Power Analysis for Models of Change in Cluster Randomized Designs.

Field experiments in education frequently assign entire groups such as schools to treatment or control conditions. These experiments incorporate sometimes a longitudinal component where for example students are followed over time to assess differences in the average rate of linear change, or rate of acceleration. In this study, we provide methods for power analysis in three-level polynomial change models for cluster randomized designs (i.e., treatment assigned to units at the third level). Power computations take into account clustering effects at the second and third levels, the number of measurement occasions, the impact of sample sizes at different levels (e.g., number of schools or students), and covariates effects. An illustrative example that shows how power is influenced by the number of measurement occasions, and sample sizes and covariates at the second or third levels is presented.