Confidence Interval Size Simulation

gistfile1.txt

## from https://statmodeling.stat.columbia.edu/2024/03/07/relating-t-statistics-and-the-relative-width-of-confidence-intervals/#comment-2335932
# but fixed up due to blog damage

nsim = 10000

lengthOfCI = rep(NaN, nsim)
containsPM = rep(NaN, nsim)

for(i in 1:nsim){
    y = rnorm(10, 0, 1)
    ci = t.test(y)$conf.int

    lengthOfCI[i] = diff(range(ci))

    if(ci[1] < 0){
        containsPM[i] = 1
    } else {
        containsPM[i] = 0
    }
}

binLims = seq(min(lengthOfCI) - 0.01, max(lengthOfCI) + 0.01, length.out = 20)

p = c()
nPerBin = c()

for(i in 1:(length(binLims) - 1)){
    inds = intersect(which(lengthOfCI >= binLims[i]),
                     which(lengthOfCI < binLims[i + 1]))
    p[i] = sum(containsPM[inds]) / length(inds)
    nPerBin[i] = length(inds)
}

plot(p, ylim = c(0, 1))
# Expected probability is about 0.95:
sum(p * (nPerBin / sum(nPerBin)))