662
Le logiciel R
Pour les M ´ echantillons :
inter.boot.moy <- function(y) {
moy <- boot(y,moyenne,R=999,stype="i",sim="ordinary")
boot.ci(moy,conf=0.9,type="perc")$percent[4:5]
}
res <- t(apply(simu.exp,MARGIN=2,FUN=inter.boot.moy))
11.3- prop.boot <- mean((res[,1] < 10) & (res [,2] > 10))
11.4- res.ttest <- t(apply(simu.exp,MARGIN=2,FUN=inter.mu))
prop.ttest <- mean((res.ttest[,1] < 10) & (res.ttest [,2] > 10))
B- ´
Etude des risques dans les tests d’hypoth` eses
• ´
Etude du risque de premi` ere esp` ece
11.1- n <- 20
M <- 500
ech <- rnorm(n,mean=4,sd=sqrt(1.2)) # Seulement un ´ echantillon.
simu <- replicate(M,rnorm(n,mean=4,sd=sqrt(1.2)),simplify=TRUE)
11.2- ttest <- function(x) t.test(x,mu=4)$p.value
res <- apply(simu,MARGIN=2,FUN=ttest)
11.3- (compt <- sum(res < 0.05))
compt hypoth` eses sont rejet´ ees ; on s’attend `
a rejeter 25 hypoth` eses nulles.
11.4- M <- 5000
simu <- replicate(M,rnorm(n,mean=4,sd=sqrt(1.2)),simplify=TRUE)
res <- apply(simu,MARGIN=2,FUN=ttest)
proportion <- mean(res < 0.05)
proportion
11.5- n <- 100
M <- 5000
simu <- replicate(M,rchisq(n,df=1),simplify=TRUE)
ttest <- function(x) t.test(x,mu=1)$p.value
res.chi2 <- t(apply(simu,MARGIN=2,FUN=ttest))
proportion <- mean(res.chi2 < 0.05)
proportion
11.6- n <- 10
M <- 5000
simu <- replicate(M,rchisq(n,df=1),simplify=TRUE)
ttest <- function(x) t.test(x,mu=1)$p.value