# Latin Square p.158-163
tab.4.9 <- matrix(c(24,17,18,26,22,20,24,38,31,30,19,30,26,26,20,24,27,27,23,29,24,36,21,22,31),nc=5)
tab.4.9.df <- data.frame(y=as.vector(tab.4.9),
batch=factor(rep(1:5,5)),
op=factor(rep(1:5,each=5)),
trt=factor(c(1,2,3,4,5,2,3,4,5,1,3,4,5,1,2,4,5,1,2,3,5,1,2,3,4)))

plot(y~op+batch+trt,tab.4.9.df)
y.lm <- lm(y~trt+factor(batch)+factor(op),tab.4.9.df)
anova(y.lm)