When we vary the strength of the IV (as measured by R2), holding the effect size constant at 0.2, we observe that as R2 decreases, power approaches its maximum more slowly as nX increases (Figure 2). Thus, the value of nX needed to obtain more than 90% of the maximum power is higher when the first-stage R2 is low. In the scenarios simulated here, to achieve greater than 90% power, nX needed to be approximately 2,000 (20% of nY), 3,500 (35%), 5,000 (50%), and 7,500 (75%) for first-stage R2 values of 0.015, 0.01, 0.007, and 0.004, respectively. Using a 2-sample IV approach, results were very similar (Web Figure 2), with slightly lower power for most scenarios compared with the subsample IV approach.
