Demonstrates the chi-square distribution under the null for DFs 1 through 6

chi-square-null.R

# Demonstration of chi-square distribution from chi-square tests under the null
# By Nick Brown, February 2022.
# Licence: CC-0

set.seed(2)

df.range <- 1:6      # range of DFs for which to generate plots
loops <- 10000       # number of cases to generate (more gives better precision)
N <- 5000            # range of numbers in tables

cst <- vector(mode="list", length=length(df.range))
sizes <- (df.range * 2) + 2

for (s in sizes) {
  df <- (s / 2) - 1
  cst[[df]] <- rep(NA, loops)
  for (l in 1:loops) {
    res <- matrix(as.integer(runif(s) * N), ncol=2)
    cst[[df]][l] <- chisq.test(res)$statistic
  }
}

for (cs in 1:length(cst)) {
  hist(cst[[cs]]
      , main=paste0("Chi-square distribution, DF=", cs)
      , xlab=paste0("Chi-square statistic with N=", N)
  )
}