# From Walpole, Myers, Myers, Ye, 9th ed., Table 13.9

# Is time for the assembling of a particular product different among
# four machines (treatments)? Six operators (blocks).

time <- c(42.5, 39.3, 39.6, 39.9, 42.9, 43.6,
  39.8, 40.1, 40.5, 42.3, 42.5, 43.1,
  40.2, 40.5, 41.3, 43.4, 44.9, 45.1,
  41.3, 42.2, 43.5, 44.2, 45.9, 42.3)

operator <- factor(rep(1:6, 4))
machine <- factor(rep(1:4, each=6))

fit1 <- aov(time~machine)
summary(fit1)

resid1=residuals(fit1)
qqnorm(resid1)
qqline(resid1) # doesn't look normally distributed
library(nortest)
ad.test(resid1) # Anderson-Darling test of normality

fit2 <- aov(time~machine+operator)
summary(fit2)

resid2=residuals(fit2)
qqnorm(resid2)
qqline(resid2) # better
ad.test(resid2)