# Equivalence Testing Under Privacy Constraints

arXiv: https://arxiv.org/abs/2604.06499 · HTML: https://mlsanity.com/paper/2604.06499/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 57 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing](https://mlsanity.com/paper/1602.03090/) (2016)
- [Hypothesis Testing for Differentially Private Linear Regression](https://mlsanity.com/paper/2206.14449/) (2022)
- [Differentially Private Inference for Binomial Data](https://mlsanity.com/paper/1904.00459/) (2019)
- [An accurate percentile method for parametric inference based on asymptotically biased estimators](https://mlsanity.com/paper/2405.05403/) (2024)
- [Cybersecurity and Frequent Cyber Attacks on IoT Devices in Healthcare: Issues and Solutions](https://mlsanity.com/paper/2501.11250/) (2025)
- [Fiducial Matching: Differentially Private Inference for Categorical Data](https://mlsanity.com/paper/2507.11762/) (2025)

## Abstract (arXiv)

Protecting individual privacy is essential across research domains, from socio-economic surveys to big-tech user data. This need is particularly acute in healthcare, where analyses often involve sensitive patient information. A typical example is comparing treatment efficacy across hospitals or ensuring consistency in diagnostic laboratory calibrations, both requiring privacy-preserving statistical procedures. However, standard equivalence testing procedures for differences in proportions or means, commonly used to assess average equivalence, can inadvertently disclose sensitive information. To address this problem, we develop differentially private equivalence testing procedures that rely on simulation-based calibration, as the finite-sample distribution is analytically intractable. Our approach introduces a unified framework, termed DP-TOST, for conducting differentially private equivalence testing of both means and proportions. Through numerical simulations and real-world applications, we demonstrate that the proposed method maintains type-I error control at the nominal level and achieves power comparable to its non-private counterpart as the privacy budget and/or sample size increases, while ensuring strong privacy guarantees. These findings establish a reliable and practical framework for privacy-preserving equivalence testing in high-stakes fields such as healthcare, among others.