Differentially Private ANOVA Testing

By Zachary Campbell, Andrew Bray, Anna M. Ritz, Adam Groce. 2017

29 citations recorded by the source corpus.

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 sufficient 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.

Subfields: Artificial Intelligence, Computer Science Applications

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Citations in the corpus

The structure of optimal private tests for simple hypotheses (2018, background): “One line of work [WLK15, GLRV16, KR17, KSF17, CBRG18, SGHG + 19, CKS + 19] designs differentially private versions of popular test statistics for testing goodness-of-ﬁt, closeness, and independence, as well as private ANOVA, focusing on the performance at small sample sizes.”
Differentially Private Nonparametric Hypothesis Testing (2019, background): “Two works have studied differentially private versions of one-way analysis of variance (ANOVA) [5,31].”
Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation (2019, background): “Mean estimation also naturally arises in hypothesis testing [33, 18, 7, 9, 10, 8].”
Improved Differentially Private Analysis of Variance (2019, background): “While it may be tempting to compute the p-value using the reference distribution for the non-private statistic one is estimating, this may yield wildly inaccurate results [3], because adding noise to the statistic increases the probability of outlier output values.”