data <- matrix(scan(),ncol=6,byrow=TRUE)
1 1 1 1 1 14   1 1 1 0 0 11.5  1 1 0 1 0 12  1 1 0 0 1 12.5 
2 3 1 1 1 10   2 3 1 0 0 8     2 3 0 1 0 7   2 3 0 0 1 9 
1 2 1 1 0 13   1 2 1 0 1 14    1 2 0 1 1 13  1 2 0 0 0 10 
2 4 1 1 0 13   2 4 1 0 1 15    2 4 0 1 1 14  2 4 0 0 0 11 

data

Burgers1 <- data.frame(data)
colnames(Burgers1) <- c("rep","person","patty","cheese","mayo","taste")

Burgers1$rep       <- as.factor(Burgers1$rep)
Burgers1$person       <- as.factor(Burgers1$person)
Burgers1$patty       <- as.factor(Burgers1$patty)
Burgers1$mayo       <- as.factor(Burgers1$mayo)
Burgers1$cheese       <- as.factor(Burgers1$cheese)


summary(aov(taste ~ rep + Error(rep/person) + patty*mayo*cheese, data = Burgers1))


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

library(afex)

Burgers1.afex1  <- mixed(taste ~ rep + (1|rep:person) +patty*mayo*cheese -patty:mayo:cheese,
                         data = Burgers1)

summary(Burgers1.afex1)

nice(Burgers1.afex1)

 # looking at the nearly significant interaction

lsmip(Burgers1.afex1, mayo ~ cheese)


 # this approach is like the split-plot approach from Chapter 14 

Burgers1 <- within(Burgers1,
            {
              ABC <- NA
              ABC[person == 1] <- 'odd'
              ABC[person == 2] <- 'even'
              ABC[person == 3] <- 'odd'
              ABC[person == 4] <- 'even'
            } )

Burgers1.afexSPF  <- mixed(taste ~ ABC + (1|rep:ABC) +patty*mayo*cheese -patty:mayo:cheese,
                         data = Burgers1)

summary(Burgers1.afexSPF)

nice(Burgers1.afexSPF)

lsmeans(Burgers1.afexSPF, ~mayo)