data toymanova;
input trt x1 x2;
cards;
1 9 3
1 6 2
1 9 7
2 0 4
2 2 0
3 3 8
3 1 9
3 2 7
run;
proc glm;
class trt;
model x1 x2 = trt;
manova h=trt/printe printh;
run;
quit;

                                                    The SAS System                 10:33 Saturday, October 3, 2009   1

                                                  The GLM Procedure

                                               Class Level Information

                                            Class         Levels    Values

                                            trt                3    1 2 3


                                       Number of Observations Read           8
                                       Number of Observations Used           8

                                                    The SAS System                 10:33 Saturday, October 3, 2009   2

                                                  The GLM Procedure

Dependent Variable: x1

                                                         Sum of
                 Source                      DF         Squares     Mean Square    F Value    Pr > F

                 Model                        2     78.00000000     39.00000000      19.50    0.0044

                 Error                        5     10.00000000      2.00000000

                 Corrected Total              7     88.00000000


                                  R-Square     Coeff Var      Root MSE       x1 Mean

                                  0.886364      35.35534      1.414214      4.000000


                 Source                      DF       Type I SS     Mean Square    F Value    Pr > F

                 trt                          2     78.00000000     39.00000000      19.50    0.0044


                 Source                      DF     Type III SS     Mean Square    F Value    Pr > F

                 trt                          2     78.00000000     39.00000000      19.50    0.0044

                                                    The SAS System                 10:33 Saturday, October 3, 2009   3

                                                  The GLM Procedure

Dependent Variable: x2

                                                         Sum of
                 Source                      DF         Squares     Mean Square    F Value    Pr > F

                 Model                        2     48.00000000     24.00000000       5.00    0.0642

                 Error                        5     24.00000000      4.80000000

                 Corrected Total              7     72.00000000


                                  R-Square     Coeff Var      Root MSE       x2 Mean

                                  0.666667      43.81780      2.190890      5.000000


                 Source                      DF       Type I SS     Mean Square    F Value    Pr > F

                 trt                          2     48.00000000     24.00000000       5.00    0.0642


                 Source                      DF     Type III SS     Mean Square    F Value    Pr > F

                 trt                          2     48.00000000     24.00000000       5.00    0.0642

                                                    The SAS System                 10:33 Saturday, October 3, 2009   4

                                                  The GLM Procedure
                                          Multivariate Analysis of Variance

                                                E = Error SSCP Matrix

                                                          x1                x2

                                        x1                10                 1
                                        x2                 1                24


                       Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r|

                                         DF = 5             x1             x2

                                         x1           1.000000       0.064550
                                                                       0.9033

                                         x2           0.064550       1.000000
                                                        0.9033

                                                    The SAS System                 10:33 Saturday, October 3, 2009   5

                                                  The GLM Procedure
                                          Multivariate Analysis of Variance

                                           H = Type III SSCP Matrix for trt

                                                          x1                x2

                                        x1                78               -12
                                        x2               -12                48


                              Characteristic Roots and Vectors of: E Inverse * H, where
                                           H = Type III SSCP Matrix for trt
                                                E = Error SSCP Matrix

                              Characteristic               Characteristic Vector  V'EV=1
                                        Root    Percent              x1              x2

                                  8.07638502      81.24      0.31342700     -0.04314847
                                  1.86503757      18.76      0.04671111      0.19994803


                MANOVA Test Criteria and F Approximations for the Hypothesis of No Overall trt Effect
                                          H = Type III SSCP Matrix for trt
                                                E = Error SSCP Matrix

                                                S=2    M=-0.5    N=1

                   Statistic                        Value    F Value    Num DF    Den DF    Pr > F

                   Wilks' Lambda               0.03845535       8.20         4         8    0.0062
                   Pillai's Trace              1.54078842       8.39         4        10    0.0031
                   Hotelling-Lawley Trace      9.94142259       9.94         4         4    0.0235
                   Roy's Greatest Root         8.07638502      20.19         2         5    0.0040

                            NOTE: F Statistic for Roy's Greatest Root is an upper bound.
                                    NOTE: F Statistic for Wilks' Lambda is exact.