Causal Inference from Possibly Unbalanced Split-Plot Designs: A Randomization-based Perspective

Rahul Mukerjee; Tirthankar Dasgupta

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arXiv · 1906.08420

Causal Inference from Possibly Unbalanced Split-Plot Designs: A Randomization-based Perspective

Rahul Mukerjee·Tirthankar Dasgupta

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Abstract

Split-plot designs find wide applicability in multifactor experiments with randomization restrictions. Practical considerations often warrant the use of unbalanced designs. This paper investigates randomization based causal inference in split-plot designs that are possibly unbalanced. Extension of ideas from the recently studied balanced case yields an expression for the sampling variance of a treatment contrast estimator as well as a conservative estimator of the sampling variance. However, the bias of this variance estimator does not vanish even when the treatment effects are strictly additive. A careful and involved matrix analysis is employed to overcome this difficulty, resulting in a new variance estimator, which becomes unbiased under milder conditions. A construction procedure that generates such an estimator with minimax bias is proposed.

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BibTeX RIS

Rahul Mukerjee, Tirthankar Dasgupta. 2019-06-20. Causal Inference from Possibly Unbalanced Split-Plot Designs: A Randomization-based Perspective. https://arxiv.org/abs/1906.08420

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