Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The study uses a blocked randomized design with randomization within the 2 × 2 programme/track blocks in each two waves: Economics and Econometrics, each split into Dutch-language and international tracks. We assume a two-sided test with a 5 percent significance level, 80 percent power, individual-level randomization, no clustering, and equal treatment-control allocation.
The calculation assumes 8 blocks across the two waves, an average block size of 350 students, and approximately 2,800 students in total, with about 1,400 students assigned to treatment and 1,400 to control. We use a conservative specification with no additional level-1 covariates and no assumed variance explained by blocks or covariates. Under these assumptions, the minimum detectable effect size for continuous main outcomes is approximately 0.11 standard deviations. For course grades measured on a 1–10 scale, this corresponds to about 0.16 grade points, assuming a standard deviation of 1.5 grade points.
For binary persistence outcomes, the minimum detectable effect depends on the baseline rate. With this planned sample size, the study can detect effects of approximately 4.6 percentage points for an outcome with a 25 percent baseline rate, 5.3 percentage points for a 50 percent baseline rate, and 4.6 percentage points for a 75 percent baseline rate. The actual MDE may be slightly smaller when including block fixed effects and baseline covariates in the analysis.