uweziegenhagen.de

To highlight how confidence intervals cover in 1-\alpha cases the true parameter I hacked together a little R code based on code from http://paleocave.sciencesortof.com/2013/03/writing-a-for-loop-in-r/ and http://www.cyclismo.org/tutorial/R/confidence.html

• I define a function which takes as parameter „runs“ the number of confidence intervals to compute
• result is the vector of results, it will contain TRUE values for those intervals that cover the true parameter and FALSE for those which don’t
• for each run I draw a sample of 10000 points from N(0,1)
• I then calculate the mean and standard deviation of the sample
• before calculating the limits of the confidence interval, „left“ and „right“
• Since I know the true mu is 0 I can check if 0 falls into this interval, the result of this check is stored in the i-th column of the result vector
• finally I calculate the summary of the result vector. On average 95% percent of all intervals will cover the true mu, 0.

If I find some more time I will add some functionality to run this code on multiple cores as well as a graphical visualisation of the intervals.

confInt <- function(runs){
	result<-NULL
	for (i in 1:runs) {
		data<-rnorm(10000)
		n<-length(data)
		a<-mean(data)
		s<-sd(data)
		error <- qnorm(0.975)*s/sqrt(n)
		left <- a-error
		right <- a+error
		result[i] = left<0 & 0<right
	}
	result
}
summary(confInt(100))

EDIT: Using some more ggplot2 code I have the graphical visualization ready:

confInt <- function(runs){
	x<-1:runs
	mu<-NULL
	sigma<-NULL
	result<-NULL
	vleft<-NULL
	vright<-NULL
 
	for (i in 1:runs) {
		data<-rnorm(1000)
		n<-length(data)
		a<-mean(data)
		mu[i]<-a
		s<-sd(data)
		sigma[i]<-s
		error <- qnorm(0.975)*s/sqrt(n)
		left <- a-error
		right <- a+error
 
		result[i] = left<0 & 0<right
		vleft[i] = left	
		vright[i] = right
}
	data.frame(x,mu,sigma,result,vleft,vright)
}
 
 
df<-confInt(100)
 
require(ggplot2)
 
myplot<-ggplot(df, aes(x = x, y = mu)) +
  geom_point(size = 2) +
  geom_errorbar(aes(ymax = vleft, ymin = vright,colour=result*3))
myplot + theme_bw() 
summary(df)

See http://stackoverflow.com/questions/30289894/plotting-confidence-intervals-from-a-dataframe/30290123#30290123 for an alternative solution.

Here’s a simple example how to create a pie-chart (in PDF format) with R’s ggplot2 library.

pdf(file = "g:/test.pdf")
library("ggplot2")

df <- data.frame(
  Legende = c("male", "female", "child"),
  werte = c(20, 20,60)
)

blue <- rgb(26/255, 115/255, 186/255, 1) 
yellow <- rgb(255/255, 219/255, 67/255, 1) 
orange <- rgb(181/255, 75/255, 5/255, 1)

ggplot(df, aes(x = "", y = werte, fill = Legende)) +
	geom_bar(width = 1, stat = "identity") +
  	scale_fill_manual(values =  c(blue, yellow, orange)) +
  	coord_polar("y", start = 0) +
	labs(title = "Ein einfacher Pie-Chart")  +
	xlab("X-Achse") +
	ylab("Y-Achse") 
  
dev.off()

Mit Sweave lässt sich R Code direkt in LaTeX Dokumente einbetten und ausführen. Dokumente lassen sich auf diese Weise sehr einfach automatisieren und dynamisieren. Ein weiterer Vorteil ist, dass auch immer die richtigen Grafiken und Tabellen im TeX Dokument landen.

Auf der 42. Dante Tagung in Dortmund habe ich zu dem Thema einen kurzen Vortrag gehalten, hier sind die Folien: uweziegenhagen-dante2010

Anfang 2009 war ein interessanter Artikel zu R in der NY Times: http://www.nytimes.com/2009/01/07/technology/business-computing/07program.html?_r=3.