Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The study will recruit 6,000 caregiver–adolescent pairs (2,000 per stratum: Venezuelan migrants, internally displaced persons, and non-displaced Colombians) and randomize them across three main experimental arms. With a two-tailed test at $\alpha$ = 0.05, this sample provides high statistical power to detect modest but policy-relevant changes in caregiver and adolescent outcomes.
Under standard assumptions of individual randomization with balanced allocation, no clustering, and covariate adjustment, the minimum detectable effect (MDE) for pooled treatment versus control contrasts is approximately 0.09 standard deviations with 80\% power. For pairwise comparisons between treatment arms (e.g., caregiver-only vs. caregiver+adolescent, needs-based vs. full content), the MDE increases slightly to 0.11–0.12 SD, reflecting reduced effective sample size. Subgroup analyses stratified by displacement status (2,000 pairs per stratum) yield MDEs of approximately 0.16–0.18 SD, which remain within the range of meaningful effects documented in the parenting and mental health literature.
These calculations assume 10\% attrition between baseline and endline, consistent with prior survey experience in displaced and low-income populations in Colombia. If attrition is lower, detectable effects will be correspondingly smaller. The study also benefits from repeated measurement of several outcomes at baseline and endline, which further increases power by allowing for precision gains from covariate adjustment.
Taken together, the sample size is sufficient to detect effect sizes comparable to those found in meta-analyses of parenting interventions in fragile and low-resource settings (0.2–0.5 SD), ensuring that even conservative estimates of program impacts will be detectable with high confidence.