Demonstration of the concept of confidence intervals

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Description

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

Usage

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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

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

Examples

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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)

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