Inference in Experiments Conditional on Observed Imbalances in Covariates

Per Johansson Department of Statistics, Uppsala University, Uppsala, Sweden; IFAU, Uppsala, Sweden; Tsinghua University, Beijing, China Mattias Nordin Department of Statistics, UCFS and Urban Lab, Uppsala University, Uppsala, Sweden

Statistics Theory and Methods mathscidoc:2206.33001

The American Statistician, 00, (0), 1-11, 2022.4
Double-blind randomized controlled trials are traditionally seen as the gold standard for causal inferences as the difference-in-means estimator is an unbiased estimator of the average treatment effect in the experiment. The fact that this estimator is unbiased over all possible randomizations does not, however, mean that any given estimate is close to the true treatment effect. Similarly, while predetermined covariates will be balanced between treatment and control groups on average, large imbalances may be observed in a given experiment and the researcher may therefore want to condition on such covariates using linear regression. This article studies the theoretical properties of both the difference-in-means and OLS estimators conditional on observed differences in covariates. By deriving the statistical properties of the conditional estimators, we can establish guidance for how to deal with covariate imbalances.
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  title={Inference in Experiments Conditional on Observed Imbalances in Covariates},
  author={Per Johansson, and Mattias Nordin},
  booktitle={The American Statistician},
Per Johansson, and Mattias Nordin. Inference in Experiments Conditional on Observed Imbalances in Covariates. 2022. Vol. 00. In The American Statistician. pp.1-11.
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