R help - Dec 2006 - split-plot multiple comparisons

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 
	[[alternative HTML version deleted]]

Thank you for your example.  I am now using it an example in the MMC
Mean--mean Multiple Comparisons plot in the HH package on CRAN.  The
source for HH_1.17 is on CRAN in Austria as of this morning.  The
Windows and MacOS binaries will be on CRAN in a few days and will then
propagate to the mirrors.

Until then, you can get the R Windows binary directly from me at

http://astro.ocis.temple.edu/~rmh/HH/HH_1.17.zip          ## R Windows binary
http://astro.ocis.temple.edu/~rmh/HH/HH_1.17.tar.gz       ## source
http://astro.ocis.temple.edu/~rmh/HH/HH_1.17_S_WIN386.zip ## S-Plus 8 Windows
binary

The S-Plus 8 package is also available at
http://csan.insightful.com/

After you install and load HH with

library(HH)
?MMC

will give the complete example.


Some comments on the example.

The first interaction2wt figure shows parallel traces in the blocks,
visually confirming that the blocks appear to be orthogonal to the
treatments.

The second interaction2wt figure shows a hint of the hibrido:nitrogeno
interaction since the P3732 trace is monotone increasing in nitrogen
and the others bend back.

The MMC plot shows very clearly that the hybrids fall into two
different groups, with LH74, P3747, and P3732 in one group and with
Mol17 and A632 in the other group.  There is a non-significant
distinction between LH74 and the two P37** varieties.

The MMC plot needs the tiebreaker in this example because observed
means for several of the groups are almost identical.

The MMC plot is described in

Journal of Computational & Graphical Statistics 
2006, vol. 15, no. 4, pp. 937 - 955 
Mean-Mean Multiple Comparison Displays for Families of Linear Contrasts
Richard M. Heiberger; Burt Holland 

Abstract
Traditional tabular and graphical displays of results of simultaneous
confidence intervals or hypothesis tests are deficient in several
respects. Expanding on earlier work, we present new mean-mean multiple
comparison graphs that succinctly and compactly display the results of
traditional procedures for multiple comparisons of population means or
linear contrasts involving means. The MMC plot can be used with
unbalanced, multifactor designs with covariates. After reviewing the
construction of these displays in the S language (S-Plus and R), we
demonstrate their application to four multiple comparison scenarios.