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In fairness audits, a standard objective is to detect whether a givenalgorithm performs substantially differently between subgroups. Properlypowering the statistical analysis of such audits is crucial for obtaininginformative fairness assessments, as it ensures a high probability of detectingunfairness when it exists. However, limited guidance is available on the amountof data necessary for a fairness audit, lacking directly applicable resultsconcerning commonly used fairness metrics. Additionally, the consideration ofunequal subgroup sample sizes is also missing. In this tutorial, we addressthese issues by providing guidance on how to determine the required subgroupsample sizes to maximize the statistical power of hypothesis tests fordetecting unfairness. Our findings are applicable to audits of binaryclassification models and multiple fairness metrics derived as summaries of theconfusion matrix. Furthermore, we discuss other aspects of audit study designsthat can increase the reliability of audit results.

A Brief Tutorial on Sample Size Calculations for Fairness Audits