# Comparing Population Means under Local Differential Privacy: with Significance and Power

arXiv: https://arxiv.org/abs/1803.09027 · HTML: https://mlsanity.com/paper/1803.09027/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2018.

## Built on by (most cited first, 5 of 5)

- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation](https://mlsanity.com/paper/2202.07194/) (2022)
- [Decentralized Collaborative Learning with Probabilistic Data Protection](https://mlsanity.com/paper/2208.10674/) (2022)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [DPpack: An R Package for Differentially Private Statistical Analysis and Machine Learning](https://mlsanity.com/paper/2309.10965/) (2023)

## Abstract (arXiv)

A statistical hypothesis test determines whether a hypothesis should be rejected based on samples from populations. In particular, randomized controlled experiments (or A/B testing) that compare population means using, e.g., t-tests, have been widely deployed in technology companies to aid in making data-driven decisions. Samples used in these tests are collected from users and may contain sensitive information. Both the data collection and the testing process may compromise individuals' privacy. In this paper, we study how to conduct hypothesis tests to compare population means while preserving privacy. We use the notation of local differential privacy (LDP), which has recently emerged as the main tool to ensure each individual's privacy without the need of a trusted data collector. We propose LDP tests that inject noise into every user's data in the samples before collecting them (so users do not need to trust the data collector), and draw conclusions with bounded type-I (significance level) and type-II errors (1 - power). Our approaches can be extended to the scenario where some users require LDP while some are willing to provide exact data. We report experimental results on real-world datasets to verify the effectiveness of our approaches.