Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The study is designed as a cluster-randomized experiment at the school level. We plan to recruit approximately 74 schools with an average of 30 students per school (around 2,200 student observations in total). We consider two primary outcomes: (i) a standardized outcome and (ii) a binary indicator for which we assume a control-group mean of approximately 0.8.
Schools are assigned to treatment and control using pairwise randomization at the cluster level. We assume a two-sided significance level of 5 percent, 80 percent power, intra-cluster correlation of 5 percent, and the inclusion of pair fixed effects and individual-level covariates that explain 30 percent of the between-school residual variance and 30 percent of the within-school variance. The minimum detectable effect size is around 0.156 standard deviations for the standardized outcome and 6.2 percentage points for the binary outcome.