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rats <- read.table("rats.dat",header=T)
rats
plot(time ~ treat + poison,data=rats)

interaction.plot(rats$treat,rats$poison,rats$time)
interaction.plot(rats$poison,rats$treat,rats$time)

interaction.model <- lm(time ~ treat + poison + treat:poison,data=rats)
summary(interaction.model)
# how to test all of the interaction terms at once?
noi.model <- lm(time ~ treat + poison,data=rats)
anova(interaction.model,noi.model)

plot(interaction.model$fitted.values,rstudent(interaction.model))
plot(noi.model$fitted.values,rstudent(noi.model))
# okay, no significant interaction
summary(noi.model)
# how to test all of the poison terms at once?
nop.model <- lm(time ~ treat,data=rats)
anova(noi.model,nop.model)

# also:
not.model <- lm(time ~ poison,data=rats)
anova(not.model,noi.model)

# so each of the main effects is significant, though the interaction is
# not.  This allows us to test the main effects independent of one
# another.
TukeyHSD(aov(time ~ treat,data=rats))
plot(time~treat,data=rats)
TukeyHSD(aov(time ~ poison,data=rats))
plot(time~poison,data=rats)


## another try:
int.model <- lm( log(time) ~ poison + treat + poison:treat,data=rats)
no.int.model <- lm( log(time) ~ poison + treat,data=rats)
anova(int.model,no.int.model)

plot(int.model$fitted.values,rstudent(int.model))

no.poi.model <- lm( log(time) ~ treat,data=rats)
anova(no.poi.model,no.int.model)

no.trt.model <- lm( log(time) ~ poison,data=rats)
anova(no.trt.model,no.int.model)
TukeyHSD(aov(log(time)~poison,data=rats))
plot(log(time)~poison,data=rats)
plot(log(time)~treat,data=rats)
rats