MANOVA CRF-32 Example Same data as Assignment 8 data crf32; input a b y1 y2; cards; 1 1 10 21 1 1 12 22 1 1 9 19 1 1 10 21 1 1 14 23 1 2 9 14 1 2 8 15 1 2 11 16 1 2 9 17 1 2 9 17 2 1 11 23 2 1 14 27 2 1 13 24 2 1 15 26 2 1 14 24 2 2 11 15 2 2 12 18 2 2 10 16 2 2 9 17 2 2 9 18 3 1 8 17 3 1 7 15 3 1 10 18 3 1 8 17 3 1 7 19 3 2 9 22 3 2 8 18 3 2 10 17 3 2 9 19 3 2 8 19 ; proc glm; classes a b; model y1 y2 = a b a*b; manova h=a b a*b m=(1 -1); run; ---------------------------------------------------------------------------- General Linear Models Procedure Class Level Information Class Levels Values A 3 1 2 3 B 2 1 2 Number of observations in data set = 30 Dependent Variable: Y1 Sum of Mean Source DF Squares Square F Value Pr > F Model 5 93.1000000 18.6200000 9.80 0.0001 Error 24 45.6000000 1.9000000 Corrected Total 29 138.7000000 R-Square C.V. Root MSE Y1 Mean 0.671233 13.64757 1.37840 10.1000 Dependent Variable: Y1 Source DF Type I SS Mean Square F Value Pr > F A 2 57.8000000 28.9000000 15.21 0.0001 B 1 14.7000000 14.7000000 7.74 0.0104 A*B 2 20.6000000 10.3000000 5.42 0.0114 Source DF Type III SS Mean Square F Value Pr > F A 2 57.8000000 28.9000000 15.21 0.0001 B 1 14.7000000 14.7000000 7.74 0.0104 A*B 2 20.6000000 10.3000000 5.42 0.0114 Dependent Variable: Y2 Sum of Mean Source DF Squares Square F Value Pr > F Model 5 283.466667 56.693333 24.30 0.0001 Error 24 56.000000 2.333333 Corrected Total 29 339.466667 R-Square C.V. Root MSE Y2 Mean 0.835035 7.983581 1.52753 19.1333 Dependent Variable: Y2 Source DF Type I SS Mean Square F Value Pr > F A 2 42.466667 21.233333 9.10 0.0011 B 1 112.133333 112.133333 48.06 0.0001 A*B 2 128.866667 64.433333 27.61 0.0001 Source DF Type III SS Mean Square F Value Pr > F A 2 42.466667 21.233333 9.10 0.0011 B 1 112.133333 112.133333 48.06 0.0001 A*B 2 128.866667 64.433333 27.61 0.0001 General Linear Models Procedure Multivariate Analysis of Variance M Matrix Describing Transformed Variables Y1 Y2 MVAR1 1 -1 Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SS&CP Matrix for A E = Error SS&CP Matrix Variables have been transformed by the M Matrix Characteristic Percent Characteristic Vector V'EV=1 Root MVAR1 0.13655914 100.00 0.12700013 Manova Test Criteria and Exact F Statistics for the Hypothesis of no Overall A Effect on the variables defined by the M Matrix Transformation H = Type III SS&CP Matrix for A E = Error SS&CP Matrix S=1 M=0 N=11 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.87984863 1.6387 2 24 0.2152 Pillai's Trace 0.12015137 1.6387 2 24 0.2152 Hotelling-Lawley Trace 0.13655914 1.6387 2 24 0.2152 Roy's Greatest Root 0.13655914 1.6387 2 24 0.2152 Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SS&CP Matrix for B E = Error SS&CP Matrix Variables have been transformed by the M Matrix Characteristic Percent Characteristic Vector V'EV=1 Root MVAR1 0.73602151 100.00 0.12700013 Manova Test Criteria and Exact F Statistics for the Hypothesis of no Overall B Effect on the variables defined by the M Matrix Transformation H = Type III SS&CP Matrix for B E = Error SS&CP Matrix S=1 M=-0.5 N=11 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.57602973 17.6645 1 24 0.0003 Pillai's Trace 0.42397027 17.6645 1 24 0.0003 Hotelling-Lawley Trace 0.73602151 17.6645 1 24 0.0003 Roy's Greatest Root 0.73602151 17.6645 1 24 0.0003 Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SS&CP Matrix for A*B E = Error SS&CP Matrix Variables have been transformed by the M Matrix Characteristic Percent Characteristic Vector V'EV=1 Root MVAR1 0.75591398 100.00 0.12700013 Manova Test Criteria and Exact F Statistics for the Hypothesis of no Overall A*B Effect on the variables defined by the M Matrix Transformation H = Type III SS&CP Matrix for A*B E = Error SS&CP Matrix S=1 M=0 N=11 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.56950398 9.0710 2 24 0.0012 Pillai's Trace 0.43049602 9.0710 2 24 0.0012 Hotelling-Lawley Trace 0.75591398 9.0710 2 24 0.0012 Roy's Greatest Root 0.75591398 9.0710 2 24 0.0012