Randomization Tests that Condition on Non-Categorical Covariate Balance

TL;DR

This paper introduces a new conditional randomization test that accounts for non-categorical covariate balance, improving power and validity over existing methods, applicable to any covariate type.

Contribution

It develops the first randomization test that conditions on covariate balance for any covariate type, enhancing analysis flexibility and statistical power.

Findings

The proposed test is more powerful than unconditional tests.

It is valid both unconditionally and conditionally on covariate balance.

Performance is comparable to model-adjusted test statistics.

Abstract

A benefit of randomized experiments is that covariate distributions of treatment and control groups are balanced on average, resulting in simple unbiased estimators for treatment effects. However, it is possible that a particular randomization yields covariate imbalances that researchers want to address in the analysis stage through adjustment or other methods. Here we present a randomization test that conditions on covariate balance by only considering treatment assignments that are similar to the observed one in terms of covariate balance. Previous conditional randomization tests have only allowed for categorical covariates, while our randomization test allows for any type of covariate. Through extensive simulation studies, we find that our conditional randomization test is more powerful than unconditional randomization tests and other conditional tests. Furthermore, we find that our conditional randomization test is valid (1) unconditionally across levels of covariate balance, and (2) conditional on particular levels of covariate balance. Meanwhile, unconditional randomization tests are valid for (1) but not (2). Finally, we find that our conditional randomization test is similar to a randomization test that uses a model-adjusted test statistic.