Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
From the literature, we can assume that, prior to the intervention, approximately 50% of children in our context will consume at least one portion of fruit and vegetables in the school canteen (one out of two children). For the power analysis, we consider the following parameters: a Type I error rate α = 0.05, a power of 1 - β = 0.8, and a moderate effect size of 0.3. Consumption will be recorded twice a week for three weeks in each school, resulting in six observations per child during each phase. Data collection will follow a timeline based on four phases: baseline (before the intervention), during the intervention, post-intervention, and three months after the intervention — leading to a total of (maximum) 6 × 4 = 24 observations per child.
Expecting a 0.4 variation rate, with the above-mentioned parameters, 93 pupils are needed in each group.
Having multiple observations per child helps to mitigate potential absences during data collection. Hence, we plan for a sample size of 100 children per group, which allows for potential attrition over time, resulting in a total sample of 500 pupils.