This interactive visualisation is a great way of explaining or visualising what a given Cohen’s d effect size actually means in the real world.

Enter the d in question, or by clicking the cogwheel you can enter means and standard deviations, and the slightly-arcane-seeming resulting ’d' value is translated into an explanation rather easier to get one’s head around.

For example:

With a Cohen’s d of 0.80, 78.8% of the “treatment” group will be above the mean of the “control” group (Cohen’s U3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the “treatment” group will have a higher score than a person picked at random from the “control” group (probability of superiority).

Moreover, in order to have one more favorable outcome in the “treatment” group compared to the “control” group, we need to treat 3.5 people on average. This means that if there are 100 people in each group, and we assume that 20 people have favorable outcomes in the “control” group, then 20 + 28.3 people in the “treatment” group will have favorable outcomes.