CS112 14.1 ancillary code

set.seed(123)

# create storage vectors
# to store the means for each experiment

storage.corr <- c()
storage.uncorr <- c()

# "PULL THE *CORR* LEVER"
# correlated data

corr.lever <- function()
{
  return(c(
    rep(rbinom(n = 1, size = 1, prob = 0.5), 10),
    rep(rbinom(n = 1, size = 1, prob = 0.5), 10),
    rep(rbinom(n = 1, size = 1, prob = 0.5), 10),
    rep(rbinom(n = 1, size = 1, prob = 0.5), 10),
    rep(rbinom(n = 1, size = 1, prob = 0.5), 10)))
}

# "PULL THE *UNCORR* LEVER"
# uncorrelated data
uncorr.lever <- function()
{
  return(rbinom(n = 50, size = 1, prob = 0.5))
}

# run 1000 experiments (simulated trials)
for(i in 1:1000)
{
  storage.corr[i] <- mean(corr.lever())
}

for(i in 1:1000)
{
  storage.uncorr[i] <- mean(uncorr.lever())
}

# Was the standard deviation of the means derived from uncorrelated data
# LOWER than the standard deviation of the means derived from correlated data?
# Across all the simulated trials (for the whole shebang)?
sd(storage.uncorr) < sd(storage.corr)
cat("uncorrelated data standard deviation:", sd(storage.uncorr)
cat("correlated data standard deviation:", sd(storage.corr))

######
###### You saw it happen once, but was it a fluke?
###### We should repeat the whole shebang (repeat the repititions) and find out...
######

# create a storage vector for the results of each shebang
# keeping track of whether/not the uncorrelated data set wins (has lower sd)
# each time...
uncorr.wins <- c()

# now we run the whole shebang each time...
for(k in 1:100)
{
  if(k %% 10 == 0) {cat(k, "% -- ", sep = "")}
  
  storage.corr <- c()
  storage.uncorr <- c()
  
  # run 1000 experiments (simulated trials)
  # we will draw data from a standard normal distribution 
  # to keep things as simple as possible
  
  for(i in 1:1000)
  {
    storage.corr[i] <- mean(corr.lever())
  }
  
  for(i in 1:1000)
  {
    storage.uncorr[i] <- mean(uncorr.lever())
  }
  
  uncorr.wins[k] <- sd(storage.uncorr) < sd(storage.corr)
  
}

# to see if uncorr data produces lower error (i.e., if uncorr wins)...
print(uncorr.wins)