Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculations for the initial nudge RCT were conducted using the R simR package. The outcome variable of interest in all calculations is the adoption of improved sweetpotato varieties (a dichotomous variable). The other outcome of interest in this study was the extent of adoption measured by the quantity of vines of ISVs purchased, which is a continuous variable. In most behavioural studies, dichotomous variables generally require larger samples to detect effects than continuous variables, hence we focused only on the binary adoption variable. We used a base rate of adoption of 9%, which implies a standard deviation of approximately 0.29. Estimates were based upon a mixed logit analysis, with households nested in villages. We assumed a correlation of adoption within a village of 0.10. An economically significant result requires an increase in adoption of approximately 20 to 25% points. We also assumed a control and one treatment condition, targeting rejection of the null that the treatment is equivalent to the control. We found that with n=1000 (100 villages, 10 households per village) we would detect an increase in adoption of 20% points with 97% probability and 15% points with 80% probability. In order to cater for potential drop-offs and missouts due to unavailability, we targeted 120 villages (clusters) with about 60 villages implementing the full program, and the balance serving as a control. We surveyed 10 randomly selected households per village to obtain more detailed information on adoption behaviour, including the use of second or third-generation seeds, demographic information, and exposure to the messaging/interventions. This allowed us to estimate the broader impact of the program, and also to examine the populations most affected.
For the trialpack intervention, power analysis allows us to detect, reasonably well, the effect of trialpack with a random sample of 8 households per village. With this sample of 8 households per village in the 120 villages, and maintaining nudge treatment and control and the other parameters above, we will be able to detect a 50% effect with probability 0.73. Going with 8 households per village/cluste results in a total sample size of 960 households, for the second part of this study. As before, the outcome variable of interest is the adoption of ISVs.