`Time for a New Angle!': Unravel the Mystery of Split-Plot Designs via the Potential Outcomes Prism
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CitationZhao, Anqi. 2016. `Time for a New Angle!': Unravel the Mystery of Split-Plot Designs via the Potential Outcomes Prism. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.
AbstractThis manuscript investigates two different approaches, namely the Neymanian randomization based (Neyman, 1923) method and the Bayesian model based (Rubin, 1978) method, towards the causal inference for 2-by-2 split-plot designs (Jones and Nachtsheim, 2009), both under the potential outcomes framework (Neyman, 1923; Rubin, 1974, 1978, 2005).
Chapter 1 -- Chapter 5. Given two 2-level factors of interest, a 2-by-2 split-plot design (a) takes each of the 2-by-2 = 4 possible factorial combinations as a treatment, (b) identifies one factor as 'whole-plot,' (c) divides the experimental units into blocks, and (d) assigns the treatments in such a way that all units within the same block receive the same level of the whole-plot factor. Assuming the potential outcomes framework, we propose in Chapters 1 — 5 a randomization-based estimation procedure for causal inference under such designs. Sampling variances of the point estimates are derived in closed form as linear combinations of the between- and within-block covariances of the potential outcomes. Results are compared to those under complete randomizations as measures of design efficiency. Interval estimates are constructed based on conservative estimates of the sampling variances, and the frequency coverage properties evaluated via simulation. Superiority over existing model-based alternatives is reported under a variety of settings for both binary and continuous outcomes.
Chapter 6. Causal inference compares the differences in outcomes over a particular set of experiment units. Whereas the randomization-based Neymanian inference focuses on the experimental units directly involved in the study, the introduction of Bayesian inferential framework provides a principled way to extend such finite population concerns to the super-population (Rubin, 1978). We outline in this chapter the explicit procedure for analyzing 2-by-2 split-plot designs under this framework, and illustrate the various technical issues in the actual implementation via examples.
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