Multilevel experiments have been widely used in education and social sciences to evaluate causal effects of interventions. Two key considerations in designing experimental studies are statistical power and the minimal use of resources. Optimal design framework simultaneously addresses both considerations. This dissertation extends previous optimal design frameworks by developing a more general optimal sample allocation framework that allows sampling costs to vary across both levels of the hierarchy and treatment conditions while relaxing the proportion of units assigned to the treatment condition. The dissertation includes five chapters. Chapter one introduces the studies and their context. Chapter two develops optimal sampling extensions that allow sampling costs to vary across hierarchical levels and treatment conditions for two- and three-level cluster-randomized trials. Chapter three further extends these developments to two- and three-level multisite randomized trials. Chapter four further extends these developments to four-level experiments. The structure of each main chapter (chapters two to four) includes the review of previous frameworks, the development of a more general framework, the demonstration of the utility of the proposed framework by comparing with previous frameworks, and a sensitivity analysis of the proposed framework against the misspecification of design parameter values. The results show that the proposed framework and solutions can frequently identify designs with more statistical precision than previous frameworks even when some parameters are constrained due to immutable practical concerns. The results also suggest that the gains in statistical precision and design efficiency identified by the proposed framework are fairly robust to misspecifications of the cost structure and the values of incidental design parameters (e.g., intraclass correlation coefficient). By using the proposed framework, researchers can plan studies using fewer resources to achieve a desired level of statistical power or having a smaller detectable effect size under the same level of power and budget. The proposed framework is implemented in the R package odr. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]