Chapter 4: Aggregated Designs: RD Design Theory and Design

The RD Design Effect for the MDE Calculations

To calculate MDEs, standard errors of the impact estimates must be divided by standard deviations of the outcome measures (see equation [1]). What standard deviations should be used in the MDE calculations for RD designs?

In principle, impact estimates under RD designs pertain to only those units with scores right around the cutoff value. Thus, one option would be to use standard deviations for these units only. These standard deviations, however, are likely to be much smaller than the full-population values that are used for RA designs. Thus, I do not adopt this approach, because it would likely lead to serious (and somewhat artificial) increases in MDEs for RD designs relative to RA designs.

A second option would be to use standard deviations based on the models in (5) and (8). These two standard deviations are likely to differ because, as discussed, σYRD2 ≈ σYRA2 +2α1α2σTS. However, because these differences are a function of the unknown parameters α1 and α2, they would be difficult to compute without further assumptions.

Instead, I assume the same standard deviation for both the RD and RA designs that pertain to the study “superpopulation,” even if this population is not delineated precisely. Under this approach, the square root of the RD design effect in (11) for the variance calculations applies to the MDE calculations.