  We consider the conditional randomization test as a way to account for
covariate imbalance in randomized experiments. The test accounts for covariate
imbalance by comparing the observed test statistic to the null distribution of
the test statistic conditional on the observed covariate imbalance. We prove
that the conditional randomization test has the correct significance level and
introduce original notation to describe covariate balance more formally.
Through simulation, we verify that conditional randomization tests behave like
more traditional forms of covariate adjustmet but have the added benefit of
having the correct conditional significance level. Finally, we apply the
approach to a randomized product marketing experiment where covariate
information was collected after randomization.
