# Optimal Sample Size/Power Analysis for Panel Data

I'm running a economic experiment. From a previous pilot I already know which size of treatment-effect I can expect. Each participant plays 20 rounds, so it't a repeated measures approach. I want to know the minimum number of participants i will need to get the same results (same effect size at 5% significance level) as in the pilot.

I already tried to use this formula to determine the sample size, based on $$\alpha=0.05$$, $$\beta=0.20$$ and an effect magnitude of $$\frac{1}{10}$$ of a sd :

$$n_o=2(1,96+0,84)^2(10)^2=1568$$

However this treats each observation as independent, which they are not due to the panel structure. I do multiple regressions, using both fixed-effects and tobit models. Is there an easy way to get the optimal sample size? I'm thinking about simulating the data, but getting the within subject correlation right might be tricky.

• If you want to "get the same results as in the pilot.", then recruit the same number of participants as in the pilot. – user158565 Oct 18 '18 at 21:08