2.9. Analysis
Measured baseline characteristics for all participants were summarized by arms. To ensure the conditional normality assumption was satisfied, the distributions of outcome measures were examined. Appropriate transformations were performed if needed. Between-group changes in all outcomes were compared using constrained linear mixed-effects models, accounting for visit (baseline, 3 months, and 6 months) and intervention group by visit interaction as independent variables. This model uses all available longitudinal data and imposes a constraint of a common baseline mean between groups as a result of randomization [We explored effect modification by race/ethnic group by adding race/ethnic group and interaction between race/ethnic and intervention groups in the constrained linear mixed-effects models for main beverage outcomes. Any statistically significant interactions would indicate that the intervention effect is different by race/ethnic group. Further, given that our intervention period spanned multiple seasons, and in light of the known association between beverage intake and season (more SSB and water are consumed during warm weather months), we ran additional models adjusting for season (winter or spring vs. summer or fall) of each measure. Multiple comparisons were not corrected due to the fact that this was a pilot study. A 