Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Based on data from previous trials conducted by the research team in El Salvador, the raw intra-cluster correlation for students within the same school is 0.3. However, after controlling for baseline covariates (sex, age, baseline score, grade and randomization strata) the intra-cluster correlation lowers to 0.21.
Based on administrative data from the schools, there are roughly 130 students in grades 1--6. However, since we will focus on students from grades 2--5, and we won't conduct tests with every student in Grades 2 and 3, but rather a sample of 10 students in each grade, we assume we will have data from 70 students per schools: 10 from grade 2, 10 from grade 3, 25 from grade 4 and 25 from grade 5. We will track these students until the end of the 2026 academic year (when they are in grades 3--6). We assume there is a 10% attrition between the baseline and the endline, and so that we will have data from 63 students at the endline.
We assume (conservatively) that the baseline covariates (e.g., the baseline test score, age, and gender) explain 40% the variance. This calculation is based on data from a previous trial ran by the research team in El Salvador.
The current design assumes there are 100 schools in the full treatment arm, 50 in the targeted instruction arm and 100 control schools. Therefore, we can detect an effect size of at least (MDE) 0.177SD with power 80% using a 5% test of level when comparing the targeted instruction treatment against the control or when comparing the two treatments against each other. The MDE when comparing the full EIP package against the control is 0.145SD.