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arXiv · 2507.03725

Differentially private scale testing via rank transformations and percentile modifications

Joshua Levine·Kelly Ramsay
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Abstract

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.

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Joshua Levine, Kelly Ramsay. 2025-07-04. Differentially private scale testing via rank transformations and percentile modifications. https://arxiv.org/abs/2507.03725

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