We contribute to debate about causal inferences in educational research in two ways. First, we quantify how much bias there must be in an estimate to invalidate an inference. Second, we utilize Rubin's causal model to interpret the bias necessary to invalidate an inference in terms of sample replacement. We apply our analysis to an inference of a positive effect of Open Court Curriculum on reading achievement from a randomized experiment, and an inference of a negative effect of kindergarten retention on reading achievement from an observational study. We consider details of our framework, and then discuss how our approach informs judgment of inference relative to study design. We conclude with implications for scientific discourse.

We conducted a theory-based analysis of the underlying structure of the Tripod student perception survey instrument using the Measures of Effective Teaching (MET) database (N = 1,049 middle school math class sections; N = 25,423 students). Multilevel item factor analyses suggested that an alternative bifactor structure best fit the Tripod items, and preliminary evidence suggests that both the general responsivity and the classroom management-specific dimensions are positively associated with teacher value-added scores. In our discussion, we consider the distinct characterizing features of adolescents as raters of teaching, the implications for teacher professional learning opportunities, and key areas for future research.

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Recently, there has been an increase in the number of cluster randomized trials (CRTs) to evaluate the impact of educational programs and interventions. These studies are often powered for the main effect of treatment to address the ''what works'' question. However, program effects may vary by individual characteristics or by context, making it important to also consider power to detect moderator effects. This article presents a framework for calculating statistical power for moderator effects at all levels for two-and three-level CRTs. Annotated R code is included to make the calculations accessible to researchers and increase the regularity in which a priori power analyses for moderator effects in CRTs are conducted.