Hi R-users
I'm trying to do multivariate analysis of variance of a experiment with
3 treatments, 2 variables and 5 replicates.
The procedure adopted in SAS is as follow, but I'm having difficulty in
to implement the contrasts for comparison of all treatments in R.
I have already read manuals and other materials about manova in R, but
nothing about specific contrasts were found in them, just regarding buit
contrasts, such as contr.helmert, contr.poly, contr.treatment and
contr.sum. How to get output similar to that from SAS, mainly for the
three first contrasts, once that fourth contrast is contr.helmert?

### SAS
INPUT

proc glm;
   classes TRA;
   model X1 X2 = TRA;
   contrast 'TESTE vs TURFE'	TRA 1 -1  0;
   contrast 'TESTE vs TURNA' 	TRA 1  0 -1;
   contrast 'TURFE vs TURNA'	TRA 0  1 -1;

   contrast 'Ho:TESTE=TURFE=TURNA' TRA 1  1 -2,
                                   TRA 1 -1  0;
   manova h=TRA / printe printh;
   run;

OUTPUT (some parts were removed)

...
Dependent Variable: X1

Source                  DF            Sum of Squares              Mean
Square   F Value     Pr > F
Model                    2                7.24764000
3.62382000     94.96     0.0001
Error                   12                0.45796000
0.03816333
Corrected Total         14                7.70560000

Source                  DF                 Type I SS              Mean
Square   F Value     Pr > F
TRA                      2                7.24764000
3.62382000     94.96     0.0001
Source                  DF               Type III SS              Mean
Square   F Value     Pr > F
TRA                      2                7.24764000
3.62382000     94.96     0.0001

Contrast                DF               Contrast SS              Mean
Square   F Value     Pr > F
TESTEMUNHA vs TURFE      1                5.14089000
5.14089000    134.71     0.0001
TESTEMUNHA vs TURNA      1                0.01521000
0.01521000      0.40     0.5397
TURFE vs TURNA           1                5.71536000
5.71536000    149.76     0.0001
Ho:TESTE=TURFE=TURNA     2                7.24764000
3.62382000     94.96     0.0001

...
Dependent Variable: X2

Source                  DF            Sum of Squares              Mean
Square   F Value     Pr > F
Model                    2                0.09817333
0.04908667      6.22     0.0140
Error                   12                0.09472000
0.00789333
Corrected Total         14                0.19289333

Source                  DF                 Type I SS              Mean
Square   F Value     Pr > F
TRA                      2                0.09817333
0.04908667      6.22     0.0140
Source                  DF               Type III SS              Mean
Square   F Value     Pr > F
TRA                      2                0.09817333
0.04908667      6.22     0.0140

Contrast                DF               Contrast SS              Mean
Square   F Value     Pr > F
TESTEMUNHA vs TURFE      1                0.02116000
0.02116000      2.68     0.1275
TESTEMUNHA vs TURNA      1                0.02809000
0.02809000      3.56     0.0837
TURFE vs TURNA           1                0.09801000
0.09801000     12.42     0.0042
Ho:TESTE=TURFE=TURNA     2                0.09817333
0.04908667      6.22     0.0140

...
      Manova Test Criteria and F Approximations for the Hypothesis of no
Overall TRA Effect
                    H = Type III SS&CP Matrix for TRA   E = Error SS&CP
Matrix

                                      S=2    M=-0.5    N=4.5

           Statistic                     Value          F      Num DF
Den DF  Pr > F

           Wilks' Lambda              0.02042803    32.9813         4
22  0.0001
           Pillai's Trace             1.24157026     9.8222         4
24  0.0001
           Hotelling-Lawley Trace    35.12690920    87.8173         4
20  0.0001
           Roy's Greatest Root       34.75791615   208.5475         2
12  0.0001

...
                         Manova Test Criteria and Exact F Statistics for
                     the Hypothesis of no Overall TESTEMUNHA vs TURFE
Effect
            H = Contrast SS&CP Matrix for TESTEMUNHA vs TURFE   E =
Error SS&CP Matrix

                                       S=1    M=0    N=4.5

           Statistic                     Value          F      Num DF
Den DF  Pr > F

           Wilks' Lambda              0.03437322   154.5083         2
11  0.0001
           Pillai's Trace             0.96562678   154.5083         2
11  0.0001
           Hotelling-Lawley Trace    28.09241176   154.5083         2
11  0.0001
           Roy's Greatest Root       28.09241176   154.5083         2
11  0.0001

...
                         Manova Test Criteria and Exact F Statistics for
                     the Hypothesis of no Overall TESTEMUNHA vs TURNA
Effect
            H = Contrast SS&CP Matrix for TESTEMUNHA vs TURNA   E =
Error SS&CP Matrix

                                       S=1    M=0    N=4.5

           Statistic                     Value          F      Num DF
Den DF  Pr > F

           Wilks' Lambda              0.65512498     2.8953         2
11  0.0977
           Pillai's Trace             0.34487502     2.8953         2
11  0.0977
           Hotelling-Lawley Trace     0.52642630     2.8953         2
11  0.0977
           Roy's Greatest Root        0.52642630     2.8953         2
11  0.0977

...
                         Manova Test Criteria and Exact F Statistics for
                        the Hypothesis of no Overall TURFE vs TURNA
Effect
              H = Contrast SS&CP Matrix for TURFE vs TURNA   E = Error
SS&CP Matrix

                                       S=1    M=0    N=4.5

           Statistic                     Value          F      Num DF
Den DF  Pr > F

           Wilks' Lambda              0.03988589   132.3934         2
11  0.0001
           Pillai's Trace             0.96011411   132.3934         2
11  0.0001
           Hotelling-Lawley Trace    24.07152574   132.3934         2
11  0.0001
           Roy's Greatest Root       24.07152574   132.3934         2
11  0.0001

...
                          Manova Test Criteria and F Approximations for
                     the Hypothesis of no Overall Ho:TESTE=TURFE=TURNA
Effect
           H = Contrast SS&CP Matrix for Ho:TESTE=TURFE=TURNA   E =
Error SS&CP Matrix

                                      S=2    M=-0.5    N=4.5

           Statistic                     Value          F      Num DF
Den DF  Pr > F

           Wilks' Lambda              0.02042803    32.9813         4
22  0.0001
           Pillai's Trace             1.24157026     9.8222         4
24  0.0001
           Hotelling-Lawley Trace    35.12690920    87.8173         4
20  0.0001
           Roy's Greatest Root       34.75791615   208.5475         2
12  0.0001


### R
X1 =
c(4.63,4.38,4.94,4.96,4.48,6.03,5.96,6.16,6.33,6.08,4.71,4.81,4.49,4.43,
4.56)
X2 =
c(0.95,0.89,1.01,1.23,0.94,1.08,1.05,1.08,1.19,1.08,0.96,0.93,0.87,0.82,
0.91)
Trat = as.factor(c(rep("TESTE",5),rep("TURFE",5), rep("TURNA",5)))
Y = cbind(X1,X2)
fit = manova(Y ~ Trat)
summary.aov(fit)
summary(fit, test= "Wilks")

ANOVA:
 Response X1 :
            Df Sum Sq Mean Sq F value    Pr(>F)    
Trat         2 7.2476  3.6238  94.956 4.407e-08 ***
Residuals   12 0.4580  0.0382                      
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

 Response X2 :
            Df   Sum Sq  Mean Sq F value  Pr(>F)  
Trat         2 0.098173 0.049087  6.2187 0.01402 *
Residuals   12 0.094720 0.007893                  
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

MANOVA:
          Df  Wilks approx F num Df den Df    Pr(>F)    
Trat       2  0.020   32.981      4     22 5.302e-09 ***
Residuals 12                                            
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1


Any suggestions are much appreciated.

__________________________________________________________
Eng. Agr., M.Sc. Eduardo Dutra de Armas
__________________________________________________________
Centro de Energia Nuclear na Agricultura (CENA/USP)
Laboratório de Ecotoxicologia
Av.Centenário 303, C.P. 96, CEP 13400-970, Piracicaba, SP, Brasil
__________________________________________________________


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