I. Purpose of the Study: Detecting whether interventions work or not (through main effect analysis) can provide empirical evidence regarding the causal linkage between malleable factors (e.g., interventions) and learner outcomes. In complement, moderation analyses help delineate for whom and under what conditions intervention effects are most salient. Such analyses provide empirical evidence that is the source material for effective policy development (Raudenbush & Liu, 2000; Spybrook, Kelcey, Dong, 2016; Dong et al., 2018, 2021; IES & NSF, 2013). The purpose of this study is to improve the design of experiments by developing optimal design strategies for experiments probing moderation and main effects. II. Background and Relevant Literature: Differential Sampling Costs Across Treatment Conditions and Levels: In real-world experimental designs, researchers must consider sampling costs, fixed budgets, and complex differences in sampling costs across treatment conditions and levels/units. For example, in a multisite-randomized trial to evaluate the effects of the Reading Recovery program on students' reading achievement, the costs of adding a treated student may additionally include the resources for delivering 60- to 100-days of 30-minute individual lessons, the professional development of teachers, and the supplemental work time of teachers as intervention providers (May et al., 2015). There are a broad range of documented experiments with differential costs across treatment conditions and levels (Springer et al., 2011; Greenleaf et al., 2011; Jacob et al., 2015; Jayanthi et al., 2017; Clements et al., 2011; Lewis et al., 2013; Hiscock et al., 2008). Sample Allocation and Optimal Design: III. Research Design We use the following two-step macro structures to develop the proposed framework. Optimal Design of Experiments Detecting Moderation Effects: We use the (multivariate) first-order derivative method to develop the optimal design framework for moderation effects. This approach has been used to develop the optimal design for main effects (Shen & Kelcey, 2020, 2022a, 2022b). Optimal Design of Experiments Investigating Moderation and Main Effects: We use a meta-heuristic optimization method, ant colony optimization (ACO; Dorigo & Stützle, 2004; Socha & Dorigo, 2008), to identify the optimal sample allocation in experiments investigating both moderation and main effects. The procedures of implementing the ACO algorithm to identify the jointly optimal sample allocation, including validation methods, are presented in Appendix A. IV. Preliminary Results: Next, we present the results for two-level multisite randomized trial with a site-level binary moderator as an example to demonstrate the feasibility of the research design and the utility of the proposed work. We do not include covariates in this example to ease the presentation. We omit the statistical models and other equations because of the space limitations. Optimal Sample Allocation for Moderation Effects: Unconstrained Optimal Sample Allocation: The resulting optimal design parameters (individual-level sample size per cluster) and (proportion of units in the treatment) must satisfy the two equations in Appendix A. Although there are no algebraic solutions for the optimal and from the two equations, we can solve for the roots numerically through iteration. This iteration method has been outlined in Shen & Kelcey (2020) and implemented in the R package odr. Power Analysis in Optimal Design: Once optimal design parameters are identified, we can perform power analysis using these parameters. The power analysis results in optimal design will have these features: Approximately achieving the maximum statistical power under the same budget and using the least resources to produce the fixed power. The same features are valid under a constraint if used in obtaining a constrained optimal sample allocation. Optimal Sample Allocation for Moderation and Main Effects: To identify the optimal sample allocation detecting both moderation and main effects in the same two-level multisite trial, we can use the ACO algorithm presented in Appendix B. Illustration: Let the cost structures of sampling be , , (e.g., May et al., 2015), intraclass correlation coefficient be 0.20 ( ; e.g., Hedges & Hedberg, 2007), treatment-by-site variance be 0.01 ( ), and the proportion of treatment-by-site variance explained by the moderator be 0.30 ( ). Optimal Sample Allocation for Moderation Effects: The identified optimal design parameters for moderation effects are and . The statistical power is maximized at the optimal allocation under the same budget (Figure 1). When designs are sub-optimal, they will require additional budget percentages (ABP) than the optimal one to maintain the same level of statistical power (Figure 2). Jointly Optimal Sample Allocation for the Moderation and Main Effects: In terms of the jointly optimal allocation for both moderation and main effects in the two-level multisite trials, the ACO algorithm can efficiently identify jointly optimal allocation. It returns results within one second for 300 iterations that can provide precise enough results. The results show that when a design departs from the jointly optimal sample allocation, power decreases for at least one of the effects under the same budget (see Figures 3 to 5). V. Contribution to the Field: This study will enrich the knowledge base for future design literature as the proposed framework can be extended to other types of designs. This study and its application in the field have great potential to shift the next-generation studies to more effective and efficient ones. The updated package odr not only will facilitate the computation, but its power analysis functions explicitly accommodating costs and budget will also encourage thoughtful consideration of efficient design strategies.