The SAS System 1 The GLM Procedure Number of observations 12 The SAS System 2 The GLM Procedure Multivariate Analysis of Variance M Matrix Describing Transformed Variables time1 time2 time3 MVAR1 1 -1 0 MVAR2 0 1 -1 MVAR3 0 0 1 MVAR4 0 0 0 MVAR5 0 0 0 M Matrix Describing Transformed Variables time4 time5 time6 MVAR1 0 0 0 MVAR2 0 0 0 MVAR3 -1 0 0 MVAR4 1 -1 0 MVAR5 0 1 -1 The SAS System 3 The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Contrast SSCP Matrix for Parallelism E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 MVAR2 MVAR3 MVAR4 MVAR5 10.0833621 87.38 1.91452560 1.41690702 0.09529171 -4.79392374 -1.58481788 1.4558983 12.62 0.72883470 -0.08532604 -0.72318256 0.32006826 0.80989187 0.0000000 0.00 -0.52580054 1.13351615 1.12218980 0.66023877 1.61137801 0.0000000 0.00 0.04062234 2.07578997 -0.39252579 0.33525065 0.00000000 0.0000000 0.00 -0.88796758 -1.49186381 1.88767646 2.36499869 0.00000000 MANOVA Test Criteria and F Approximations for the Hypothesis of No Overall Parallelism Effect on the Variables Defined by the M Matrix Transformation H = Contrast SSCP Matrix for Parallelism E = Error SSCP Matrix S=2 M=1 N=1.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.03673822 4.22 10 10 0.0164 Pillai's Trace 1.50259168 3.63 10 12 0.0192 Hotelling-Lawley Trace 11.53926039 5.54 10 5.3333 0.0316 Roy's Greatest Root 10.08336212 12.10 5 6 0.0043 NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic for Wilks' Lambda is exact. The SAS System 4 The GLM Procedure Multivariate Analysis of Variance M Matrix Describing Transformed Variables time1 time2 time3 MVAR1 1 1 1 M Matrix Describing Transformed Variables time4 time5 time6 MVAR1 1 1 1 The SAS System 5 The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Contrast SSCP Matrix for Parallelism E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 2.73854158 100.00 0.13930471 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of No Overall Parallelism Effect on the Variables Defined by the M Matrix Transformation H = Contrast SSCP Matrix for Parallelism E = Error SSCP Matrix S=1 M=0 N=3.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.26748398 12.32 2 9 0.0026 Pillai's Trace 0.73251602 12.32 2 9 0.0026 Hotelling-Lawley Trace 2.73854158 12.32 2 9 0.0026 Roy's Greatest Root 2.73854158 12.32 2 9 0.0026 The SAS System 6 The GLM Procedure Multivariate Analysis of Variance M Matrix Describing Transformed Variables time1 time2 time3 MVAR1 1 0 0 MVAR2 0 1 0 MVAR3 0 0 1 MVAR4 0 0 0 MVAR5 0 0 0 MVAR6 0 0 0 M Matrix Describing Transformed Variables time4 time5 time6 MVAR1 0 0 0 MVAR2 0 0 0 MVAR3 0 0 0 MVAR4 1 0 0 MVAR5 0 1 0 MVAR6 0 0 1 The SAS System 7 The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Contrast SSCP Matrix for Parallelism E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 MVAR2 MVAR3 MVAR4 MVAR5 MVAR6 16.4620712 91.67 0.44563771 0.16559149 3.71973633 2.59172224 -1.97369803 -2.05016312 1.4962812 8.33 -0.10648028 0.69782421 1.00995781 -1.83793656 -0.00241038 0.81777848 0.0000000 0.00 3.32730545 -0.31854674 -0.25249677 -3.58417070 3.62602375 -0.14771597 0.0000000 0.00 -1.73113921 1.16558139 -4.44740227 2.59413919 -0.10885312 0.18950170 0.0000000 0.00 0.61225216 -1.74973990 0.23782180 0.32469219 -0.92136247 1.60399406 0.0000000 0.00 -0.64789232 -1.80988191 1.83560849 0.00000000 0.00000000 0.00000000 MANOVA Test Criteria and F Approximations for the Hypothesis of No Overall Parallelism Effect on the Variables Defined by the M Matrix Transformation H = Contrast SSCP Matrix for Parallelism E = Error SSCP Matrix S=2 M=1.5 N=1 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.02294091 3.73 12 8 0.0350 Pillai's Trace 1.54213714 2.81 12 10 0.0559 Hotelling-Lawley Trace 17.95835240 4.49 12 6 0.0383 Roy's Greatest Root 16.46207115 13.72 6 5 0.0057 NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic for Wilks' Lambda is exact. The SAS System 8 The GLM Procedure Number of observations 12 The SAS System 9 The GLM Procedure Multivariate Analysis of Variance M Matrix Describing Transformed Variables time1 time2 time3 MVAR1 1 0 0 MVAR2 0 1 0 MVAR3 0 0 1 MVAR4 0 0 0 MVAR5 0 0 0 M Matrix Describing Transformed Variables time4 time5 time6 MVAR1 0 0 -1 MVAR2 0 0 -1 MVAR3 0 0 -1 MVAR4 1 0 -1 MVAR5 0 1 -1 The SAS System 10 The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Contrast SSCP Matrix for Time (if parallel) E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 MVAR2 MVAR3 MVAR4 MVAR5 194.577958 100.00 -2.21013837 0.20116803 3.13045318 4.09384461 -3.70026426 0.000000 0.00 0.08611396 0.61749617 -2.53780193 2.85993379 0.01371699 0.000000 0.00 -0.04951066 0.57250101 -0.05981370 -1.01237783 1.85914536 0.000000 0.00 0.56417554 -2.66683439 1.85034535 0.00000000 0.00000000 0.000000 0.00 0.22436250 0.55576849 0.00000000 0.00000000 0.00000000 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of No Overall Time (if parallel) Effect on the Variables Defined by the M Matrix Transformation H = Contrast SSCP Matrix for Time (if parallel) E = Error SSCP Matrix S=1 M=1.5 N=1.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.00511305 194.58 5 5 <.0001 Pillai's Trace 0.99488695 194.58 5 5 <.0001 Hotelling-Lawley Trace 194.57795814 194.58 5 5 <.0001 Roy's Greatest Root 194.57795814 194.58 5 5 <.0001 Characteristic Roots and Vectors of: E Inverse * H, where H = Contrast SSCP Matrix for Time (not parallel) E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 MVAR2 MVAR3 MVAR4 MVAR5 201.955018 97.98 -2.21161993 0.21573327 3.07255838 4.15253514 -3.70237711 2.803391 1.36 0.06413901 0.45001717 -2.53626501 2.72132507 -0.02519485 1.358809 0.66 0.51731475 -1.00386903 0.54573022 0.59518347 0.13436472 The SAS System 11 The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Contrast SSCP Matrix for Time (not parallel) E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 MVAR2 MVAR3 MVAR4 MVAR5 0.000000 0.00 -0.09130789 0.68834995 -0.26540055 -0.88024015 1.84994061 0.000000 0.00 -0.30312189 2.53767153 -1.85095037 0.43066173 0.00000000 MANOVA Test Criteria and F Approximations for the Hypothesis of No Overall Time (not parallel) Effect on the Variables Defined by the M Matrix Transformation H = Contrast SSCP Matrix for Time (not parallel) E = Error SSCP Matrix S=3 M=0.5 N=1.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.00054921 13.42 15 14.204 <.0001 Pillai's Trace 2.30820682 4.67 15 21 0.0007 Hotelling-Lawley Trace 206.11721853 64.48 15 5.5455 <.0001 Roy's Greatest Root 201.95501841 282.74 5 7 <.0001 NOTE: F Statistic for Roy's Greatest Root is an upper bound. The SAS System 12 The GLM Procedure Number of observations 12 The SAS System 13 The GLM Procedure Multivariate Analysis of Variance M Matrix Describing Transformed Variables time1 time2 time3 MVAR1 1 0 0 MVAR2 0 1 0 MVAR3 0 0 1 MVAR4 0 0 0 MVAR5 0 0 0 M Matrix Describing Transformed Variables time4 time5 time6 MVAR1 0 0 -1 MVAR2 0 0 -1 MVAR3 0 0 -1 MVAR4 1 0 -1 MVAR5 0 1 -1 The SAS System 14 The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Contrast SSCP Matrix for Time (group1 only) E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 MVAR2 MVAR3 MVAR4 MVAR5 36.1120997 100.00 -2.13306283 0.05144122 3.62255754 3.38226481 -3.57277161 0.0000000 0.00 -0.33969855 0.79956919 -1.76077801 3.02556615 -0.01832656 0.0000000 0.00 0.51645106 -0.00326945 -0.05277558 -0.06354575 0.05741355 0.0000000 0.00 0.20565068 0.25184499 0.56563317 -2.31643909 2.09290134 0.0000000 0.00 0.53744307 -2.73221853 1.76678886 0.00000000 0.00000000 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of No Overall Time (group1 only) Effect on the Variables Defined by the M Matrix Transformation H = Contrast SSCP Matrix for Time (group1 only) E = Error SSCP Matrix S=1 M=1.5 N=1.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.02694539 36.11 5 5 0.0006 Pillai's Trace 0.97305461 36.11 5 5 0.0006 Hotelling-Lawley Trace 36.11209974 36.11 5 5 0.0006 Roy's Greatest Root 36.11209974 36.11 5 5 0.0006