An interesting phenomenon with (perhaps extreme?) data in PET-PEESE

Effect-size-D.R

set.seed(1)

# Number of datasets to generate.
iter <- 1000

# Generate random sample sizes.
# Initially I only put the Nmin parameter there to avoid silly sizes like 0 or 1,
#  but then I found that something interesting happens.
# Try setting Nmean to 10 instead of 50, so that all sample sizes are 20, and watch
#  what happens to the correlation between d and its SE.
# For extra impact of this, try setting n2 equal to n1 (uncomment the line below).
Nmean <- 50
Nmin <- 20
n1 <- pmax(floor(runif(iter) * 2 * Nmean), Nmin)
n2 <- floor(n1 * (0.9 + (runif(iter) * 0.3)))     # add a bit of variation
#n2 <- n1

# Generate random effect sizes.
d <- runif(iter) * 0.4 + 0.2    # range 0.2-0.6; put a # before the * to have a range from 0 to 1

# Compute SE of Cohen's d.
# Formula from http://willgervais.com/blog/2015/6/25/putting-pet-peese-to-the-test-1
t1a <- (n1 + n2) / (n1 * n2)
t1b <- (d ^ 2) / (2 * (n1 + n2 - 2))
t2 <- (n1 + n2) / (n1 + n2 - 2)
t2 <- 1
se <- sqrt((t1a + t1b) * t2)

# Run the PET regression. It's interesting to plot() this.
wls <- lm(d ~ se, weights=(1 / se^2))

# Compute relative effect of the d term in that formula.
d_term <- t1b / t1a

# Report.
cat("Mean (SD) N1: ", mean(n1), " (", sd(n1), ")   Mean N2: ", mean(n2), " (", sd(n2), ")",
    "\nMean (SD) d: ", mean(d), " (", sd(d), ")   Mean (SD) SE:", mean(se), " (", sd(se), ")",
    "\nMean (SD) fractional effect of d term: ", mean(d_term), " (", sd(d_term), ")",
    "\nCorrelation between d and its SE: ", cor(d, se),
    "\n", sep="")