Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power was estimated based on the treatment effects of parenting interventions documented in the literature (Emmers et al. 2021) between study arms for the primary and secondary outcomes: 1) caregiver-level parenting outcomes, 2) child development outcomes. Our sample size estimates account for randomization at the cluster level at 0.05 significance level. For positive parenting behavior, the power of the design was calculated given a 0.39 standard deviation effect (Emmers et al. 2021), assuming an intra-cluster correlation of 0.01, and a cluster size of 8 babies per village. For the home learning environment, the power of the design was calculated, assuming a 0.31 standard deviation effect (Cunha et al., 2024), an intra-cluster correlation of 0.01, and a cluster size of 8 babies per village. For child development outcome, the power of the design was calculated given a 0.26 standard deviation effect (Emmers et al. 2021), assuming an intra-cluster correlation of 0.01 and a cluster size of 8 babies per village. Based on these reference effect sizes, our study design has a power of 0.99, 0.99, and 0.94 when different outcomes are used as the outcome variable, respectively.