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Multiple hypothesis testing in experimental economics

Published online by Cambridge University Press:  14 March 2025

John A. List ,
Azeem M. Shaikh  and
Yang Xu Open the ORCID record for Yang Xu [Opens in a new window]
John A. List*
Affiliation:
Department of Economics, University of Chicago, 5757 S University Ave, Chicago, IL 60637, USA
Azeem M. Shaikh*
Affiliation:
Department of Economics, University of Chicago, 5757 S University Ave, Chicago, IL 60637, USA
Yang Xu*
Affiliation:
Department of Economics, University of Chicago, 5757 S University Ave, Chicago, IL 60637, USA
*
jlist@uchicago.edu
amshaikh@uchicago.edu
yangxu@uchicago.edu
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Abstract

The analysis of data from experiments in economics routinely involves testing multiple null hypotheses simultaneously. These different null hypotheses arise naturally in this setting for at least three different reasons: when there are multiple outcomes of interest and it is desired to determine on which of these outcomes a treatment has an effect; when the effect of a treatment may be heterogeneous in that it varies across subgroups defined by observed characteristics and it is desired to determine for which of these subgroups a treatment has an effect; and finally when there are multiple treatments of interest and it is desired to determine which treatments have an effect relative to either the control or relative to each of the other treatments. In this paper, we provide a bootstrap-based procedure for testing these null hypotheses simultaneously using experimental data in which simple random sampling is used to assign treatment status to units. Using the general results in Romano and Wolf (Ann Stat 38:598–633, 2010), we show under weak assumptions that our procedure (1) asymptotically controls the familywise error rate—the probability of one or more false rejections—and (2) is asymptotically balanced in that the marginal probability of rejecting any true null hypothesis is approximately equal in large samples. Importantly, by incorporating information about dependence ignored in classical multiple testing procedures, such as the Bonferroni and Holm corrections, our procedure has much greater ability to detect truly false null hypotheses. In the presence of multiple treatments, we additionally show how to exploit logical restrictions across null hypotheses to further improve power. We illustrate our methodology by revisiting the study by Karlan and List (Am Econ Rev 97(5):1774–1793, 2007) of why people give to charitable causes.

Keywords

ExperimentsMultiple hypothesis testingMultiple treatmentsMultiple outcomesMultiple subgroupsRandomized controlled trialBootstrapBalance

JEL classification

C12: Hypothesis Testing: General C14: Semiparametric and Nonparametric Methods: General
Type
Original Paper
Information
Experimental Economics , Volume 22 , Issue 4 , December 2019 , pp. 773 - 793
Copyright
Copyright © 2019 Economic Science Association

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Footnotes

Documentation of our procedures and our Stata and Matlab code can be found at https://github.com/seidelj/mht.

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