Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Considering an ICC of 0.07, approximately 368 schools, and around 108 students per school in treatment-eligible classes (about 32 high-achieving students per school), the minimum detectable effect (MDE) for the gender interaction among high achievers is 7.5 percentage points, corresponding to approximately 0.16 standard deviations, assuming mean recommendation rates of 55% for high-achieving boys and 34% for high-achieving girls. The MDE for the average treatment effect on all students in treatment-eligible classes is around 4.5 percentage points, or 0.12 standard deviations. We expect to achieve higher power once we control for teacher characteristics (from surveys) and rich baseline information on students (from INVALSI administrative and survey data).