Abstract
In observational studies of discrimination, the most common statistical approaches consider either the rate at which decisions are made (benchmark tests) or the success rate of those decisions (outcome tests). Both tests, however, have well-known statistical limitations, sometimes suggesting discrimination even when there is none. Despite the fallibility of the benchmark and outcome tests individually, here we prove a surprisingly strong statistical guarantee: Under a common nonparametric assumption, at least one of the two tests must be correct; consequently, when both tests agree, they are guaranteed to yield correct conclusions. We present empirical evidence that the underlying assumption holds approximately in several important domains, including lending, education, and criminal justice-and that our hybrid test is robust to the moderate violations of the assumption that we observe in practice. Applying this approach to 2.8 million police stops across California, we find evidence of widespread racial discrimination.