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Journal of Causal Inference

Ed. by Imai, Kosuke / Pearl, Judea / Petersen, Maya Liv / Sekhon, Jasjeet / van der Laan, Mark J.

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2193-3685
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Bridging Finite and Super Population Causal Inference

Peng Ding / Xinran Li / Luke W. Miratrix
Published Online: 2017-04-27 | DOI: https://doi.org/10.1515/jci-2016-0027

Abstract

There are two general views in causal analysis of experimental data: the super population view that the units are an independent sample from some hypothetical infinite population, and the finite population view that the potential outcomes of the experimental units are fixed and the randomness comes solely from the treatment assignment. These two views differs conceptually and mathematically, resulting in different sampling variances of the usual difference-in-means estimator of the average causal effect. Practically, however, these two views result in identical variance estimators. By recalling a variance decomposition and exploiting a completeness-type argument, we establish a connection between these two views in completely randomized experiments. This alternative formulation could serve as a template for bridging finite and super population causal inference in other scenarios.

Keywords: completeness; finite population correction; potential outcomes; simple random sample; variance of individual causal effects

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About the article

Published Online: 2017-04-27


Citation Information: Journal of Causal Inference, Volume 5, Issue 2, 20160027, ISSN (Online) 2193-3685, DOI: https://doi.org/10.1515/jci-2016-0027.

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