random-correlation.R

# Simple demonstration of mean absolute correlation with random data.
# By Nick Brown, February 2020. License: CC-0.

library(ggplot2)

set.seed(1)
iter <- 1000

# Create data frame to contain correlation results, excluding CI (which is a list)
ct.names <- names(cor.test(1:3, 3:1))    # little hack: correlation is perfect, so no CI
cors <- data.frame(matrix(ncol=length(ct.names), nrow=iter))
names(cors) <- ct.names

cat("Sample size\tN significant\tMean r\t\tMean absolute r\n")
for (n in c(10, 30, 100, 300, 1000, 3000, 10000)) {
  max.abs.r <- 0
  total.r <- 0
  total.abs.r <- 0

  for (i in 1:iter) {
    s1 <- rnorm(n, 0, 1)
    s2 <- rnorm(n, 0, 1)
    ct <- cor.test(s1, s2)

    cors[i,] <- ct[1:ncol(cors)]
    r <- ct$estimate
    abs.r <- abs(r)

    total.r <- total.r + r
    total.abs.r <- total.abs.r + abs(r)
    if (abs(r) > max.abs.r) {
      max.abs.r <- abs(r)
      if (n <= 30) {
        max.plot.r <- r
        max.data <- data.frame(s1, s2)
      }
    }
  }

  n.sig <- nrow(cors[(cors$p.value < 0.05),])
  mean.r <- total.r / iter
  mean.abs.r <- total.abs.r / iter
  cat(sprintf("%d", n), "\t\t", n.sig, "\t\t", sprintf("%.3f", mean.r), "\t\t", sprintf("%.3f", mean.abs.r), "\n", sep="")
}

ggplot(max.data, aes(x=s1, y=s2)) +
  geom_point(colour="red") +
  geom_smooth(method="lm", formula=y~x, se=FALSE) +
  annotate(geom="label", label=sprintf("r=%.3f", max.plot.r), x=1.5, y=1.5, fill="white") +
  labs(x="Sample 1", y="Sample 2")