Plotting confidence intervals from a chance experiment in R

Question

I am trying to make an illustrative plots for showing students the meaning and nature of frequentist confidence intervals over repeated trials of a chance experiment. I sample from a normal distribution and estimate confidence intervals.

get.ci<-function(x,alpha=.05,n){
M<-mean(x)
se<-sd(x)/sqrt(n)
t<-qt(1-alpha/2,df=n-1)
ci<-c(M-se*t,M+se*t)
return(c(M,ci))
}

n=100
mu=100
sig=20
ci<-matrix(ncol=3,nrow=1000)
for(i in 1:1000){
  x<-rnorm(n,mu,sig)
  ci[i,]<-get.ci(x,n=n)
}

Now I would like to plot ci in a row of experiments, where the x-axis denotes row number of ci and y-axis denotes point estimates M with upper and lower bounds connected with a line. Then I want to add an abline and hope it becomes visually evident that a proportion (ie 100*alpha%) of CIs does not cover the true value, ie

low.viol<-ci[,2]>100
up.viol<-ci[,3]<100
(sum(low.viol)+sum(up.viol))/1000

How should I make this plot in R?

Answer 1

I think you need to order them for anything to become "visually apparent". Compare:

# unordered
plot(range(1:nrow(ci)), range(ci), type = "n")
segments(x0 = 1:nrow(ci), x1 = 1:nrow(ci), y0 = ci[, 2], y1 = ci[, 3], col = "gray80")
points(1:nrow(ci), ci[, 1], pch = ".")

# ordered
ci.ordered <- ci[order(ci[, 1]), ]
plot(range(1:nrow(ci.ordered)), range(ci.ordered), type = "n")
segments(x0 = 1:nrow(ci.ordered), x1 = 1:nrow(ci.ordered),
         y0 = ci.ordered[, 2], y1 = ci.ordered[, 3], col = "gray80")
points(1:nrow(ci.ordered), ci.ordered[, 1], pch = ".")
abline(h = 100)

Colored based on overlap or not:

far.off <- ci.ordered[, 2] > 100 | ci.ordered[, 3] < 100
plot(range(1:nrow(ci.ordered)), range(ci.ordered), type = "n")
segments(x0 = 1:nrow(ci.ordered), x1 = 1:nrow(ci.ordered),
         y0 = ci.ordered[, 2], y1 = ci.ordered[, 3],
         col = c("gray80", "firebrick2")[far.off + 1])
points(1:nrow(ci.ordered), ci.ordered[, 1], pch = ".")
abline(h = 100)

Answer 2

If I understand the question correctly, in standard R graphics, it would look something like that :

plot(ci[,1], type="n", ylim=c(89,110))
lines(ci[,2],col="red")
lines(ci[,3],col="blue")
abline(100,0)

But then, to clearly show the proportion of CI not containing mu, I'm not so sure how to help you