code to repeat a box model

box-model.R

# box model

box <- c(0, 1)  # the box
N <- 10  # the number of draws to take from the box
n_reps <- 10000  # the number of times to take and sum N draws from the box

# create a function to take and sum N draws from the box n_reps times
box_model <- function(box, N, n_reps) {
  sums <- numeric(n_reps)
  for (i in 1:n_reps) {
    draws <- sample(box, size = N, replace = TRUE)  # take N draws with replacement
    sums[i] <- sum(draws)  # sum (and store) the sum of the N draws
  }
  # print results
  box_SD <- sqrt(mean((box - mean(box))^2))
  cat(paste0("The expected value of the sum is ", round(N*mean(box), 1), ".\n"))
  cat(paste0("The SE of the sum is ", round(sqrt(N)*box_SD, 1), ".\n"))
  cat(paste0("The observed average of the ", n_reps, " sums is ", round(mean(sums), 1), ".\n"))
  cat(paste0("The observed SD of the ", n_reps, " sums is ", round(sqrt(mean((sums - mean(sums))^2)), 1), ".\n"))
  return(sums)
}

# n_reps times, take N draws and sum them, resulting in n_reps sums;
# or n_reps repetitions of the box model
sums <- box_model(box = box, N = N, n_reps = n_reps)

# comparing the histogram of the box to the histogram of the sums
library(ggplot2)
qplot(box)
qplot(sums)