Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We focus on the primary outcomes measured in year 2 of our intervention. For health utilization, the standardized MDE for receiving health care among all individuals is 0.15 standard deviation (SD), with a 94% power, corresponding to a 6.7 percentage point (pp) increase in health care receipt. For individuals aged 5–17 and 18–60, the MDEs are also 0.15 SD with power levels of 90% and 85%, respectively, corresponding to a 6.2 pp and 6.5 pp increase in health care receipt. Regarding health outcomes, the MDE for days sick across all individuals is 0.15 SD with 99% power, equating to a 0.74-day reduction in days sick. For school-aged children (5–17), the MDE is 0.15 SD with 95% power, corresponding to a 0.52-day reduction, while for individuals aged 18–60, it is 0.15 SD with 95% power, translating to a 0.75-day reduction. In terms of schooling outcomes, the MDE for days of school missed among children aged 5–17 is 0.11 SD with 83% power, representing a 0.22-day reduction in school absences. For labor market outcomes, the MDE for the likelihood of currently working for pay among individuals aged 18–60 is 0.14 with 81% power, corresponding to a 5.7 pp increase. Additionally, the MDE for days of usual work activity missed among all individuals is 0.07 SD with 87% power, reflecting a 0.24-day reduction. These results indicate the study's strong ability to detect meaningful changes across a range of outcomes, with standardized MDEs ranging from 0.07 to 0.15 SD and high statistical power (≥80%) across all measures.
Throughout the power analysis, we assume 20% random attrition rates per year. We also include allowance for the increase in precision due to the inclusion of covariates as follows: 13% increase in R-2 from individual covariates; 8% increase in R-2 from village-level covariates; an increase in R-2 of 27% from HF covariates. These parameters are based upon regression estimates using covariates correlated with days sick and days of usual activity missed due to sickness. We use empirical ICCs at various levels taken from either the 2019-2020 UNPS or 2016 Uganda DHS.