Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We use data from a recent village clustered RCT that we did with Indian rice farmers (Emerick et al., 2016). The plot-level crop yield is 2,817 kg per ha with a standard deviation of 1,354. The intra-cluster correlation (ICC) is 0.3449. This is high for the average cluster RCT, but not for agricultural outcomes which tend to be more correlated within villages. For this reason, our RCT uses 150 villages, rather than a smaller number of villages with more farmers per village.
The strata fixed effects and baseline yields explain 17.9 percent of the variation in yield. We assume that we will obtain similar predictive power with our stratification and conditioning on the baseline outcome. Finally, we assume that each farmer will have 1.5 plots in the potential command area of the tank, making 12 observations per village.
Using these parameters, we estimate a MDE of 433 kilograms per hectare on the pooled treatment effects. This is 0.32 standard deviations or about 15 percent of the mean yield. This seems like reasonable MDE, particularly since irrigation can be transformative. For instance, Jones et al (2021) find that irrigation increases cash profits by about 50% in Rwanda.