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.
Our primary comparison compares the control group pooled with arm 1 against arm 2 (pooling 2A and 2B). For this comparison, at our central sample size estimate of 2000 individuals, with individual-level randomization, and given the baseline probabilities defined above, our minimum detectable effect sizes are:
Baseline 0.2: 5.0 percentage points
Baseline 0.1: 3.8 percentage points
Baseline 0.05: 2.7 percentage points
We will also compare each of the individual arms against each other. Power for these comparisons is smaller as we are comparing the 500 students in each arm against each other, as opposed to the 1000 students in each group that result once we pool arms as pre-specified above. For these comparisons, we have power of:
Baseline 0.2: 7.1 percentage points
Baseline 0.1: 5.3 percentage points
Baseline 0.05: 3.9 percentage points
The figure in the attached supporting documents and materials illustrates power under different assumptions about sample size and the baseline outcome level.