Sequential Hypothesis Testing for Black-Box Fairness Audits

Audits of deployed AI systems often have to decide whether a system violates a behavioral requirement before the auditor can assemble a large, fixed test set. This paper develops a sequential testing framework for black-box fairness auditing. We formalize an audit as a pre-specified hypothesis test on a disparity functional and instantiate the procedure with Wald’s Sequential Probability Ratio Test (SPRT). The framework separates three choices that are often conflated in fairness evaluations: the fairness construct to be audited, the tolerance threshold that makes a disparity practically or legally material, and the statistical risks that the auditor is willing to incur. We evaluate the approach in two studies. In controlled simulations, sequential audits detect violations of statistical parity, equal opportunity, and equalized odds while, under the studied designs, typically using fewer samples than fixed-sample two-proportion tests. In a German Credit case study, the same protocol detects persistent disparities in a baseline classifier and in a classifier trained without the sensitive attribute, while producing substantially fewer bias flags after demographic-parity constrained training. The results show that sequential tests can make fairness audits more sample-efficient, but also that nominal error guarantees require careful pre-registration, treatment of composite hypotheses, multiple-testing correction, and validation under the actual sampling protocol. We further stress-test the procedure on a fair equalized-odds model and derive reporting recommendations for finite-budget audits.