conf.int: Demonstration of the concept of confidence intervals

In animation: A Gallery of Animations in Statistics and Utilities to Create Animations

Description

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

Usage

conf.int(level = 0.95, size = 50, cl = c("red", "gray"), ...)

Arguments

level	the confidence level (1 - α), e.g. 0.95
size	the sample size for drawing samples from N(0, 1)
cl	two different colors to annotate whether the confidence intervals cover the true mean (cl[1]: no; cl[2]: yes)
...	other arguments passed to plot.default

Details

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.

Value

A list containing

level	confidence level
size	sample size
CI	a matrix of confidence intervals for each sample
CR	coverage rate

Author(s)

Yihui Xie

References

Examples at https://yihui.org/animation/example/conf-int/

George Casella and Roger L. Berger. Statistical Inference. Duxbury Press, 2th edition, 2001.

animation documentation built on Oct. 7, 2021, 9:18 a.m.