Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Using a two-level classroom-cluster design with α=0.05 (two-tailed), power=0.80, ICC=0.18, 100 clusters, average cluster size=30, 50/50 allocation, and covariates explaining 45% of within-cluster variance (baseline maths grades) and 35% of between-cluster variance, the MDES is 0.206 SD on the student-level standardised mathematics score