# When testing for a difference between effect sizes, is test power affected by their respective magnitude?

When comparing two effect sizes with a statistical test, does it matter for the test's power whether these effect sizes themselves are large or small?

Imagine you are planning an experiment in which you compute an effect (difference between two conditions) for two groups (A,B). You want to show that the effect is larger in one group than the other, i.e. your hypothesis is effect(A) > effect(B). Assuming that the difference between the groups is equivalent to Cohen's D = 0.5, what is the required sample size to reach a power of 0.8?

In hypothetical experiment I the effect sizes in both groups are 1 and 1.5, the difference between them is 0.5.

In hypothetical expeirment II the effect sizes in both groups are 0.1 and 0.6. Again, the difference is 0.5.

Although the difference between the two groups is the same in both experiments, I would assume that experiment II requires a larger sample size. After all, the effects are located on a much smaller scale than in experiment 1. I have been told an a priori power analysis needs to take this into account (the magnitude of the effects that are being compared), but I do not really know how, and it's hard to find answers to this very specific problem on the web.

How can I take this into account in my a priori power analysis? I'm using G*Power and unfortunately, I can't simply answer this by simulating data (have to use a validated method).

• Forgot to mention - for the sake of a priori power analysis, both groups would have the same variance and N; it's just their means that are different, and thus they show different effect sizes for a manipulation. – Chris Sep 10 '14 at 10:37