
Dear R user,

I am new with split-plot designs and I have problems with multiple comparisons.

This data correspond to an split-plot experiment with two replications 
(bloque).(Hoshmand, 2006 pp 138). Briefly, the whole-plot factor is 
Nitrogen concentration ("nitrogeno") and the subplot factor is the variety 
of corn ("hibrido"). The aim is to determine if  major differences in yield 
response to nitrogen fertilization exists among 5 hibrids of corn.

yield<-c(130,150,170,165,
          125,150,160,165,
          110,140,155,150,
          115,140,160,140,
          115,170,160,170,
          135,170,190,185,
          150,160,180,200,
          135,155,165,175,
          130,150,175,170,
          145,180,195,200)

hibrido<-factor(rep(c(rep("P3747",4),rep("P3732",4),rep("Mol17",4),rep("A632",4),rep("LH74",4)),2)) 


bloque<-factor(c(rep("I",20),rep("II",20)))

nitrogeno<-factor(rep(c("0","70","140","210"),10))

maiz<-data.frame(yield,hibrido,bloque,nitrogeno)
names(maiz)<-c("yield","hibrido","bloque","nitrogeno")

options(contrasts=c("contr.helmert","contr.poly"))

I fit the model

maiz.aov<-aov(yield~hibrido+nitrogeno+nitrogeno*hibrido+Error(bloque/nitrogeno))

and I try the orthogonal contrasts

summary(maiz.aov,split=list(hibrido=list(c1=1,c2=2,c3=3,c4=4)))

Error: bloque
           Df Sum Sq Mean Sq F value Pr(>F)
Residuals  1 4100.6  4100.6

Error: bloque:nitrogeno
           Df  Sum Sq Mean Sq F value   Pr(>F)
nitrogeno  3 12051.9  4017.3  42.756 0.005825 **
Residuals  3   281.9    94.0
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: Within
                         Df  Sum Sq Mean Sq F value    Pr(>F)
hibrido                  4 2466.25  616.56 20.5521 3.820e-06 ***
   hibrido: c1            1 1501.56 1501.56 50.0521 2.629e-06 ***
   hibrido: c2            1  438.02  438.02 14.6007  0.001504 **
   hibrido: c3            1  301.04  301.04 10.0347  0.005968 **
   hibrido: c4            1  225.63  225.63  7.5208  0.014458 *
hibrido:nitrogeno       12  863.75   71.98  2.3993  0.051992 .
   hibrido:nitrogeno: c1  3  454.69  151.56  5.0521  0.011893 *
   hibrido:nitrogeno: c2  3   72.40   24.13  0.8044  0.509595
   hibrido:nitrogeno: c3  3  276.04   92.01  3.0671  0.058027 .
   hibrido:nitrogeno: c4  3   60.62   20.21  0.6736  0.580663
Residuals               16  480.00   30.00
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


I understand that the line "hibrido: c1" means that the first and second 
levels of "hibrido" are statistically significant, but I am not sure about 
the interpretation of the lines "hibrido:nitrogeno: c1".

Does it means that the first and second levels of hibrido are statistically 
significant according to the levels of the variable "nitrogeno"? If this is 
so, how can I guess the levels of "nitrogeno" in which they are different?

I also would like to answer questions such as the following

for a particular level of "nitrogeno", is the mean of the first level of 
"hibrido" different than the second (third, fourth, fifth) ?

Given a level of "hibrido", is its mean different "deppending" of the level 
of "nitrogeno"?

Is the mean of yield within the first level of "hibrido" an "nitrogeno" 
different than the mean of yield within the second level of "hibrido" and 
the third of "nitrogeno"?

Thank you very much,

Tomás Goicoa 
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