Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculations were performed for a stratified randomized design (individual randomization blocked by school) using the 'Within' estimator (School Fixed Effects) at a 5% significance level with 80% power.
Primary Scenario (Target): With a planned sample of 800 students (approx. 40 schools), and assuming that the inclusion of baseline covariates and school fixed effects yields an effective R-squared of 0.30, the design has 80% power to detect a Minimum Detectable Effect (MDE) of 0.235 standard deviations in the primary outcome.
Sensitivity Analysis:
We recognize that power depends on recruitment success. We estimated the sample size required to detect a small effect size of 0.179 SD.
- Cluster Design (Conservative): If we were forced to randomize at the school level (ICC=0.05), detecting 0.179 SD would require 1,569 students (79 schools).
- Optimistic Scenario (Higher Enrollment): If recruitment exceeds expectations and reaches 920 students across 46 schools, then:
The MDE improves to 0.179 SD under the planned stratified individual-randomization design. This represents the best-case scenario given our design and assumptions.
All power calculations were conducted using standard formulas for clustered and stratified experimental designs (Bloom 2005; McKenzie 2012), incorporating the variance reduction from covariate adjustment and fixed effects.