  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. Longitudinal data analyzing
interventions 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.
