Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Based on the overall sample of 1,400 children in each arm, and assuming 15% attrition, the MDE is 0.133 SD at 90% power and 0.115 SD at 80% for comparing any two groups. Estimating proportions, as a number of behavior level outcomes are likely to be binary variables, this sample size is able to capture 6.6 percentage point (pp) changes from a 50% level at 90% power. These power calculations are for intention to treat (ITT) effects by assuming 100% take-up. However, based on the ongoing pilot, we anticipate take-up rates of around 80%, and achieving the 6.6pp difference in ITT would require a real change of 8.3pp. However, the study will also look at the impact by sub-group (e.g. sex of the child). If we take half of the sample for this sub-group analysis, the MDEs are 0.188 SD or 9.4 pp at 90% power (compared to 0.133 SD and 6.6 pp for full sample). (These estimates do not account for repeated survey measures. MDE should be a bit smaller if we consider those).