Conjuring Power from a Theory of Change: The PWRD Method for Trials with Anticipated Variation in Effects

Abstract

We present an aggregation scheme that increases power in randomized controlled trials and quasi-experiments when the intervention possesses a robust and well-articulated theory of change. Intervention studies using longitudinal data often include multiple observations on individuals, some of which may be more likely to manifest a treatment effect than others. An intervention’s theory of change provides guidance as to which of those observations are best situated to exhibit that treatment effect. Our power-maximizing weighting for repeated-measurements with delayed-effects scheme, PWRD aggregation, converts the theory of change into a test statistic with improved asymptotic relative efficiency, delivering tests with greater statistical power. We illustrate this method on an IES-funded cluster randomized trial testing the efficacy of a reading intervention designed to assist early elementary students at risk of falling behind their peers. The salient theory of change holds program benefits to be delayed and non-uniform, experienced after a student’s performance stalls. In this instance, the PWRD technique’s effect on power is found to be comparable to that of doubling the number of clusters in the experiment.