feed.data=read.table(".../feederfloor.txt",header=TRUE)
attach(feed.data)

#two-way with interactions
model.interaction=aov(weight~floor+trough+floor:trough)
summary(model.interaction)

#two-way without interactions (main effects only):
model.main=aov(weight~floor+trough)
summary(model.main)
#or, to get standard errors for the main effects, use summary.lm
summary.lm(model.main)

#you can compute the means for each treatment:
mu.HH=mean(weight[(floor=="H")&(trough=="H")])
mu.HL=mean(weight[(floor=="H")&(trough=="L")])
mu.LH=mean(weight[(floor=="L")&(trough=="H")])
mu.LL=mean(weight[(floor=="L")&(trough=="L")])

#compute mean for High Floor - Low Floor groups
mean(weight[floor=="H"])-mean(weight[floor=="L"])
#compute mean for High Feeder - Low Feeder groups
mean(weight[trough=="H"])-mean(weight[trough=="L"])


#second example
#first modify the data, as dscribed by the problem:
weight[(floor=="H")&(trough=="L")]=weight[(floor=="H")&(trough=="L")]-8
#then fit the model with interaction
model2.interaction=aov(weight~floor+trough+floor:trough)
summary(model2.interaction)#--->strong interaction effect
summary.lm(model2.interaction)
#to get sigma hat:
sigma.hat=sqrt(summary(model2.interaction)[[1]][4,3])

#to answer specific questions based on linear combinations:
#compare means of low and high floor when trough is low
mean(weight[(floor=="H")&(trough=="H")])-mean(weight[(floor=="L")&(trough=="H")])
#to compute standard error of this linear combination:
sigma.hat*sqrt(1/10+1/10)#n1=n2=10 in this case