Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Utilizing the Optimal Design Software, we conduct a power calculation to determine the optimal sample size needed for this study. Since we lack pre-intervention data on variables of the students, we are unable to estimate the expected effect size of the intervention precisely. As such, we are conservative in our estimates and hypothesize a low to medium effect size (0.15 - 0.2) in our power calculations, assuming to a modest improvement in student outcomes due to the interventions. Such an effect size is commonly observed in low-cost educational research (Kraft, 2020). Given that the students belong to similar socio-economic backgrounds and come from the same locality, we expect a moderate intra-cluster correlation coefficient (0.25), suggesting sizeable similarity among students within each school. This similarity implies a larger sample size to achieve the desired statistical power.
Given the sample size of 6,000 from 500 clusters and expected values for relevant parameters, our study will achieve more than 85% power in detecting an effect of 0.15 to 0.2.