# Improved Differentially Private Analysis of Variance

arXiv: https://arxiv.org/abs/1903.00534 · HTML: https://mlsanity.com/paper/1903.00534/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2019.

## Built on by (most cited first, 9 of 9)

- [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)
- [Private measurement of nonlinear correlations between data hosted across multiple parties](https://mlsanity.com/paper/2110.09670/) (2021)
- [Differentially private Bayesian tests](https://mlsanity.com/paper/2401.15502/) (2024)
- [Differentially private ratio statistics](https://mlsanity.com/paper/2505.20351/) (2025)
- [Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond](https://mlsanity.com/paper/2509.04919/) (2025)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [Optimal Rates for Differentially Private Hypothesis Testing with E-values](https://mlsanity.com/paper/2605.28952/) (2026)
- [Differentially Private Conditional Independence Testing](https://mlsanity.com/paper/2306.06721/) (2023)

## Abstract (arXiv)

Hypothesis testing is one of the most common types of data analysis and forms the backbone of scientific research in many disciplines. Analysis of variance (ANOVA) in particular is used to detect dependence between a categorical and a numerical variable. Here we show how one can carry out this hypothesis test under the restrictions of differential privacy. We show that the F-statistic, the optimal test statistic in the public setting, is no longer optimal in the private setting, and we develop a new test statistic F1 with much higher statistical power. We show how to rigorously compute a reference distribution for the F1 statistic and give an algorithm that outputs accurate p-values. We implement our test and experimentally optimize several parameters. We then compare our test to the only previous work on private ANOVA testing, using the same effect size as that work. We see an order of magnitude improvement, with our test requiring only 7% as much data to detect the effect.