Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Our randomization is at the individual level, so we do not take clusters into account in our power calculations. For inference on outcomes at the individual level, and considering individual-level randomization, assuming power 0.8, significance 0.05, an R-squared of 30% when predicting the outcome with baseline measurements, and an attrition of 20%.
We first discuss testing the effect of participating in high-quality centers. For the following analysis, we consider the comparison between participating in a high-quality center and not participating in one. We consider a one-sided test. Initial pieces of information coming from administrative data show that our compliance will be relatively low, with many families not taking the offer of slots, or not being able to be re-contacted by the ministry. We estimate the difference in take-up of the group offered the high-quality centers compared with the rest of the children to be close to 29%. Then, our assumptions give us a MDE of 0.45.
Then, we study the differences between attending centers and not attending. The assumptions are the same. The test is two-sided this time, as some of the literature shows negative impacts from child care in some population groups. With 1008 children offered treatment, and an average difference in take-up rate of 24%, our assumptions give us a MDE of 0.47.
These calculations are too conservative, given that we also have the waitlist and the distance to the centers as additional instruments, and their help in determining the take-up is not considered in these calculations. We expect them to be very relevant in increasing our statistical power.