Differentially private scale testing via rank transformations and percentile modifications
This work addresses the need for privacy-preserving statistical tests in data analysis, representing an incremental improvement by adapting existing rank test methods to differential privacy.
The authors tackled the problem of performing differentially private two-sample scale tests by developing RPST tests, which are differentially private and control type I error, with simulations showing the tradeoff between power and sensitivity based on rank transformation growth rates.
We develop a class of differentially private two-sample scale tests, called the rank-transformed percentile-modified Siegel--Tukey tests, or RPST tests. These RPST tests are inspired both by recent differentially private extensions of some common rank tests and some older modifications to non-private rank tests. We present the asymptotic distribution of the RPST test statistic under the null hypothesis, under a very general condition on the rank transformation. We also prove RPST tests are differentially private, and that their type I error does not exceed the given level. We uncover that the growth rate of the rank transformation presents a tradeoff between power and sensitivity. We do extensive simulations to investigate the effects of the tuning parameters and compare to a general private testing framework. Lastly, we show that our techniques can also be used to improve the differentially private signed-rank test.