Permutation Tests for Experimental Data

38 Pages Posted: 8 Nov 2021 Last revised: 3 Apr 2023

See all articles by Charles A. Holt

Charles A. Holt

University of Virginia - Department of Economics

Sean Sullivan

University of Iowa College of Law

Date Written: Apr 1, 2023


This article surveys the use of nonparametric permutation tests for analyzing experimental data. The permutation approach, which involves randomizing or permuting features of the observed data, is a flexible way to draw statistical inferences in common experimental settings. It is particularly valuable when few independent observations are available, a frequent occurrence in controlled experiments in economics and other social sciences. The permutation method constitutes a comprehensive approach to statistical inference. In two-treatment testing, permutation concepts underlie popular rank-based tests, like the Wilcoxon and Mann-Whitney tests. But permutation reasoning is not limited to ordinal contexts. Analogous tests can be constructed from the permutation of measured observations—as opposed to rank-transformed observations—and we argue that these tests should often be preferred. Permutation tests can also be used with multiple treatments, with ordered hypothesized effects, and with complex data-structures, such as hypothesis testing in the presence of nuisance variables. Drawing examples from the experimental economics literature, we illustrate how permutation testing solves common challenges. Our aim is to help experimenters move beyond the handful of overused tests in play today and to instead see permutation testing as a flexible framework for statistical inference.

Keywords: permutation test, randomization test, experimental economics, nonparametric

JEL Classification: C12, C14, C90

Suggested Citation

Holt, Charles A. and Sullivan, Sean, Permutation Tests for Experimental Data (Apr 1, 2023). U Iowa Legal Studies Research Paper No. 2022-31, Experimental Economics, Available at SSRN: or

Charles A. Holt

University of Virginia - Department of Economics ( email )

P.O. Box 400182
Rouss Hall #114
Charlottesville, VA 22904-4182
United States
(804) 924-7894 (Phone)

Sean Sullivan (Contact Author)

University of Iowa College of Law ( email )

Melrose and Byington
Iowa City, IA 52242
United States


Do you have negative results from your research you’d like to share?

Paper statistics

Abstract Views
PlumX Metrics