[R] ANOVA: Help with SSQ decomposition and contrasts

[Jose Claudio Faria]

# Dear R list,
#
# A have a doubt about SSQ decomposition and contrasts with ANOVAs.
# So, I would like a tip from more advanced R users.

# Below my data, the basic script and my doubts:

# Data
r   = paste('r', gl(3, 8), sep='')
e   = paste('e', rep(gl(2, 4), 3), sep='')
tra = sort(paste('t', rep(1:6, 4), sep=''))
y   = c(26.2, 26.0, 25.0, 25.4, 24.8, 24.6, 26.7, 25.2,
         25.7, 26.3, 25.1, 26.4, 19.6, 21.1, 19.0, 18.6,
         22.8, 19.4, 18.8, 19.2, 19.8, 21.4, 22.8, 21.3)
dF  = data.frame(r, e, tra, y)

# Graphic
par(mfrow=c(2,1))
interaction.plot(dF$r, dF$e, dF$y,
                  col = 'blue', ylab = 'Y', xlab = 'R')

interaction.plot(dF$e, dF$r, dF$y,
                  col = 'blue', ylab = 'Y', xlab = 'R')

# ANOVAs
av0 = aov(y ~ tra, data=dF)
summary(av0)

av1 = aov(y ~ r*e, data=dF)
summary(av1)

av2 = aov(y ~ r/e, data=dF)
e_r = summary(av2, split = list('r:e' = list(
               'e1 vs e2/r1' = 1, 'e1 vs e2/r2' = 2, 'e1 vs e2/r3' = 3)))
e_r

av3 = aov(y ~ e/r, data=dF)
r_e = summary(av3, split = list('e:r' = list(
              'r/e1' = c(1,3), 'r/e2' = c(2,4))))
r_e

# My Doubts

# a) How to make SSQ decomposition to complete the ANOVA below?

#                    Df  Sum Sq Mean Sq F value    Pr(>F)
# e                    1  19.082  19.082  14.875  0.001155
# e:r                  4 156.622  39.155  30.524 8.438e-08
#   e:r: r/e1          2  87.122  43.561  33.958 7.776e-07
#     r1 vs (r2, r3)   1       ?       ?       ?         ?
#     r2 vs r3         1       ?       ?       ?         ?
#   e:r: r/e2          2  69.500  34.750  27.090 3.730e-06
#     r1 vs (r2, r3)   1       ?       ?       ?         ?
#     r2 vs r3         1       ?       ?       ?         ?
# Residuals   18  23.090   1.283

# b) How to make SSQ decomposition to complete the ANOVA below?

#                    Df  Sum Sq Mean Sq F value    Pr(>F)
# e                    1  19.082  19.082  14.875  0.001155
# e:r                  4 156.622  39.155  30.524 8.438e-08
#   e:r: r/e1          2  87.122  43.561  33.958 7.776e-07
#     r2 vs (r1, r3)   1       ?       ?       ?         ?
#     r1 vs r3         1       ?       ?       ?         ?
#   e:r: r/e2          2  69.500  34.750  27.090 3.730e-06
#     r2 vs (r1, r3)   1       ?       ?       ?         ?
#     r1 vs r3         1       ?       ?       ?         ?
# Residuals   18  23.090   1.283

# TIA,
-- 
Jose Claudio Faria
Brasil/Bahia/UESC/DCET
Estatistica Experimental/Prof. Adjunto
mails:
  joseclaudio.faria at terra.com.br
  joseclaudio.faria at oi.com.br
  jc_faria at uesc.br
  jc_faria at uol.com.br
tel: 73-3634.2779