ABSTRACT

In the paired data setting, the sign test is often described in statistical textbooks as a test for comparing differences between the medians of two marginal distributions. There is an implicit assumption that the median of the differences is equivalent to the difference of the medians when employing the sign test in this fashion. We demonstrate however that given asymmetry in the bivariate distribution of the paired data, there are often scenarios where the median of the differences is not equal to the difference of the medians. Further, we show that these scenarios will lead to a false interpretation of the sign test for its intended use in the paired data setting. We illustrate the false-interpretation concept via theory, a simulation study, and through a real-world example based on breast cancer RNA sequencing data obtained from the Cancer Genome Atlas (TCGA).

 抽象的

在配对数据设置中，符号检验通常在统计教科书中描述为比较两个边际分布中位数之间差异的检验。有一个隐含的假设，即以这种方式采用符号检验时，差异的中位数等于中位数的差。然而，我们证明，鉴于配对数据的二元分布的不对称性，经常存在差异中位数不等于中位数差的情况。此外，我们表明这些场景将导致对符号测试在配对数据设置中的预期用途的错误解释。我们通过理论、模拟研究以及基于从癌症基因组图谱 (TCGA) 获得的乳腺癌 RNA 测序数据的现实示例来说明错误解释的概念。