Multilevel Design Parameters to Plan Cluster-Randomized Intervention Studies on Student Achievement in Elementary and Secondary School

To plan cluster-randomized trials with sufficient statistical power todetect intervention effects on student achievement, researchers needmultilevel design parameters, including measures of between-class-room and between-school differences and the amounts of varianceexplained by covariates at the student, classroom, and school level.Previous research has mostly been conducted in the United States,focused on two-level designs, and limited to core achievementdomains (i.e., mathematics, science, reading). Using representativedata of students attending grades 1–12 from three German longitu-dinal large-scale assessments (3,963 ≤ N ≤ 14,640), we used three-and two-level latent (covariate) models to provide design parametersand corresponding standard errors for a broad array of domain-spe-cific (e.g., mathematics, science, verbal skills) and domain-general(e.g., basic cognitive functions) achievement outcomes. Three covari-ate sets were applied comprising (a) pretest scores, (b) sociodemo-graphic characteristics, and (c) their combination. Design parametersvaried considerably as a function of the hierarchical level, achieve-ment outcome, and grade level. Our findings demonstrate the needto strive for an optimal fit between design parameters and targetresearch context. We illustrate the application of design parametersin power analyses.