[R] SSQ decomposition and contrasts with ANOVA

[Jose Claudio Faria]

Dear R list,

Please, could someone help me with SSQ decomposition and contrasts.
Below my data, graphic, ANOVAs and my doubt:

# Data
a   = paste('a', gl(3, 8), sep='')
b   = paste('b', gl(2, 4, 24), 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(a, b, tra, y)

# Graphic
par(mfrow=c(2,1))
interaction.plot(dF$a, dF$b, dF$y,
                  ylab = 'y', xlab = 'a')

interaction.plot(dF$b, dF$a, dF$y,
                  ylab = 'y', xlab = 'b')

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

av1 = aov(y ~ a*b, data=dF)
summary(av1)

av2 = aov(y ~ a/b, data=dF)
b_a = summary(av2, split = list('a:b' = list(
               'b1 vs b2/a1' = 1, 'b1 vs b2/a2' = 2, 'b1 vs b2/a3' = 3)))
b_a

av3 = aov(y ~ b/a, data=dF)
a_b = summary(av3, split = list('b:a' = list(
              'a/b1' = c(1,3), 'a/b2' = c(2,4))))
a_b

# My doubts
a) How to make the SSQ decomposition to complete the ANOVA below?
--------------------------------------------------------
                    Df   Sum Sq Mean Sq F value    Pr(>F)
b                   1   19.082  19.082  14.875  0.001155
b:a                 4  156.622  39.155  30.524 8.438e-08
--------------------------------------------------------
  b:a: a/b1         (2) (87.122) 43.561  33.958 7.776e-07
--------------------------------------------------------
    a1 vs (a2, a3)   1        ?       ?       ?         ?
    a2 vs a3         1        ?       ?       ?         ?
--------------------------------------------------------
  b:a: a/b2         (2) (69.500) 34.750  27.090 3.730e-06
--------------------------------------------------------
    a1 vs (a2, a3)   1        ?       ?       ?         ?
    a2 vs a3         1        ?       ?       ?         ?
--------------------------------------------------------
Residuals   18  23.090   1.283
--------------------------------------------------------

b) How to make the SSQ decomposition to complete the ANOVA below?
--------------------------------------------------------
                    Df   Sum Sq Mean Sq F value    Pr(>F)
b                   1   19.082  19.082  14.875  0.001155
b:a                 4  156.622  39.155  30.524 8.438e-08
--------------------------------------------------------
  b:a: a/b1         (2) (87.122) 43.561  33.958 7.776e-07
--------------------------------------------------------
    a2 vs (a1, a3)   1        ?       ?       ?         ?
    a1 vs a3         1        ?       ?       ?         ?
--------------------------------------------------------
  b:a: a/b2         (2) (69.500) 34.750  27.090 3.730e-06
--------------------------------------------------------
    a2 vs (a1, a3)   1        ?       ?       ?         ?
    a1 vs a3         1        ?       ?       ?         ?
--------------------------------------------------------
Residuals   18  23.090   1.283
--------------------------------------------------------

Or, In this case, how can I to test these constrasts?

Thanks for any help,
-- 
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