Inference in Experiments With Matched Pairs

Yuehao Bai, Joseph P. Romano and Azeem Shaikh

Journal of the American Statistical Association, 2022, vol. 117, issue 540, 1726-1737

Abstract: This article studies inference for the average treatment effect in randomized controlled trials where treatment status is determined according to a “matched pairs” design. By a “matched pairs” design, we mean that units are sampled iid from the population of interest, paired according to observed, baseline covariates and finally, within each pair, one unit is selected at random for treatment. This type of design is used routinely throughout the sciences, but fundamental questions about its implications for inference about the average treatment effect remain. The main requirement underlying our analysis is that pairs are formed so that units within pairs are suitably “close” in terms of the baseline covariates, and we develop novel results to ensure that pairs are formed in a way that satisfies this condition. Under this assumption, we show that, for the problem of testing the null hypothesis that the average treatment effect equals a prespecified value in such settings, the commonly used two-sample t-test and “matched pairs” t-test are conservative in the sense that these tests have limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level. We show, however, that a simple adjustment to the standard errors of these tests leads to a test that is asymptotically exact in the sense that its limiting rejection probability under the null hypothesis equals the nominal level. We also study the behavior of randomization tests that arise naturally in these types of settings. When implemented appropriately, we show that this approach also leads to a test that is asymptotically exact in the sense described previously, but additionally has finite-sample rejection probability no greater than the nominal level for certain distributions satisfying the null hypothesis. A simulation study and empirical application confirm the practical relevance of our theoretical results.

Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2021.1883437 (text/html)
Access to full text is restricted to subscribers.

Related works:
Working Paper: Inference in Experiments with Matched Pairs (2019)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:117:y:2022:i:540:p:1726-1737

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2021.1883437

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().