论文标题
强大的Spearman相关系数置换测试
A Robust Spearman Correlation Coefficient Permutation Test
论文作者
论文摘要
在这项工作中，我们表明Spearman的相关系数测试约为$ H_0：ρ_s= 0 $在大多数统计软件包中发现的$ $ the Orty上是不正确的，并且当未满足双变量正态性假设或样本量很小时性能差。这些测试的历史作品是一个无法验证的假设，即原始数据的近似双变量正态性证明使用经典近似值证明了合理的合理性。通常，人们普遍认为，大约$ρ_s= 0 $的测试对于偏离双变量正态性是强大的。实际上，我们发现在某些情况下违反了双变量正态性假设对最常用的测试的I型误差控制有严重影响。为了解决此问题，我们开发了一项可靠的置换测试，用于测试一般假设$ H_0：ρ_s= 0 $。拟议的测试基于适当的学生统计数据。我们将证明，当两个配对变量不相关但取决于两个配对变量时，理论上测试在一般环境中是无效的。在模拟研究中，在一系列分布假设和样本量之间证明了这种所需的特性，即使样本量很小，拟议的测试在各种设置上都表现出强大的I型误差控制。我们证明了该测试在TCGA乳腺癌患者的转录组数据和PSA水平和年龄的数据集中的实例中应用。
In this work, we show that Spearman's correlation coefficient test about $H_0:ρ_s=0$ found in most statistical software packages is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. The historical works about these tests make an unverifiable assumption that the approximate bivariate normality of original data justifies using classic approximations. In general, there is common misconception that the tests about $ρ_s=0$ are robust to deviations from bivariate normality. In fact, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the most commonly utilized tests. To address this issue, we developed a robust permutation test for testing the general hypothesis $H_0: ρ_s=0$. The proposed test is based on an appropriately studentized statistic. We will show that the test is theoretically asymptotically valid in the general setting when two paired variables are uncorrelated but dependent. This desired property was demonstrated across a range of distributional assumptions and sample sizes in simulation studies, where the proposed test exhibits robust type I error control across a variety of settings, even when the sample size is small. We demonstrated the application of this test in real world examples of transcriptomic data of the TCGA breast cancer patients and a data set of PSA levels and age.
