Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Our primary outcomes are all binary / probability outcomes, so for power calculations we use the standard formula for the variance of a proportion. The minimum detectable effect size then depends on the baseline probability of the outcome and the sample size in each arm. We have limited information about the baseline probabilities for most primary outcomes, but we expect many to fall between 0.05 and 0.2. Below we present power under baseline probabilities of 0.05, 0.1, and 0.2. We assume assignment of 1500 students to C, 400 to T1, and 100 to T2, as in our central estimate for sample size described above.
For comparisons of arm T1 against C, we have the following MDEs:
Baseline 0.05: 3.4 pp
Baseline 0.1: 4.7 pp
Baseline 0.2: 6.3 pp
For comparisons of arm T2 against C, we have the following MDEs:
Baseline 0.05: 6.3 pp
Baseline 0.1: 8.7 pp
Baseline 0.2: 11.6 pp