Sampling-based Randomised Designs for Causal Inference under the Potential Outcomes Framework

TY - JOUR

T1 - Sampling-based Randomised Designs for Causal Inference under the Potential Outcomes Framework

AU - Branson, Zach

AU - Dasgupta, Tirthankar

N1 - Publisher Copyright: © 2019 The Authors. International Statistical Review © 2019 International Statistical Institute

PY - 2020/4/1

Y1 - 2020/4/1

N2 - We establish the inferential properties of the mean-difference estimator for the average treatment effect in randomised experiments where each unit in a population is randomised to one of two treatments and then units within treatment groups are randomly sampled. The properties of this estimator are well understood in the experimental design scenario where first units are randomly sampled and then treatment is randomly assigned but not for the aforementioned scenario where the sampling and treatment assignment stages are reversed. We find that the inferential properties of the mean-difference estimator under this experimental design scenario are identical to those under the more common sample-first-randomise-second design. This finding will bring some clarifications about sampling-based randomised designs for causal inference, particularly for settings where there is a finite super-population. Finally, we explore to what extent pre-treatment measurements can be used to improve upon the mean-difference estimator for this randomise-first-sample-second design. Unfortunately, we find that pre-treatment measurements are often unhelpful in improving the precision of average treatment effect estimators under this design, unless a large number of pre-treatment measurements that are highly associative with the post-treatment measurements can be obtained. We confirm these results using a simulation study based on a real experiment in nanomaterials.

AB - We establish the inferential properties of the mean-difference estimator for the average treatment effect in randomised experiments where each unit in a population is randomised to one of two treatments and then units within treatment groups are randomly sampled. The properties of this estimator are well understood in the experimental design scenario where first units are randomly sampled and then treatment is randomly assigned but not for the aforementioned scenario where the sampling and treatment assignment stages are reversed. We find that the inferential properties of the mean-difference estimator under this experimental design scenario are identical to those under the more common sample-first-randomise-second design. This finding will bring some clarifications about sampling-based randomised designs for causal inference, particularly for settings where there is a finite super-population. Finally, we explore to what extent pre-treatment measurements can be used to improve upon the mean-difference estimator for this randomise-first-sample-second design. Unfortunately, we find that pre-treatment measurements are often unhelpful in improving the precision of average treatment effect estimators under this design, unless a large number of pre-treatment measurements that are highly associative with the post-treatment measurements can be obtained. We confirm these results using a simulation study based on a real experiment in nanomaterials.

KW - causal inference

KW - experimental design

KW - potential outcomes

KW - randomised experiments

KW - survey sampling

UR - http://www.scopus.com/inward/record.url?scp=85071777767&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071777767&partnerID=8YFLogxK

U2 - 10.1111/insr.12339

DO - 10.1111/insr.12339

M3 - Article

SN - 0306-7734

VL - 88

SP - 101

EP - 121

JO - International Statistical Review

JF - International Statistical Review

IS - 1

ER -