Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The effect sizes and standard deviations were obtained from our pilot sessions under treatments T1 and T2. For the primary outcome (the total environmental benefit index of rewarded projects): mean: 4.42 (T1), 3.83 (T2); standard deviation: 0.14 (T1), 0.52 (T2). The statistical power of the planned sample size is 89% (rank-sum test) and 92% (t-test) when testing an effect size of 10% of the mean of T1, using the standard deviations of T1 and T2, respectively, at a two-tailed significance level of 5%. For the secondary outcome (total evaluation fees): mean: 15.42 (T1), 21.25 (T2); standard deviation: 0.52 (T1), 3.93 (T2). The statistical power of the planned sample size is 84% (rank-sum test) and 90% (t-test) when testing an effect size of 20% of the mean of T1, using the standard deviations of T1 and T2, respectively, at a two-tailed significance level of 5%. These powers were simulated in Stata with 1,000 replications as per Campos-Mercade (2024).