  Randomized response is one of the oldest and most well-known methods for
analyzing confidential data. However, its utility for differentially private
hypothesis testing is limited because it cannot achieve high privacy levels and
low type I error rates simultaneously. In this article, we show how to overcome
this issue with the subsample and aggregate technique. The result is a
general-purpose method that can be used for both frequentist and Bayesian
testing. {{We illustrate the performance of our proposal in three scenarios:
goodness-of-fit testing for linear regression models, nonparametric testing of
a location parameter with the Wilcoxon test, and the nonparametric
Kruskal-Wallis test.
