Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Exact power calculations given our empirical strategy are complicated. While our treatment indicator is assigned at the respondent level, the experimental variation varies at the respondent-firm level. We also are using an instrumental variables estimation approach that includes pre- and post-intervention measurement and additional control variables. To gain some understanding of power, we will compute the required sample size to detect a 0.15 SD effect under pure, individual randomization and assume a design effect of 4. At α = .05, β = .80, we need about 700 respondent-firm pairs in each of the four treatment-control groups (placebo, political, environmental, and diversity) or 2,800 total respondent firm-pairs under pure randomization. Scaling 2,800 by the design effect of 4, this gives a requirement of 11,200 respondent-firm pairs. Since our survey provides 5 firms for each respondent, this leads to a required sample size of 2,240 respondents. Given our 2,500 respondents, we can detect a minimum effect size between 0.14 and 0.15 standard deviations.