Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Our simulations, based on 1,000 Monte Carlo replications for each outcome, show that with 3,200 respondents, the design achieves approximately 80% empirical power to detect effects ranging from 0.08 to 0.11 in probability units, depending on the outcome. Specifically, the estimated empirical power and corresponding minimum detectable effects (MDE) are as follows: 0.795 power for High-value Bet (0.085), 0.790 power for High-value Business (0.105), 0.811 power for Low-value Bet (0.084), and 0.786 power for Low-value Business (0.112). These MDEs correspond to effects between 8 and 11 percentage points, which represent realistic magnitudes for behavioral responses in survey experiments of this type.