Single- and Multilevel Perspectives on Covariate Selection in Randomized Intervention Studies on Student Achievement

Well-chosen covariates boost the design sensitivity of individually and cluster-randomized trials. We provide guidance on covariate selection generating an extensive compilation of single- and multilevel design parameters on student achievement. Embedded in psychometric heuristics, we analyzed (a) covariate types of varying bandwidth-fidelity, namely domain-identical (IP), cross-domain (CP), and fluid intelligence (Gf) pretests, as well as sociodemographic characteristics (SC); (b) covariate combinations quantifying incremental validities of CP, Gf, and/or SC beyond IP; and (c) covariate time lags of 1–7 years, testing validity degradation in IP, CP, and Gf. Estimates from six German samples (1868 ≤ N ≤ 10,543) covering various outcome domains across grades 1–12 were meta-analyzed and included in precision simulations. Results varied widely by grade level, domain, and hierarchical level. In general, IP outperformed CP, which slightly outperformed Gf and SC. Benefits from coupling IP with CP, Gf, and/or SC were small. IP appeared most affected by temporal validity decay. Findings are applied in illustrative scenarios of study planning and enriched by comprehensive Online Supplemental Material (OSM) accessible via the Open Science Framework (OSF; https://osf.io/nhx4w).