This tutorial is based on the lecture found at https://class.coursera.org/statinference-033/lecture/269.

Consider the dataset generated below.

library(UsingR)
## Loading required package: MASS
## Loading required package: HistData
## Loading required package: Hmisc
## Loading required package: grid
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
## Loading required package: ggplot2
## 
## Attaching package: 'Hmisc'
## 
## The following objects are masked from 'package:base':
## 
##     format.pval, round.POSIXt, trunc.POSIXt, units
## 
## 
## Attaching package: 'UsingR'
## 
## The following object is masked from 'package:ggplot2':
## 
##     movies
## 
## The following object is masked from 'package:survival':
## 
##     cancer
data(father.son)
x<-father.son$sheight
n<-length(x)

Now we resample using the single dataset given B = 10,000 times and produce a matrix with the results.

B<-10000 ##number of resamples
resamples<-matrix(sample(x,n*B,replace=TRUE),B,n)
resampledMedians<-apply(resamples,1,median)
sd(resampledMedians)
## [1] 0.08331873
quantile(resampledMedians,c(0.025,0.975))
##     2.5%    97.5% 
## 68.44579 68.81461

We visualize the operations executed above.

library(ggplot2)
g<-ggplot(data.frame(medians=resampledMedians),aes(x=medians))
g<-g+geom_histogram(color="black",fill="lightblue",binwidth=0.05)
g

The plot above estimates the sampling distribution of the median.