animation (version 2.0-5)

conf.int: Demonstration of the concept of confidence intervals

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 $(1 - \alpha)$, 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]: yes; cl[2]: no)

...

other arguments passed to plot.default

Value

• A list containing
• level
  confidence level
• size
  sample size
• CI
  a matrix of confidence intervals for each sample
• CR
  coverage rate

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.

References

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

http://animation.yihui.name/mathstat:confidence_interval

Examples

oopt = ani.options(interval = 0.1, nmax = ifelse(interactive(), 
    100, 2))
## 90\% interval
conf.int(0.9, main = "Demonstration of Confidence Intervals")

## save the animation in HTML pages
saveHTML({
    ani.options(interval = 0.15, nmax = ifelse(interactive(), 
        100, 10))
    par(mar = c(3, 3, 1, 0.5), mgp = c(1.5, 0.5, 0), tcl = -0.3)
    conf.int()
}, img.name = "conf.int", htmlfile = "conf.int.html", ani.height = 400, 
    ani.width = 600, title = "Demonstration of Confidence Intervals", 
    description = c("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."))

ani.options(oopt)