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The gold standard for identifying causal relationships is a randomizedcontrolled experiment. In many applications in the social sciences andmedicine, the researcher does not control the assignment mechanism and insteadmay rely upon natural experiments, regression discontinuity designs, RCTs withattrition, or matching methods as a substitute to experimental randomization.The standard testable implication of random assignment is covariate balancebetween the treated and control units. Covariate balance is therefore commonlyused to validate the claim of "as-if" random assignment. We develop a newnonparametric test of covariate balance. Our Classification Permutation Test(CPT) is based on a combination of classification methods (e.g. logisticregression or random forests) with Fisherian permutation inference. The CPT isguaranteed to have correct coverage and is consistent under weak assumptions onthe chosen classifier. To illustrate the gains of using the CPT, we revisitfour real data examples: Lyall (2009); Green and Winik (2010); Eggers andHainmueller (2009); and Rouse (1995). Monte Carlo power simulations are used tocompare the CPT to two existing nonparametric tests of equality of multivariatedistributions.

The Classification Permutation Test: A Nonparametric Test for Equality of Multivariate Distributions