Recent years have seen an increased interest in quantitative educational research studies that use random assignment (RA) to evaluate the causal impacts of educational interventions (Angrist, 2004). The multi-level structure of the public education system in the United States often leads to experimental designs where naturally occurring clusters (eg. schools) are utilized to recruit participants (eg. students) into a study and/or as units that are randomized into one of two experimental conditions. When multiple clusters are recruited to participate in a research study but individuals within clusters are randomly assigned to experimental conditions the resulting experimental design is often referred to as a "multi-site" design. When clusters are utilized as the unit of randomization the resulting experimental design is generally called a "cluster randomized" or "hierarchical" design. While designs that use some form of random assignment are generally preferred for making causal inferences about treatment effects, RA designs are not always practical or feasible (Shadish, Cook and Campbell, 2002). The next best alternative to a random assignment design is often the regression discontinuity (RD) design. The same clustering issues that arise with random assignment studies also impact regression discontinuity studies. The score variable may be measured at any of many different levels in the educational hierarchy while outcome measurements are obtained at a lower level in the hierarchy. These sorts of situations lead to "hierarchical" regression discontinuity (RD) designs. An important component of planning experiments with clustering (whether they be multi-site or cluster randomized designs) is to determine the optimal within and between cluster sample sizes subject to a cost constraint. The current paper builds on previous work by Schochet (2008, 2009) in order to provide formulas for the optimal sample size at each level of a two-level regression discontinuity design. The paper also provides optimal sample size formulas for unbalanced random assignment designs (such formulas have not previously appeared in the literature). Optimal sample sizes for RD designs are compared to the optimal samples sizes for the corresponding RA designs. One table is appended.