Inference
Understanding effect sizes
12 min
Learning goals
- •You can convert between d, r, g, OR, and CLES and know their limits.
- •You can intuitively interpret the overlap coefficient and P(X > Y).
- •You can place Cohen's labels next to the empirical benchmarks from psychology.
Overlap coefficient (OVL)
80.3 %
Share of area both densities have in common. At d = 0, OVL is 100 %.
P(X > Y) — common language ES
63.8 %
Probability that a random person from group B is higher than a random person from group A (McGraw & Wong 1992)
Cohen's U₃
69.1 %
Percentage of group B that lies above the median of group A.
Cohen's U₁
33.0 %
Share of the combined population that belongs to only one of the two groups (outside the overlap).
Number Needed to Treat (NNT)
5.2
How many people must one treat to gain one additional case above the control median? (Kraemer & Kupfer 2006)
How to read this: At an effect of d = 0.50, the two distributions overlap by 80 %. If you randomly draw one person from each group, the person from group B is higher with a probability of 64 %. This is a medium difference — visible, but the distributions still overlap noticeably.