Comparing population means under local differential privacy: With significance and power

Abstract

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.