  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.
