Analysis methods
REGRESSION
In the primary analysis of the primary outcome, child-specific composite test scores at endline will be compared between intervention and control arms using a linear regression model with randomisation arm and the stratification factors (and no other variables) as predictor variables. To take account of the cluster-randomisation, robust standard errors, allowing for the clustering, will be used here and elsewhere. Linear mixed models (with cluster as a random effect) which are also termed hierarchical or multilevel models are commonly used for the analysis of cluster randomised trials. The advantage of an approach using robust standard errors over linear mixed models is that homoscedasticity assumptions are not made.The adjusted difference in means will be divided by the SD of the test score in the control arm to give a standardised difference, with a nonparametric bootstrap confidence interval (bias corrected and accelerated, 2000 replications at cluster level) computed for this.Secondary outcomes that are continuous will be analysed using the same approach as above.Secondary analyses will extend the linear regression model (with robust standard errors that allow for clustering) for the primary outcome described above to (separately) investigate interactions by caste, gender, male and female primary caregiver literacy, village population and wealth.Secondary outcomes that are dichotomous (such as whether the child was enrolled in school) will be expressed as odds ratios with 95% confidence intervals obtained from a GEE model with a binary outcome, a logit link, and a ‘working’ assumption of independence, with robust standard errors to take account of clustering.