Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
For the power calculations (which were conducted using the clustersampsi command in Stata 16), we have 36 clusters per arm and an average of 20 individuals per cluster with a coefficient of variation in the cluster size of 0.27. We calculate minimum detectable effects (MDEs) at the 95% confidence level with 80% power.
First, we estimate the MDE for a binary indicator for grade 10 completion. At baseline, all adolescents are enrolled in school. We assume that that the control group will have a mean of 0.76 at follow-up, based on estimated dropout rates from the 2019 Multiple Indicator Cluster Survey (MICS), and that the intra-cluster correlation (ICC) is 0.07, based on the baseline ICC for aspirations for highest grade. Thus, the MDE in enrollment is 10 percentage points (pp) (0.23 standard deviations (SD)) when comparing either of the two treatment arms to the control group. This indicates that we would be able to detect statistically significant differences in grade 10 completion at the 95% level of confidence with 80% power if the mean in either treatment group is greater than 0.86. This MDE is in line with typical effect sizes in the education literature of between 0.05 and 0.23 SD at the 25th and 75th percentiles, respectively (Evans and Yuan, 2019).
We additionally estimate MDEs between the control group and a single treatment arm for our primary outcome measures of grit, malleability, and growth mindset. We use baseline data to estimate control group mean, SD, and ICC for each outcome.
-- For grit, the MDE is 0.26 SD, assuming a control group mean of 2.73 out of 4 and an ICC of 012.
-- For malleability, the MDE is 0.29 SD, assuming a control group mean of 3.02 out of 4 and an ICC 0.13. For
-- For Growth Mindset, the MDE is 0.27, assuming a control group mean of 2.73 out of 4 and an ICC of 0.19.
These are in line with the expected range of impacts based on earlier work with a Grit Intervention by Alan, Boneva, and Ertac (2019), who find impacts of between 0.29 SD and 0.35 SD for these same outcomes.
The above power calculations are conservative and we are better powered if we compare the whole treatment group of 63 schools to the control group of 36 schools.
Finally, we estimate MDEs between the GM and the GM+GR treatment arms for a measure of four education-related gender attitudes. We use baseline data to estimate a control group mean of 0.760 out of 4 on a gendered attitudes scale and an ICC of 0.14. The MDE is 0.29 SD.