Stratified Sampling in R (part 1)

Stratified Sampling explained and demonstrated with a simulated example.

part 2 of this series:    • Stratified Sampling in R (part 2)  
part 3 of this series:    • Stratified Sampling in R (part 3)  

R code:
#Stratified Sampling
#alternative to SRS
#divide population into k non-overlapping distinct subpopulations called strata
#Why Stratify?
#1 - interested in learning about the subpopulation; perhaps to compare them later
#2 - convenient for organizing data collection
#3 - improve precision of your estimate; smaller error of estimation; especially
when strata are homogenous; efficiency gain

set.seed(9850)
df = data.frame(gender=rep(c("F","M"),c(6000,4000)), ht=c(rnorm(6000, mean=60, sd=5),rnorm(4000, mean=90, sd=5)))

#Population parameters (mu, sigma, strata, etc)
mean(df$ht)
table(df$gender)
var(df$ht)
sd(df$ht)
aggregate(df$ht ~ df$gender, FUN=mean)
aggregate(df$ht ~ df$gender, FUN=sd)

#Generating 1000 SRS, size n=50, for purposes of measuring precision of estimate for mu
set.seed(9850)
xbar = apply(replicate(1000, sample(df$ht, 50)), 2, FUN=mean)
mean(xbar)
var(xbar)
sd(xbar)
sigmasq_xbar = ((var(df$ht) * (length(df$ht) - 1)) / length(df$ht)) / 50
sigmasq_xbar_hat = var(xbar)

#proportional stratified RS using gender for strata
table(df$gender) / nrow(df) * 50
#30 F and 20 M
xbarStrat = NA
set.seed(9850)
for (i in 1:1000) {xbarStrat[i] = mean( c(df[sample(6000, 30), "ht"], df[sample(6001:10000, 20), "ht"]) ) }
mean(xbarStrat)
var(xbarStrat)
sigmasq_xbarStrat = (6000/10000)^2*(((var(df[df$gender %in% "F", "ht"])*(6000-1)) / 6000)/30)*((6000-30)/(6000-1)) +
(4000/10000)^2*(((var(df[df$gender %in% "M", "ht"]) * (4000 - 1)) / 4000)/20)*((4000-20)/(4000-1))

#visualizing the precision differential between the two sampling techniques
par(mfrow=c(1,2))
hist(xbar, freq=F, xlim=c(65,85))
lines(density(xbar), col="red")
hist(xbarStrat, freq=F, xlim=c(65,85))
lines(density(xbarStrat), col="red")