Sample size (or number of clusters) by treatment arms
Subject to budgetary and logistical constraints, we plan to assign 50% of participating students to the active control group, and evenly assign students to each of the four treatment arms, so that 12.5% of students are in each of arms T1a, T1b, T2a and T2b. Given our central estimate of 2000 participating students, this implies that we will have 250 students in each treatment arm and 1000 in the control arm. If we encounter constraints on our budget or the capacity of our mentors, we will reduce assignment to treatment evenly across the four treatment arms.
Students in the control group C will be notionally assigned (for the purpose of constructing placebo outcomes) to one of the four treatment groups in even proportions; under our main plan this will mean notionally assigning them to each of the four groups with 12.5% probability.