Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Our total baseline sample size is 50 households across 150 villages, or 7,500 participant households. To determine the required sample size, we use the 2021 Burkina Faso Demographic and Health Survey, focusing on the central-northern region. We run power analysis for each of the child marriage and FGM target groups separately, assuming a significance level of 5% (two-tailed) and statistical power of 80%. Further, we use 40 communities per study arm for calculations, to absorb risk of dropping up to 10 communities per arm due to conflict-related intervention disruption or inaccessibility. With randomization at the community level and assuming attrition of 45% at the household level (approximately 30% per year), to accommodate both mobility of host populations, as well as internally displaced households. Power analysis suggests that to detect a 12 percentage points (pp) decrease in the prevalence of child marriage, we need to survey 2,040 households (17 x 120 = 2,040 each with an unmarried adolescent girl aged 12 – 17). Further, to detect a 5 pp reduction in the prevalence of FGM, we need to survey 2,880 households (24 x 120 = 2,880 with at least one girl aged 0-4 years). This implies an unadjusted sample size of 4,920 (2,040 + 2,880). However, due to the estimated overlap in households falling into both target categories, the total sample size can be reduced by a factor of 0.84 (=1-0.16), resulting in a total required sample size of 4,133. Finally, taking into account attrition, this figure increases to ~6,000 households (or 50 households per village). We do not consider take-up in our calculations, as the community engagement treatment is designed to change outcomes on average in the community. Thus, we consider that all households living in communities with intervention activities will be reached at some level. Finally considering the additional 10 communities per arm, our total sample size requirement is approximately 50 households per community x 150 = 7,500 at baseline.