Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculations assume 150 schools per arm, 80 percent power, a two-sided 5 percent significance level, an intraclass correlation of 0.20, a coefficient of variation in cluster size of 0.50, and equal allocation across three arms. For the independently administered baseline and endline assessments, approximately 27 students will be assessed per school. The corresponding minimum detectable effect size is approximately 0.16 standard deviations without precision gains from baseline data, 0.15 standard deviations if baseline covariates explain 5 percent of outcome variation, and 0.15 standard deviations if they explain 15 percent. For the common platform-based assessments administered to approximately 75 students per school in the two treatment arms, the minimum detectable effect size is approximately 0.15 standard deviations without baseline precision gains, 0.15 standard deviations with 5 percent baseline explanatory power, and 0.14 standard deviations with 15 percent baseline explanatory power. Thus, the study is designed to detect pairwise effects of approximately 0.14–0.16 standard deviations, depending on the outcome sample and the predictive power of baseline data. These calculations apply to unadjusted pairwise comparisons and will be updated using realized cluster sizes, outcome availability, and baseline explanatory power.