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I sas this example in the book R in action, the codes in R are as follows:

library(multcomp)
attach(cholesterol)
table(trt)
trt
aggregate(response, by=list(trt), FUN=mean)
aggregate(response, by=list(trt), FUN=sd)
fit<-aov(response ~ trt)
summary(fit)

tuk<-glht(fit, linfct=mcp(trt="Tukey"))
plot(cld(tuk, level=.05), col="lightgrey")

It is written in the book that:

From these results, you can see that taking the cholesterol-lowering drug in 5 mg doses four times a day was better than taking a 20 mg dose once per day. The competitor drugD wasn’t superior to this four-times-per-day regimen. But competitor drugE was superior to both drugD and all three dosage strategies for our focus drug

What I understund is:

four times a day is better than one time a day, because the mean is higher. (mean is the right value to watch, isn't?)

DurgE is the best among all, because of the mean.

What I could not understand is:

  1. Why is four times a day better than drugD? The mean of drugD is higher.

  2. How could four times a day be compared with drugD? They are not signifikantlly different. (they both have the alphabet c in this graphic)

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@yue86231 I think you've simply misread the R manual. The book (as you've quoted) states that DrugD WASN'T (significantly) better than the 4x/day regimen. As you indicated, the post-hoc letters above the plot indicate a shared letter (c).

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  • $\begingroup$ So "The competitor drugD wasn’t superior to this four-times-per-day regimen" can also be written as: "drugD wasn't significantly better than four time a day, even though the mean of drugD is higher than four times a day". Now I understand it, thanks! $\endgroup$
    – yue86231
    Commented Dec 26, 2014 at 14:19

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