/*These data are the same as Assignment #4*/ data oneway; input group y1 y2 y3; cards; 1 19.6 5.15 9.5 1 15.4 5.75 9.1 1 22.3 4.35 3.3 1 24.3 7.55 5.0 1 22.5 8.50 6.0 1 20.5 10.25 5.0 1 14.1 5.95 18.8 1 13.0 6.30 16.5 1 14.1 5.45 8.9 1 16.7 3.75 6.0 1 16.8 5.10 7.4 2 17.1 9.00 7.5 2 15.7 5.30 8.5 2 14.9 9.85 6.0 2 19.7 3.60 2.9 2 17.2 4.05 0.2 2 16.0 4.40 2.6 2 12.8 7.15 7.0 2 13.6 7.25 3.2 2 14.2 5.30 6.2 2 13.1 3.10 5.5 2 16.5 2.40 6.6 3 16.0 4.55 2.9 3 12.5 2.65 0.7 3 18.5 6.50 5.3 3 19.2 4.85 8.3 3 12.0 8.75 9.0 3 13.0 5.20 10.3 3 11.9 4.75 8.5 3 12.0 5.85 9.5 3 19.8 2.85 2.3 3 16.5 6.55 3.3 3 17.4 6.60 1.9 ; proc glm; class group; model y1 y2 y3 = group; manova h = group; contrast '1vs2' group 1 -1 0; contrast '1vs3' group 1 0 -1; contrast '2vs3' group 0 1 -1; run; --------------------------------------------------------------------------------- The SAS System General Linear Models Procedure Class Level Information Class Levels Values GROUP 3 1 2 3 Number of observations in data set = 33 Dependent Variable: Y1 Sum of Mean Source DF Squares Square F Value Pr > F Model 2 52.9242424 26.4621212 2.70 0.0835 Error 30 293.9654545 9.7988485 Corrected Total 32 346.8896970 R-Square C.V. Root MSE Y1 Mean 0.152568 19.16873 3.13031 16.3303 Dependent Variable: Y1 Source DF Type I SS Mean Square F Value Pr > F GROUP 2 52.9242424 26.4621212 2.70 0.0835 Source DF Type III SS Mean Square F Value Pr > F GROUP 2 52.9242424 26.4621212 2.70 0.0835 --------------------------------------------------------------------------------- Dependent Variable: Y2 Sum of Mean Source DF Squares Square F Value Pr > F Model 2 3.97515152 1.98757576 0.47 0.6282 Error 30 126.28727273 4.20957576 Corrected Total 32 130.26242424 R-Square C.V. Root MSE Y2 Mean 0.030516 35.89975 2.05173 5.71515 Dependent Variable: Y2 Source DF Type I SS Mean Square F Value Pr > F GROUP 2 3.97515152 1.98757576 0.47 0.6282 Source DF Type III SS Mean Square F Value Pr > F GROUP 2 3.97515152 1.98757576 0.47 0.6282 --------------------------------------------------------------------------------- Dependent Variable: Y3 Sum of Mean Source DF Squares Square F Value Pr > F Model 2 81.8296970 40.9148485 2.88 0.0718 Error 30 426.3709091 14.2123636 Corrected Total 32 508.2006061 R-Square C.V. Root MSE Y3 Mean 0.161018 58.21603 3.76993 6.47576 Dependent Variable: Y3 Source DF Type I SS Mean Square F Value Pr > F GROUP 2 81.8296970 40.9148485 2.88 0.0718 Source DF Type III SS Mean Square F Value Pr > F GROUP 2 81.8296970 40.9148485 2.88 0.0718 --------------------------------------------------------------------------------- General Linear Models Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SS&CP Matrix for GROUP E = Error SS&CP Matrix Characteristic Percent Characteristic Vector V'EV=1 Root Y1 Y2 Y3 0.89198797 99.42 0.06410227 -0.00186162 0.05375070 0.00524207 0.58 0.01442654 0.06888879 -0.02620577 0.00000000 0.00 -0.03149580 0.05943386 0.01270798 --------------------------------------------------------------------------------- General Linear Models Procedure Multivariate Analysis of Variance Manova Test Criteria and F Approximations for the Hypothesis of no Overall GROUP Effect H = Type III SS&CP Matrix for GROUP E = Error SS&CP Matrix S=2 M=0 N=13 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.52578837 3.5382 6 56 0.0049 Pillai's Trace 0.47667015 3.0248 6 58 0.0122 Hotelling-Lawley Trace 0.89723004 4.0375 6 54 0.0021 Roy's Greatest Root 0.89198797 8.6226 3 29 0.0003 NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic for Wilks' Lambda is exact. --------------------------------------------------------------------------------- General Linear Models Procedure Dependent Variable: Y1 Contrast DF Contrast SS Mean Square F Value Pr > F 1vs2 1 36.9204545 36.9204545 3.77 0.0617 1vs3 1 42.2840909 42.2840909 4.32 0.0464 2vs3 1 0.1818182 0.1818182 0.02 0.8926 Dependent Variable: Y2 Contrast DF Contrast SS Mean Square F Value Pr > F 1vs2 1 2.04045455 2.04045455 0.48 0.4917 1vs3 1 3.68181818 3.68181818 0.87 0.3571 2vs3 1 0.24045455 0.24045455 0.06 0.8127 Dependent Variable: Y3 Contrast DF Contrast SS Mean Square F Value Pr > F 1vs2 1 70.2040909 70.2040909 4.94 0.0339 1vs3 1 51.0113636 51.0113636 3.59 0.0678 2vs3 1 1.5290909 1.5290909 0.11 0.7452 Group Centroids Group 1 -> [18.12 6.19 8.68] Group 2 -> [15.53 5.58 5.11] Group 3 -> [15.35 5.37 5.64] View plot of group centroids