# Differentially Private Nonparametric Hypothesis Testing

arXiv: https://arxiv.org/abs/1903.09364 · HTML: https://mlsanity.com/paper/1903.09364/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2019.

## Built on by (most cited first, 12 of 12)

- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021)
- [Robust Kernel Hypothesis Testing under Data Corruption](https://mlsanity.com/paper/2405.19912/) (2024)
- [Nonparametric extensions of randomized response for private confidence sets](https://mlsanity.com/paper/2202.08728/) (2022)
- [Does Differentially Private Synthetic Data Lead to Synthetic Discoveries?](https://mlsanity.com/paper/2403.13612/) (2024)
- [Private Sequential Hypothesis Testing for Statisticians: Privacy, Error Rates, and Sample Size](https://mlsanity.com/paper/2204.04597/) (2022)
- [Differentially private Bayesian tests](https://mlsanity.com/paper/2401.15502/) (2024)
- [DP-SPRT: Differentially Private Sequential Probability Ratio Tests](https://mlsanity.com/paper/2508.06377/) (2025)
- [Differentially Private Conditional Independence Testing](https://mlsanity.com/paper/2306.06721/) (2023)
- [DPpack: An R Package for Differentially Private Statistical Analysis and Machine Learning](https://mlsanity.com/paper/2309.10965/) (2023)
- [Near-Optimal Private Tests for Simple and MLR Hypotheses](https://mlsanity.com/paper/2601.21959/) (2026)

## Abstract (arXiv)

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.