Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
This study proposes to have 1200 at-risk youth between the ages of 16 and 21 to be randomly allocated into one of three groups (T0, T1, T2). With 80 percent of statistical power and an alpha of 0.05, we could capture a minimum detectable effect of 0.2 of a standard deviation (as standard in randomized experiments) with 394 individuals per group. We therefore decide to have 400 individuals in each comparison group, which provides a power of 81 percent (alpha = 0.05). With cross-randomization, statistical testing could extend to 5 groups (T0, T1, T2 and cross-randomization within T1 and T2). This is in addition to test cross-randomized groups, for which previous calculations also apply. In this case, we would have 240 individuals in each comparison group. With 80 percent of statistical power and an alpha of 0.05, this allows capturing a minimum detectable effect of 0.26 of a standard deviation.