# From Walpole, Myers, Myers, Ye, 9th ed., Table 13.1

# Does mean absorption of moisture in concrete ("betong") vary among five different concrete aggregates ("tilslag") (main part of concrete, e.g. mixtures of sand, gravel, stone, in addition to cement and water)?

concrete.data <- read.csv("http://www.math.ntnu.no/~mettela/TMA4267/Data/AGGREGATES.CSV",sep=";")

# You can view any object by typing its name:
concrete.data

# To get help on e.g. read.csv:
?read.csv

attach(concrete.data)

n <- length(moisture)
r <- length(unique(aggregate)) # or r <- length(table(aggregate))

grandmean <- mean(moisture)
means <- ave(moisture, aggregate)

SS <- sum((moisture-grandmean)^2)
MS <- SS/(n-1) # or MS <- var(moisture)

SST <- sum((means-grandmean)^2)
MST <- SST/(r-1)

SSE <- sum((moisture-means)^2)
MSE <- SSE/(n-r)

F <- MST/MSE
pf(F,r-1,n-r,lower.tail=FALSE)

# Easier:

summary(aov(moisture~as.factor(aggregate)))