Simulation showing how the same difference in means can lead to arbitrary Cohen's d

sim_cohen.R

library(ggplot2)
library(effsize)

set.seed(156226)
N <- 50
groups <- rep(c("A","B"), each = N)
means <-  rep(c(20,18), each = N)
noise <- rnorm(2*N, 0, 1)
noise <- noise - mean(noise)
df1 <- data.frame(group = groups, y = means + noise * 0.001)
df1$cohend <- round(cohen.d(y ~ group, df1)$estimate)
df2 <- data.frame(group = groups, y = means + noise)
df2$cohend <- round(cohen.d(y ~ group, df2)$estimate, 2)
df3 <- data.frame(group = groups, y = means + noise * 8)
df3$cohend <- round(cohen.d(y ~ group, df3)$estimate, 2)

ggplot(rbind(df1, df2, df3),
       aes(x = group, y = y)) + 
     stat_summary(geom = "line", group = 1) +
  geom_point(position = position_jitter(width = 0.2), alpha = 0.4) +
  facet_wrap(~cohend, labeller = "label_both") + theme_minimal()