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Technical Methods Report: Do Typical RCTs of Education Interventions Have Sufficient Statistical Power for Linking Impacts on Teacher Practice and Student Achievement Outcomes?

NCEE 2009-4065
October 2009

Chapter 2: Definition of a Mediator

For the RCTs considered in this paper, a given classroom- or teacher-level variable is considered to be a mediator if it can partly account for the relationship between the offer of treatment services and student test scores (Baron and Kenny 1986). A mediator is an intermediate outcome that is measured after random assignment and that can be affected by the treatment.

To clarify, consider a typical conceptual model diagrammed in Figure 2.1 for an RCT of a teacher professional development intervention. In this path model, the causal chain is that the offer and receipt of intervention services first improves teacher knowledge (path a), thereby improving teacher practices (path b), and ultimately student test scores (path c). In this model, teacher knowledge and practice measures are mediating outcomes that are measured for both the treatment and control groups. In some evaluations, the logic model may also have a direct link between treatment receipt and student test scores that is not via the teacher (path d).

The theoretical framework presented develops statistical power formulas for estimating a generic mediator-achievement relationship. However, the primary focus of the empirical analysis is on teacher (classroom) practice mediators and the extent to which they mediate intervention effects on test scores. Stated differently, using Figure 2.1, the focus is on path ab, the direct effect of offering the treatment on teacher practices, and path c, the direct effect of teacher practices on student achievement, which is hereafter referred to as the "mediator effect." Teacher practice mediators are of particular importance for education RCTs, because they are expensive to collect and are typically considered to be key intermediate outcomes in the causal chain for improving student achievement. Thus, for simplicity, the teacher knowledge chain is ignored for the empirical analysis (or is assumed to be subsumed in the teacher practice chain). In addition, the empirical analysis does not consider mediators measuring the quality or amount of intervention services received by treatment teachers.