Hypothesis testing is the workhorse statistical analysis in medical and social science research. In this talk I will discuss how hypothesis tests can be carried out on sensitive data while protecting privacy. In particular, we consider nonparametric tests, constructing private analogues to the classic Kruskal-Wallis, Mann-Whitney, and Wilcoxon tests. In traditional statistics, these nonparametric tests are less powerful than their parametric alternatives, which work in the special case of normally distributed data. We find that in the private setting our nonparametric tests are actually more powerful than the best known parametric tests, despite their reduced assumptions. This is joint work with Andrew Bray, Simon Couch, Zeki Kazan, and Kaiyan Shi.