Permutation tests are widely recognized as robust alternatives to tests based on normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use, existing random permutation tests lack finite-sample and assumption-free guarantees for controlling type I error in partial correlation tests. To address this ongoing challenge, we have developed a conformal test through permutation-augmented regressions, which we refer to as PALMRT. PALMRT not only achieves power competitive with conventional methods but also provides reliable control of type I errors at no more than $2\alpha$, given any targeted level $\alpha$, for arbitrary fixed designs and error distributions. We have confirmed this through extensive simulations. Compared to the cyclic permutation test (CPT) and residual permutation test (RPT), which also offer theoretical guarantees, PALMRT does not compromise as much on power or set stringent requirements on the sample size, making it suitable for diverse biomedical applications. We further illustrate the differences in a long-Covid study where PALMRT validated key findings previously identified using the t-test after multiple corrections, while both CPT and RPT suffered from a drastic loss of power and failed to identify any discoveries. We endorse PALMRT as a robust and practical hypothesis test in scientific research for its superior error control, power preservation, and simplicity. An R package for PALMRT is available at \url{https://github.com/LeyingGuan/PairedRegression}.

翻译：排列检验被广泛视为基于正态理论检验的稳健替代方法。随机排列检验常被用于评估线性模型中变量的显著性。尽管应用广泛，现有随机排列检验在偏相关系数检验中缺乏有限样本且无分布假设的I类错误控制保证。为应对这一持续挑战，我们通过排列增强回归开发了一种共形检验，称为PALMRT。PALMRT在任意固定设计和误差分布下，不仅可达到与传统方法相当的统计功效，还能在给定任意目标水平α时，将I类错误可靠控制在不超过2α的范围内。我们通过大量模拟研究验证了这一结论。与同样提供理论保证的循环排列检验（CPT）和残差排列检验（RPT）相比，PALMRT在功效上损失更少，且对样本量无严格限制，因此适用于多种生物医学应用。我们进一步通过一项长新冠研究揭示了差异：在该研究中，PALMRT验证了经多重校正后t检验识别的关键发现，而CPT和RPT均因统计功效大幅下降而未能发现任何显著结果。我们推荐PALMRT作为科学研究中稳健且实用的假设检验方法，因其在错误控制、功效保持及简洁性方面的优越表现。PALMRT的R语言包可在\url{https://github.com/LeyingGuan/PairedRegression}获取。