# Revisiting Differentially Private Hypothesis Tests for Categorical Data

arXiv: https://arxiv.org/abs/1511.03376 · HTML: https://mlsanity.com/paper/1511.03376/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2015.

## Built on by (most cited first, 4 of 4)

- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021)
- [Nonparametric extensions of randomized response for private confidence sets](https://mlsanity.com/paper/2202.08728/) (2022)
- [One-Shot Private Confidence Regions via Resampling](https://mlsanity.com/paper/2610.08460/) (2026)

## Abstract (arXiv)

In this paper, we consider methods for performing hypothesis tests on data protected by a statistical disclosure control technology known as differential privacy. Previous approaches to differentially private hypothesis testing either perturbed the test statistic with random noise having large variance (and resulted in a significant loss of power) or added smaller amounts of noise directly to the data but failed to adjust the test in response to the added noise (resulting in biased, unreliable p-values). In this paper, we develop a variety of practical hypothesis tests that address these problems. Using a different asymptotic regime that is more suited to hypothesis testing with privacy, we show a modified equivalence between chi-squared tests and likelihood ratio tests. We then develop differentially private likelihood ratio and chi-squared tests for a variety of applications on tabular data (i.e., independence, sample proportions, and goodness-of-fit tests). Experimental evaluations on small and large datasets using a wide variety of privacy settings demonstrate the practicality and reliability of our methods.