Under the weather this week, but I wanted to post this excellent graph from Twitter, showing what different Cohen’s d effect sizes mean in practice for populations:

I love this because despite the efforts of many many people, every time you see some sort of “group x is different from group y” type assertion, you still see people claiming that this either:

1. Can’t be true because they know someone in group y who is more like group x or
2. This  is completely true and every from group x is superior to every member of group y

Both are mistakes. For a more detailed look, there’s a visualization tool here that shows what these translate in to for random superiority. In other words, if you pick one person from each group randomly, what is the chance that the one from the higher group will actually have an outcome above the other person?

• For d=.2, it’s 55.6%
• For d=.5, it’s 63.8%
• For d=.8, it’s 71.4%
• For d=2, it’s 92.1%

This is good to keep in mind, as Cohen’s d is not an overly intuitive statistic for most people. Visualizations are good to help see quickly what these differences might mean on the population level.

Not the most groundbreaking point, but one that seems to bear repeating!