Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The planned sample size was determined using a conservative power analysis approach with no underlying specifying assumptions. Drawing on the existing literature, the results indicate that a sample size of approximately 2,097 (≈ 699 per treatment arm) is required to detect a treatment effect of 15% of 1 standard deviation at the 5% significance level with 80% power. However, based on empirical estimates from a pilot study (n = 122), a sample size of 1,269 (≈ 423 per treatment arm) would achieve the same 80% power to detect an MDE of 0.15 standard effect at the 5% significance level. In accordance with this, the project will aim to recruit at least 1,300 students and if feasible, up to 2,100 students to ensure that the study is not underpowered.