This article reviews the origins and use of the terms quasi-experiment and natural experiment. It demonstrates how the terms conflate whether variation in the independent variable of interest falls short of random with whether researchers find, rather than intervene to create, that variation. Using the lens of assignment--the process driving…

When designing cluster-randomized trials (CRTs), one important consideration is determining the proper sample sizes across levels and treatment conditions to cost-efficiently achieve adequate statistical power. This consideration is usually addressed in an optimal design framework by leveraging the cost structures of sampling and optimizing the…

Though previously unacknowledged, a SMART (Sequential Multiple Assignment Randomized Trial) design uses both regression discontinuity (RD) and randomized controlled trial (RCT) designs. This combination structure creates a conceptual symbiosis between the two designs that enables both RCT- and previously unrecognized, RD-based inferential claims.…

We consider a class of multiple-group individually-randomized group trials (IRGTs) that introduces a (partially) cross-classified structure in the treatment condition (only). The novel feature of this design is that the nature of the treatment induces a clustering structure that involves two or more non-nested groups among individuals in the…

Cluster-randomized trials have been widely used to evaluate the treatment effects of interventions on student outcomes. When interventions are implemented by teachers, researchers need to account for the nested structure in schools (i.e., students are nested within teachers nested within schools). Schools usually have a very limited number of…

Background: Power analyses for a cluster-randomized trial (CRT) require estimates of additional design parameters beyond those needed for an individually randomized trial. In a 2-level CRT, there are two sample sizes, the number of clusters and the number of individuals per cluster. The intraclass correlation (ICC), or the proportion of variance…

Random encouragement designs evaluate treatments that aim to increase participation in a program or activity. These randomized controlled trials (RCTs) can also assess the mediated effects of participation itself on longer term outcomes using a complier average causal effect (CACE) estimation framework. This article considers power analysis…

Multisite cluster randomized trials (MCRTs), in which, the intermediate-level clusters (e.g., classrooms) are randomly assigned to the treatment or control condition within each site (e.g., school), are among the most commonly used experimental designs across a broad range of disciplines. MCRTs often align with the theory that programs are…

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…

Background: Evidence from education randomized controlled trials (RCTs) in low- and middle-income countries (LMICs) demonstrates how interventions can improve children's educational achievement [1, 2, 3, 4]. RCTs assess the impact of an intervention by comparing outcomes--aggregate test scores--between treatment and control groups. A review of…

Researchers use test outcomes to evaluate the effectiveness of education interventions across numerous randomized controlled trials (RCTs). Aggregate test data--for example, simple measures like the sum of correct responses--are compared across treatment and control groups to determine whether an intervention has had a positive impact on student…

Single-case experimental designs (SCEDs) have a long history in clinical and educational disciplines. One underdeveloped area in advancing SCED design and analysis is understanding the process of how internal validity threats and operational concerns are avoided or mitigated. Two strategies to ameliorate such issues in SCED involve replication and…

Cluster randomized trials (CRTs) are commonly used to evaluate the causal effects of educational interventions, where the entire clusters (e.g., schools) are randomly assigned to treatment or control conditions. This study introduces statistical methods for designing and analyzing two-level (e.g., students nested within schools) and three-level…

Background: Education scientists are increasingly interested in constructing interventions that are adaptive over time to suit the evolving needs of students, classrooms, or schools. Such "adaptive interventions" (also referred to as dynamic treatment regimens or dynamic instructional regimes) determine which treatment should be offered…

Practitioners and policymakers often want estimates of the effect of an intervention for their local community, e.g., region, state, county. In the ideal, these multiple population average treatment effect (ATE) estimates will be considered in the design of a single randomized trial. Methods for sample selection for generalizing the sample ATE to…