Highly private large‐sample tests for contingency tables

Differential privacy is a foundational concept for safeguarding sensitive individual information when releasing data or statistical analysis results. In this study, we concentrate on the protection of privacy in the context of goodness‐of‐fit (GOF) and independence tests, utilizing perturbed contingency tables that adhere to Gaussian differential privacy within the high‐privacy regime, where the degrees of privacy protection increase as the sample size increases. We introduce private test procedures for GOF, independence of two variables and the equality of proportions in paired samples, similar to McNemar's test. For each of these hypothesis testing situations, we propose private test statistics based on the statistics and establish their asymptotic null distributions. We numerically confirm that Type I error rates of the proposed private test procedures are well controlled and have adequate power for larger sample sizes and effect sizes. The proposal is demonstrated in private inferences based on the American Time Use Survey data.