Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Baseline (4th grade) tests can explain about 75% of the variation in the outcome scores (5th grade, and 6th grade tests). The standard deviation of the residual scores (the unexplained variation in the outcome) is about 6.5 score points (i.e. about 0.6 population standard deviations). Based on this (and the sample sizes in treatment and control group) we estimate that the standard error for the estimated treatment effect will be 1.25 score points. The MDE (power: 80%, alpha: 5%) is then 2.8*1.25=3.5 score points, or 0.30 population level standard deviations. Our previous research on a comparable intervention in the Netherlands (but with a bigger sample size) yielded a point estimate of 3.3 score points (or about 0.28 population standard deviations). The present intervention however is more intensive (5 instead of 4 days a week, and in addition to regular math classes (rather than partly replacing regular math classes), for example).