Minimum detectable effect size for main outcomes (accounting for sample design and clustering)

The minimum detectable effect size for the CA experiment is 20 percentage points. With a two-sided test, alpha = 0.05, beta = 0.2, starting from 15 % take-up rate, we need 73 observations per treatment cell, which is entirely achievable.
The minimum detectable effect size for the Decision Maker outcomes is also 20 percentage points. However, starting from a rate of 25 %, a one-sided test, alpha = 0.05, beta = 0.2, we need 70 observations per each treatment cell.
Second experiment:
The minimum detectable effect size for the CA experiment is 23 percentage points, starting from 15 %, a onesided test, alpha = 0.05, beta = 0.20, needing 45 observations per each cell.
The minimum detectable effect for the Decision Makers is 27 percentage points. Starting from a rate of 10 %, a one-sided test, alpha = 0.05, beta = 0.2, we need 30 observations per cell.