1 48.92 1.44 79.40 42.63 49.8678 E2 1 3 2 40.76 1.91 50.80 31.54 58.4488 E3 1 3 3 45.93 1.25 61.28 52.87 59.0308 E4 1 3 4 41.30 1.76 79.76 36.85 54.1306 E5 1 3 5 43.48 1.12 62.70 55.64 57.8256 E6 1 3 6 41.04 1.90 106.93 29.96 52.2205 E7 1 3 7 42.39 2.43 91.66 59.55 55.1452 E8 1 3 8 46.97 2.05 82.95 18.32 76.2484 E9 1 3 9 47.29 1.52 78.69 14.20 57.5236 F1 2 3 1 49.45 4.09 95.74 17.85 59.0332 F2 2 3 2 51.09 2.04 52.22 38.21 74.5079 F3 2 3 3 48.10 2.88 70.88 44.75 72.3275 F4 2 3 4 42.67 1.52 75.84 31.07 54.1629 F5 2 3 5 45.92 2.38 103.55 77.78 51.6682 F6 2 3 6 45.93 1.65 78.86 53.13 53.6631 F7 2 3 7 47.28 2.91 74.25 61.46 38.2585 F8 2 3 8 44.84 2.75 73.18 19.55 73.0333 F9 2 3 9 48.64 3.01 98.58 17.98 49.9407 G1 1 4 1 57.33 1.92 78.16 51.25 68.3817 G2 1 4 2 41.28 1.75 52.04 49.52 81.6667 G3 1 4 3 44.84 1.33 84.19 74.43 77.0245 G4 1 4 4 43.75 1.96 71.05 37.79 62.9181 G5 1 4 5 42.93 0.94 72.12 64.64 73.7219 G6 1 4 6 44.30 1.67 98.76 27.37 82.1272 G7 1 4 7 50.28 1.11 65.19 50.19 81.3776 G8 1 4 8 37.39 1.74 85.44 29.54 86.6592 G9 1 4 9 49.19 2.25 101.42 24.65 69.7500 H1 2 4 1 48.10 4.44 93.61 47.30 81.0921 H2 2 4 2 64.13 5.38 52.58 25.08 77.0755 H3 2 4 3 40.22 2.55 60.75 20.62 76.8467 H4 2 4 4 52.44 2.40 117.23 43.99 79.8458 H5 2 4 5 49.46 4.04 78.51 54.70 80.9242 H6 2 4 6 50.27 2.35 76.38 58.82 78.9888 H7 2 4 7 59.79 4.04 81.88 54.87 76.9829 H8 2 4 8 59.51 2.79 70.87 16.66 77.2710 H9 2 4 9 67.94 6.25 134.64 22.10 83.1203