# W&J Example page 101.

N<-1e3

t1<-numeric(N)
t2<-numeric(N)
t3<-numeric(N)
t1n<-numeric(N)
t2n<-numeric(N)
t3n<-numeric(N)

for(i in 1:N) {
 
  x <-rnorm(10,0,1)
  y1<-rnorm(10,1,1)
  y2<-rnorm(10,1.5,1)
  y3<-rnorm(10,2,1)

  xn <-rnorm(10,0,1.25)
  y1n<-rnorm(10,1,1.25)
  y2n<-rnorm(10,1.5,1.25)
  y3n<-rnorm(10,2,1.25)


  t1[i]<-(t.test(x,y1)$p.value)
  t2[i]<-(t.test(x,y2)$p.value)
  t3[i]<-(t.test(x,y3)$p.value)

  t1n[i]<-(t.test(x,y1n)$p.value)
  t2n[i]<-(t.test(x,y2n)$p.value)
  t3n[i]<-(t.test(x,y3n)$p.value)

}

alfa <-seq(0.01,0.10,0.01)
p1 <-numeric(length(alfa))
p2 <-numeric(length(alfa))
p3 <-numeric(length(alfa))
p1n <-numeric(length(alfa))
p2n <-numeric(length(alfa))
p3n <-numeric(length(alfa))


for(j in 1:length(alfa)) {
  p1[j] <-length(t1[t1<alfa[j]])
  p2[j] <-length(t2[t2<alfa[j]])
  p3[j] <-length(t3[t3<alfa[j]])

  p1n[j]<-length(t1n[t1n<alfa[j]])
  p2n[j]<-length(t2n[t2n<alfa[j]])
  p3n[j]<-length(t3n[t3n<alfa[j]])
}

plot (alfa*100,100*p1/N,type="l",ylim=c(0,100),xlab=expression(alpha ~"(%)"),ylab="Força (%)")
lines(alfa*100,100*p2/N,col="red")
lines(alfa*100,100*p3/N,col="green")

lines(alfa*100,100*p1n/N,lty=("dashed"))
lines(alfa*100,100*p2n/N,lty=("dashed"),col="red")
lines(alfa*100,100*p3n/N,lty=("dashed"),col="green")