Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculations for the school design are based on five measures: household food security (FIES, mean 4.65 and standard deviation 2.21), weight-for-age z-scores (mean –1.12 and standard deviation 2.16), height-for-age z-scores (mean -1.11 and standard deviation 2.31), reading ability ICW index (mean –0.12 and standard deviation 0.28) and math ability ICW index (mean 0.00 and standard deviation 0.96). Data for household food security comes from a household survey targeted at capturing FIES in Madagascar in 2021 by FAO. Weight-for-age, height-for-age, and reading and math ability come from the MICS6 dataset conducted in Madagascar in 2018 by UNICEF.
Assuming 100 schools per treatment arm and 10 children per school, two follow-up observations, a correlation of 0.2 between follow-up measurements, an intra-cluster correlation of 0.2, and power of the test of 80%, yields a minimum detectable effect (MDE) of 0.16 standard deviations for food security and height-for-age, 0.17 standard deviations for weight-for-age and math ability, and 0.18 standard deviations for reading ability. With three follow-up measurements, the study would be powered to detect an effect of 0.14 standard deviations for food security, weight-for-age, and reading ability and 0.15 standard deviations for height-for-age and math ability.
In conclusion, the experiment is likely to be powered to detect impacts on food security, reading and math ability, and anthropometrics with at least three follow-up rounds of data collection at the child level.