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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