showing_stratification_advantage

strat.R

library(ggplot2)

# simulate experiments using stratification and randomization and report
# absolute difference in estimates from true treatment effect, tau. 

simExp <- function(n, tau, beta = 3){
    x <- sort(runif(n))
    W.rand <- rbinom(n,1,0.5)
    W.strat <- rep(c(0,1), n/2)
    epsilon <- rnorm(n, 0, 0.5)
    y.rand <- beta * x + tau * W.rand + epsilon
    y.strat <- beta * x + tau * W.strat + epsilon
    m.strat <- lm(y.strat ~  W.strat)
    m.rand <- lm(y.rand ~ W.rand)
    c(abs(tau - coef(m.strat)[2]), abs(tau - coef(m.rand)[2]))
}

# compare w/ a t-test
results <-data.frame(t(sapply(1:1000, function(x) simExp(100, 3))))
with(results, t.test(W.strat, W.rand))

deltaABS <- function(sample.size){
    results <-data.frame(t(sapply(1:1000, function(x) simExp(sample.size, 3))))
    mean(results$W.rand) - mean(results$W.strat)
}

sizes <- c(20, 40, 80, 160, 320, 640)
improvement <- sapply(sizes, deltaABS)
df <- data.frame(size = sizes, improvement = improvement)

g <- ggplot(data = df, aes(x = sizes, y = improvement)) + geom_point() + geom_line() +
    xlab("Sample size") +
        ylab("Stratification Improvement in Absolute Distance from True Treatment Effect") + 
    theme_bw()

png("strat_results.png")
print(g)
dev.off()