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：置换检验被广泛视为正态理论检验的稳健替代方法。随机置换检验常用于评估线性模型中变量的显著性。尽管应用广泛，现有随机置换检验在偏相关检验中缺乏有限样本和无假设前提的控制I类错误保证。针对这一持续挑战，我们通过置换增强回归开发了一种共形检验，命名为PALMRT。PALMRT不仅达到与传统方法相当的检验功效，还能在任意目标水平α下，针对任意固定设计和误差分布，将I类错误可靠控制在不超过2α的水平。大量模拟实验证实了这一点。与同样提供理论保证的循环置换检验（CPT）和残差置换检验（RPT）相比，PALMRT在检验功效上损失更少，且不对样本量设置严格限制，适用于多种生物医学应用。我们进一步在长新冠研究中展示了差异——PALMRT验证了之前经多重校正后通过t检验识别的关键发现，而CPT和RPT均因检验功效大幅降低未能识别任何结果。鉴于其优越的错误控制能力、检验功效保持性及简便性，我们推荐PALMRT作为科学研究中稳健且实用的假设检验方法。PALMRT的R软件包可从\url{https://github.com/LeyingGuan/PairedRegression}获取。