Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculations assume 18 communities allocated equally across three arms, with 6 communities per arm, approximately 50 completed endline observations per standard community, 80% power, and a 5% two-sided significance level. Because the intra-community correlation and baseline outcome prevalence are not yet known, sensitivity analyses are reported across ICC values of 0.05, 0.10, 0.15 and 0.20 and baseline binary-outcome prevalences of 10%, 15%, 20% and 25%.
Under the central planning scenario of 15% baseline prevalence and ICC = 0.10, the minimum detectable effect for a pairwise treatment-control comparison on a binary budgeting outcome is approximately 21.7 percentage points at the 5% two-sided level. Using a conservative 2.5% two-sided threshold for the two planned treatment-control comparisons, the corresponding MDE is approximately 24.6 percentage points.
For the continuous financial-planning behaviour index, under ICC = 0.10, the pairwise MDE is approximately 0.61 standard deviations without baseline precision gains. If baseline outcomes and pre-specified covariates explain 25% of endline variation, the MDE falls to approximately 0.53 standard deviations.
These are analytical planning calculations. Final power calculations will be updated using observed baseline prevalence, observed outcome variance, observed intra-community correlation, achieved sample sizes and the executed randomization.