  Hypothesis tests are a crucial statistical tool for data mining and are the
workhorse of scientific research in many fields. Here we study differentially
private tests of independence between a categorical and a continuous variable.
We take as our starting point traditional nonparametric tests, which require no
distributional assumption (e.g., normality) about the data distribution. We
present private analogues of the Kruskal-Wallis, Mann-Whitney, and Wilcoxon
signed-rank tests, as well as the parametric one-sample t-test. These tests use
novel test statistics developed specifically for the private setting. We
compare our tests to prior work, both on parametric and nonparametric tests. We
find that in all cases our new nonparametric tests achieve large improvements
in statistical power, even when the assumptions of parametric tests are met.
