Stratified Sampling in R part 3

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Stratified Sampling explained and demonstrated with a simulated example. • part 1 of this series: • Stratified Sampling in R (part 1) • part 2 of this series: • Stratified Sampling in R (part 2) • 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 )

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