# this example illustrates partial confounding with blocks ;

data <- scan(what = list(block=0,replicate=0,a=0,b=0,c=0,y=0), multi.line=F)
 1 1 0 0 0 25  1 1 0 1 1 34  1 1 1 1 1 42  1 1 1 0 0 25 
 2 1 1 1 0 43  2 1 0 0 1 30  2 1 1 0 1 40  2 1 0 1 0 33 
 3 2 1 1 1 39  3 2 0 1 0 29  3 2 0 0 0 27  3 2 1 0 1 40 
 4 2 0 1 1 38  4 2 1 0 0 37  4 2 1 1 0 46  4 2 0 0 1 34 
 5 3 0 0 0 26  5 3 0 0 1 32  5 3 1 1 0 52  5 3 1 1 1 51 
 6 3 1 0 0 43  6 3 0 1 0 34  6 3 1 0 1 40  6 3 0 1 1 36 

data

table11.5 <- data.frame(data)

 # using the within function to convert variables to factor
table11.5 <- within(table11.5, 
   { block  <- factor(block)
     replicate <- factor(replicate)
     a      <- factor(a)
     b      <- factor(b)
     c      <- factor(c) } )


summary(aov(y ~ replicate +block %in% replicate +a +b +c +a:b +a:c +b:c +a:b:c, data = table11.5))


 # it is easier to see the results using the afex package

library(afex)

table11.5.afex1  <- mixed(y ~ replicate + (1|block:replicate) +a*b*c, data = table11.5)

summary(table11.5.afex1)

nice(table11.5.afex1)

lsmeans(table11.5.afex1, ~ a)

lsmeans(table11.5.afex1, ~ b)