Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
To determine the minimum detectable effect size (MDES) accounting for the cluster randomized design, we performed power calculations based on results from our preliminary network simulations. The unit of randomization is the village, and the primary outcome is the number of adopting households per village.
Based on the simulation, the baseline adoption level under the extension officer's selection (benchmark) is estimated at 2.2 households per village. The expected adoption levels for the treatment arms are 10.4 households (Network theory-based), 2.9 households (Chairman’s informant), and 2.9 households (Gossipers) per village.
Assuming a standard deviation of 5.5 households derived from the Network group simulation and accounting for the cluster design (e.g., intra-cluster correlation), a sample size of 10 villages per arm (40 villages in total) was determined to be sufficient. This design provides >80% power to detect the expected difference of 8.2 households per village (between the Benchmark and the Network theory-based method) at a 5% significance level. The smaller differences observed in other treatments (e.g., Chairman’s informant) will be examined exploratorily.