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Prior to initial posting of the analysis plan, as well as to the posting of the first revision, preliminary statistical analyses were conducted without use of outcomes within the treatment group. This round of revisions to the analysis plan were made following our first pass at estimating a "main effect" of the treatment, and address several issues we became aware of during this process. A detailed list of the current changes is included with comments to Section VIII, at the end of this registry entry.

A novel aggregation scheme 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 w eighting for r epeated-measurements with d elayed-effects scheme, PWRD aggregation, converts the theory of change into a test statistic with improved Pitman 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. This intervention is not found to have an effect, but the PWRD technique's effect on power is found to be comparable to that of a doubling of (cluster-level) sample size.