Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Based on the baseline test, we assume that ρ =.145. We assume (conservatively) that the baseline covariates (e.g., the baseline test score, age, and gender) explain 30% the variance, and thus that σ = 0.84 ≈√1 − 0.3. Finally, taking into account attrition at the student level, we assume n =24.
Therefore, we can detect an effect size of at least (MDE) 0.21σ with power 90% (β) using a 5% test of level (α) when comparing any of the treatments to the control. When comparing any two treatment groups, we have an MDE of 0.23σ