data <- matrix(scan(),ncol=3,byrow=TRUE)
 1 1 106  
 1 1 108  
 1 2  93 
 1 2  101 
 1 2  98 
 1 3 56  
 2 1 107 
 2 1 110
 2 1 116
 2 2  63
 2 2  60
 2 3 40 
 2 3 41
 2 3 44 
 

data
  
UnbalConcrete <- data.frame(data)
colnames(UnbalConcrete) <- c("aggregate","compaction","strength")
UnbalConcrete$aggregate  <- as.factor(UnbalConcrete$aggregate)
UnbalConcrete$compaction <- as.factor(UnbalConcrete$compaction)
rm(data)

levels(UnbalConcrete$aggregate) <- c("Basalt","Silicious") 
levels(UnbalConcrete$compaction) <- c("Regular","Low","VeryLow") 

UnbalConcrete

 # the anova function applied to an lm object calculates Type I SS

anova(lm(strength ~ aggregate + compaction + aggregate:compaction, data = UnbalConcrete))



 # the car package contains a function 'Anova' that can calculate Type II or Type III SS
 # it calculates Type II SS by default

library(car)

 # this produces the results using Type II SS 
Anova(lm(strength ~ aggregate + compaction + aggregate:compaction, data = UnbalConcrete),type="II")

 # the Type III SS produced by using the type="III" argument do not match SAS results