Randomization was conducted in two stages: at the neighborhood and at the household level. The randomization design ensured a close to even split of the households in the sample among three groups: early treatment, late treatment, and control. All control households will be offered the treatment after the end of the study.
First, the neighborhoods in the sample were split into a saturation design group and a non-saturation design group based on neighborhood population estimates. Those with a current population from 50 to 200 households were assigned to the saturation design group. Those with a current population below 50 households or above 200 households were assigned to the non-saturation design group. As explained below, it was felt that the saturation design would not work well in either low population or high population neighborhoods.
The non-saturation design group of neighborhoods was randomly split into two schemes: non-saturation scheme 1 and non-saturation scheme 2. In a second stage of randomization, 67% of households in each non-saturation scheme 1 neighborhood were assigned to early treatment and 33% to late treatment. 33% of households in non-saturation scheme 2 neighborhoods were assigned to late treatment and 67% to control.
The saturation design group of neighborhoods was split into six schemes in the first stage of randomization. In saturation scheme 1 neighborhoods, all households were assigned to early treatment. In saturation scheme 6 neighborhoods, all households were assigned to control. In the second stage of randomization, 80% of households in each saturation scheme 2 neighborhood were assigned to early treatment and 20% to late treatment, 20% of households in each saturation scheme 3 neighborhood were assigned to early treatment and 80% to late treatment, 80% of households in each saturation scheme 4 neighborhood were assigned to late treatment and 20% of control, and 20% of households in each saturation scheme 5 neighborhood were assigned to late treatment and 80% to control.
This decision to split neighborhoods into a saturation design group and a non-saturation design group was made based on estimated neighborhood eligibility rates, which we defined as the number of households in the sample from a given neighborhood over the estimated number of households living in that neighborhood. For us to gain insights into how our saturation design interacts with the community effects of the program, we need there to be a correlation between the variation in our imposed saturation rates in the sample and the saturation rates of the program in the population. Our concern was that high variation in eligibility rates across neighborhoods might have led to a breakdown of this correlation. That is, two neighborhoods with the same sample saturation rate but widely different eligibility rates will have two widely different population saturation rates, meaning our sample saturation rates would not be a good proxy of population saturation rates.
Therefore, we excluded neighborhoods with a small population from the saturation design since eligibility rates in those neighborhoods were much higher than average. Similarly, we excluded neighborhoods with a large population from the saturation design since eligibility rates in those neighborhoods were much lower than average. We did select neighborhoods with their current population within an interval around the mean to take part in the saturation design group since it is in those neighborhoods where the eligibility rates were restricted to a certain range.
When determining the different neighborhood schemes, our criteria were: ensuring a close to even split of the households in the total sample among the three treatment groups, having variation in the saturation rates, and having no neighborhood with some households assigned to the early treatment group and some households assigned to the control group. This third criterion was established to avoid potential political issues that may have arisen due to the large time difference at which different households in the same community would have been offered the program had we not prevented this kind of assignment.