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Statistical hypothesis test is an important data analysis technique that has found applications in a variety of research fields. In this paper, we investigate one of the fundamental test theories: the nonparametric Sign Test (NST) theory, under the privacy-preserving context. In this context, two parties, each with a private dataset, would like to conduct a sign test on their joint dataset, but neither of them is willing to disclose its private dataset to the other party or any other third party. To support this computation, we transform the NST algorithm into a privacy-preserving two-party nonparametric sign test (P22NST) protocol. More specifically, this paper addresses this situation using a vertically partitioned data model. We design five building blocks to address this P22NSTv problem based on data disguising techniques. The performance of the protocol, in terms of security, communication and computation cost is evaluated against the solution where a trusted third party (TTP) is used. This paper proposes an alternative to address the P22NSTv problem: our P22NSTv protocol does not make use of any third party nor cryptographic primitives. Our result shows that, with some more computation and communication efforts, our protocol achieves a similar level of security as the TTP model.