conf.int {animation} | R Documentation |
This function gives a demonstration of the concept of confidence intervals in mathematical statistics.
conf.int(level = 0.95, size = 50, cl = c("red", "gray"), ...)
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 ( |
... |
other arguments passed to |
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.
A list containing
level |
confidence level |
size |
sample size |
CI |
a matrix of confidence intervals for each sample |
CR |
coverage rate |
Yihui Xie
George Casella and Roger L. Berger. Statistical Inference. Duxbury Press, 2th edition, 2001.
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)