Differentially Private ANOVA Testing
This enables researchers in sciences and social sciences to release ANOVA results from sensitive databases with provable privacy guarantees, addressing a specific statistical need.
The paper tackles the problem of conducting ANOVA tests on sensitive data while preserving differential privacy, presenting the first algorithm for this purpose and showing that a sample of several thousand observations is often sufficient to detect group variations.
Modern society generates an incredible amount of data about individuals, and releasing summary statistics about this data in a manner that provably protects individual privacy would offer a valuable resource for researchers in many fields. We present the first algorithm for analysis of variance (ANOVA) that preserves differential privacy, allowing this important statistical test to be conducted (and the results released) on databases of sensitive information. In addition to our private algorithm for the F test statistic, we show a rigorous way to compute p-values that accounts for the added noise needed to preserve privacy. Finally, we present experimental results quantifying the statistical power of this differentially private version of the test, finding that a sample of several thousand observations is frequently enough to detect variation between groups. The differentially private ANOVA algorithm is a promising approach for releasing a common test statistic that is valuable in fields in the sciences and social sciences.