## estimate standard errors and C.I.'s using bootstrapping
## data and part 2 from Data Analysis and Graphics Using R,
## by Maindonald and Braun

source('A:/cuckoos.R'); cuckoos
wren<-split(cuckoos$length,cuckoos$species)$wren
#19.8 22.1 21.5 20.9 22.0 21.0 22.3 21.0 20.3 20.9 22.0 20.0 20.8 21.2 21.0
length(wren) #15

##########################
# 1. programming on my own
##########################
nboot<-999
n<-length(wren)
x<-NULL
for (i in 1:nboot){
x<-c(x,median(sample(wren,n,replace=T)))
}
se<-sd(x); se #0.2054436
#95% confidence interval
quantile(x,c(.025,.975)) #20.9  21.5

###############################
# 2. using R built-in functions
###############################
library(boot)

## First define median.fun(), with two required arguments: 
##         data specifies the data vector, 
##         indices selects vector elements for a each resample 
median.fun <- function(data, indices){median(data[indices])} 
## Call the boot() function, with statistic=median.fun 
wren.boot <- boot(data = wren, statistic = median.fun, R = nboot)   
wren.boot 
    original     bias    std. error
t1*       21 0.04954955   0.2219365

boot.ci(boot.out=wren.boot,type="perc")
Intervals : 
Level     Percentile     
95%   (20.8, 22.0 )  
Calculations and Intervals on Original Scale