Here's a fairly simple conundrum: let's say I'm calculating the sample size needed to determine a correlation of r = 0.7 at 95% power and an alpha (two-tailed) of .05. The null is r = 0 (note I use r throughout to denote a correlation coefficient).
G*Power suggests that I need 20 participants.
Now, if I increase the null to r = 0.5, I need 131. This makes sense as there's a smaller difference between the alternative and null values.
However, if I now change the alternative hypothesis to r = 0.9 (and keep the null at r = 0.5), I need 18 participants to demonstrate the effect. Why would one require less participants to find a stronger effect (and practically speaking, you'd need to have very clean data to find a correlation of 0.9)? Surely you'd need more?