# the example from section 6.7

data <- scan(what = list(a=0,b=0,y=0), multi.line=F)
 1 1 2.1  1 2 6.8  1 3 8.4  1 4 1.4  1 5 14.6  1 6 7.9  1 7 4.8 
 2 1 1.7  2 2 8.1  2 3 8.4  2 4 1.4  2 5 12.0  2 6 3.7  2 7 4.5 
 3 1 14.4  3 2 14.8  3 3 27.0  3 4 30.9  3 5 36.5  3 6 36.4  3 7 31.4 
 4 1 57.4  4 2 62.4  4 3 37.4  4 4 63.3  4 5 65.5  4 6 65.6  4 7 59.8 
 5 1 66.2  5 2 81.7  5 3 53.3  5 4 80.7  5 5 79.7  5 6 80.8  5 7 82.4 
 6 1 75.2  6 2 94.0  6 3 74.3  6 4 87.9  6 5 93.3  6 6 87.8  6 7 80.5 
 7 1 4.1   7 2 10.2  7 3 10.7  7 4  5.5  7 5 18.1  7 6 11.4  7 7 6.1 

 data

table617 <- data.frame(data)
rm(data)

table617$a <- as.factor(table617$a)
table617$b <- as.factor(table617$b)

table617.fit <- lm(y ~ a +b +a:b, data=table617)

anova(table617.fit)



install.packages("additivityTests")

library(additivityTests)


# apparently the functions in the additivityTests package require
# input in the form of a matrix

table617mat <- matrix(table617$y, nrow=7, ncol=7, byrow=T) 

tukey.test(table617mat,alpha=.05)


# their test statistic is a bit different than in the text