/*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;
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                              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

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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

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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

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                      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


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                      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.
               
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                      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