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Statistical Power for the Comparative Regression Discontinuity Design With a Pretest No-Treatment Control Function: Theory and Evidence From the National Head Start Impact Study

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  • Yang Tang
  • Thomas D. Cook

Abstract

The basic regression discontinuity design (RDD) has less statistical power than a randomized control trial (RCT) with the same sample size. Adding a no-treatment comparison function to the basic RDD creates a comparative RDD (CRD); and when this function comes from the pretest value of the study outcome, a CRD-Pre design results. We use a within-study comparison (WSC) to examine the power of CRD-Pre relative to both basic RDD and RCT. We first build the theoretical foundation for power in CRD-Pre, then derive the relevant variance formulae, and finally compare them to the theoretical RCT variance. We conclude from this theoretical part of this article that (1) CRD-Pre’s power gain depends on the partial correlation between the pretest and posttest measures after conditioning on the assignment variable, (2) CRD-Pre is less responsive than basic RDD to how the assignment variable is distributed and where the cutoff is located, and (3) under a variety of conditions, the efficiency of CRD-Pre is very close to that of the RCT. Data from the National Head Start Impact Study are then used to construct RCT, RDD, and CRD-Pre designs and to compare their power. The empirical results indicate (1) a high level of correspondence between the predicted and obtained power results for RDD and CRD-Pre relative to the RCT, and (2) power levels in CRD-Pre and RCT that are very close. The study is unique among WSCs for its focus on the correspondence between RCT and observational study standard errors rather than means.

Suggested Citation

  • Yang Tang & Thomas D. Cook, 2018. "Statistical Power for the Comparative Regression Discontinuity Design With a Pretest No-Treatment Control Function: Theory and Evidence From the National Head Start Impact Study," Evaluation Review, , vol. 42(1), pages 71-110, February.
    • Handle: RePEc:sae:evarev:v:42:y:2018:i:1:p:71-110
    DOI: 10.1177/0193841X18776117
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    References listed on IDEAS

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    1. Jens Ludwig & Douglas L. Miller, 2007. "Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(1), pages 159-208.
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    3. repec:mpr:mprres:5863 is not listed on IDEAS
    4. Yang Tang & Thomas D. Cook & Yasemin Kisbu-Sakarya & Heinrich Hock & Hanley Chiang, 2017. "The Comparative Regression Discontinuity (CRD) Design: An Overview and Demonstration of its Performance Relative to Basic RD and the Randomized Experiment," Advances in Econometrics, in: Regression Discontinuity Designs, volume 38, pages 237-279, Emerald Group Publishing Limited.
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    11. Thomas D. Cook & William R. Shadish & Vivian C. Wong, 2008. "Three conditions under which experiments and observational studies produce comparable causal estimates: New findings from within-study comparisons," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 27(4), pages 724-750.
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