Abstract: Randomized response is one of the oldest and most well-known methods used to analyze confidential data. However, its utility for differentially private hypothesis testing is limited because it cannot simulaneously achieve high privacy levels and low type-I error rates. We overcome this problem using the subsample and aggregate technique. The result is a general-purpose method that can be used for both frequentist and Bayesian testing. We demonstrate the performance of the proposed method in three scenarios: goodness-of-fit testing for linear regression models, nonparametric testing of a location parameter using the Wilcoxon test, and the nonparametric Kruskal–Wallis test.

Key words and phrases: Bayesian hypothesis testing, differential privacy, hypothesis testing, randomized response.