

Dear R users,
I would like to understand a simple problem related to glht() multeplicity correction and linear Hypotheses testing. Given a simple lme model with two predictors (group = 3 levels; time =  2 levels) and their interaction with treatment contrast, I see that the p-values are lower and higher when I test few or many hypotheses respectively. Because I dont't have a deep knowledge of multiple comparison theory, I ask you some suggestion or explanation about the different obtained results.  
As you can see in the example below, "m1" and "m2" test a different number of hypotheses but comparing the same hypothesis a different results occurred.


time<-rep(c(rep(0,8),rep(1,8)),3)
group<-c(rep(0,16),rep(1,16),rep(2,16))
id<-c(rep(1:8,2),rep(9:16,2),rep(17:24,2))
w<-c(172.9, 185.8, 173.1, 187.3, 161.6, 167.1, 168.4, 161.1, 166.5, 175.3, 167.1, 181.9, 163.0, 167.7, 172.1, 170.3, 167.2, 183.3, 160.7,167.8, 149.6, 159.1, 164.2, 171.0, 168.6, 173.5, 161.8, 166.5, 148.4, 167.1, 166.8, 166.6, 150.6, 178.4, 166.4, 159.2, 163.2, 167.8, 136.6, 161.8, 166.1, 175.8, 175.6, 166.2, 168.5, 170.5, 152.0, 164.4)
dati<-data.frame(time,group,id,w)
dati$time<-as.factor(dati$time)
dati$group<-as.factor(dati$group)
dati$id<-as.factor(dati$id)




kp<-rbind("after Treatment: Group 1 - Controls"=c(0,1,0,0,0,0),
         "after Treatment: Group 2 - Controls"=c(0,0,1,0,0,0),
         "before Treatment: Group 1 - Controls"=c(0,1,0,0,1,0),
         "before Treatment: Group 2 - Controls"=c(0,0,1,0,0,1),
         "Controls: time trend (T1 - T0)"=c(0,0,0,-1,0,0),
         "Group 1: time trend (T1 - T0)"=c(0,0,0,-1,-1,0),
         "Group 2: time trend (T1 - T0)"=c(0,0,0,-1,0,-1))


k<-rbind("after Treatment: Group 1 - Controls"=c(0,1,0,0,0,0),
         "after Treatment: Group 2 - Controls"=c(0,0,1,0,0,0),
         "before Treatment: Group 1 - Controls"=c(0,1,0,0,1,0),
         "before Treatment: Group 2 - Controls"=c(0,0,1,0,0,1)
         )




w.lme<-lme(w~group*time,data=dati,random=~1|id)
m1<-summary(glht(w.lme,kp))
m2<-summary(glht(w.lme,k))


Thank in advances for your suggestions


Massimo 
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