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;


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                      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