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Design-Based Estimators for Average Treatment Effects for Multi-Armed RCTs

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  • Peter Z. Schochet

    (Mathematica Policy Research, Inc.)

Abstract

Design-based methods have recently been developed as a way to analyze randomized controlled trial (RCT) data for designs with a single treatment and control group. This article builds on this framework to develop design-based estimators for evaluations with multiple research groups. Results are provided for a wide range of designs used in education research, including clustered and blocked designs. Because analysis in the multi-armed setting involves pairwise contrasts across the research groups, the key methodological question addressed is: How do the estimators for the two-group design need to be adjusted for multi-armed trials? The critical insight is that in multi-armed trials where the goal is to identify the most effective treatments, the samples for each pairwise contrast are representative of the full set of randomized units, not just of themselves. The implication is that variance terms need to be adjusted slightly under the finite-population framework that can reduce precision, and blocks need to be weighted to reflect the full randomized sample in the block or biases can result. An empirical example using data from a multi-armed education RCT demonstrates the issues.

Suggested Citation

  • Peter Z. Schochet, 2018. "Design-Based Estimators for Average Treatment Effects for Multi-Armed RCTs," Journal of Educational and Behavioral Statistics, , vol. 43(5), pages 568-593, October.
    • Handle: RePEc:sae:jedbes:v:43:y:2018:i:5:p:568-593
    DOI: 10.3102/1076998618786968
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    References listed on IDEAS

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    1. Tirthankar Dasgupta & Natesh S. Pillai & Donald B. Rubin, 2015. "Causal inference from 2-super-K factorial designs by using potential outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 727-753, September.
    2. Castleman, Benjamin L. & Page, Lindsay C., 2015. "Summer nudging: Can personalized text messages and peer mentor outreach increase college going among low-income high school graduates?," Journal of Economic Behavior & Organization, Elsevier, vol. 115(C), pages 144-160.
    3. Yang L. & Tsiatis A. A., 2001. "Efficiency Study of Estimators for a Treatment Effect in a Pretest-Posttest Trial," The American Statistician, American Statistical Association, vol. 55, pages 314-321, November.
    4. repec:mpr:mprres:7723 is not listed on IDEAS
    5. Xinran Li & Peng Ding, 2017. "General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1759-1769, October.
    6. Roberto Agodini & Barbara Harris & Sally Atkins-Burnett & Sheila Heaviside & Timothy Novak & Robert Murphy, "undated". "Achievement Effects of Four Early Elementary School Math Curricula: Findings from First Graders in 39 Schools," Mathematica Policy Research Reports 467194cd2d6f4cbaba7e23745, Mathematica Policy Research.
    7. Roberto Agodini, 2009. "Achievement Effects of Four Early Elementary School Math Curricula: Findings from First Graders in 39 Schools (Conference Paper)," Mathematica Policy Research Reports a08d661306a843fa89aff4c30, Mathematica Policy Research.
    8. repec:mpr:mprres:6192 is not listed on IDEAS
    9. repec:mpr:mprres:6574 is not listed on IDEAS
    10. Hansen, Christian B., 2007. "Asymptotic properties of a robust variance matrix estimator for panel data when T is large," Journal of Econometrics, Elsevier, vol. 141(2), pages 597-620, December.
    11. repec:mpr:mprres:6573 is not listed on IDEAS
    12. Peter Z. Schochet, "undated". "Is Regression Adjustment Supported by the Neyman Model for Causal Inference? (Presentation)," Mathematica Policy Research Reports abfc39d59c714499b2fe42f68, Mathematica Policy Research.
    13. Peter Z. Schochet, "undated". "Is Regression Adjustment Supported By the Neyman Model for Causal Inference?," Mathematica Policy Research Reports 782da2242fba458eb61752f96, Mathematica Policy Research.
    14. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, January.
    15. repec:mpr:mprres:7337 is not listed on IDEAS
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