Demonstration of Confidence Intervals

Yihui Xie & Lijia Yu 2017-04-04

This function gives a demonstration of the concept of confidence intervals in mathematical statistics.

Keep on drawing samples from the Normal distribution N(0, 1), computing the intervals based on a given confidence level and plotting them as segments in a graph. In the end, we may check the coverage rate against the given confidence level.

Intervals that cover the true parameter are denoted in color cl[2], otherwise in color cl[1]. Each time we draw a sample, we can compute the corresponding confidence interval. As the process of drawing samples goes on, there will be a legend indicating the numbers of the two kinds of intervals respectively and the coverage rate is also denoted in the top-left of the plot.

The argument nmax in ani.options controls the maximum times of drawing samples.

ani.options(interval = 0.1, nmax = 100)
## 90% interval, main = "Demonstration of Confidence Intervals")

plot of chunk demo-a

This animation shows the concept of the confidence interval which depends on the observations: if the samples change, the interval changes too. At last we can see that the coverage rate will be approximate to the confidence level.