Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
- Unit: The unit of randomization and analysis is the individual faculty member. Because the intervention is assigned at the individual level, there is no clustering in the experimental design (design effect = 1).
- Standard Deviation: The expected baseline mean for the share of low-SES students nominated is 0.25 (25%), which corresponds to an expected baseline standard deviation of 0.433 (calculated as the standard deviation of a proportion: $\sqrt{0.25 \times 0.75}$).
- Percentage: Assuming a balanced total sample size of 350 faculty members (175 per arm), 80% statistical power, and a 5% significance level for a two-sided test, the minimum detectable effect size (MDES) is approximately 0.30 standard deviations. Translated into absolute percentage points (accounting for the variance of two independent proportions), the study is adequately powered to detect an absolute difference of 13.8 percentage points between the control and treatment conditions. This means the study can reliably detect an increase in the share of low-SES students nominated from the expected baseline of 25.0% in the control group to 38.8% in the treatment group.