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Abstract:
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In the paired data setting three classical tests are often recommended: 1) The paired t-test, 2) The Wilcoxon signed-rank test and 3) The sign-test. The sign-test is oftentimes touted as a robust nonparametric alternative to the t-test and Wilcoxon signed-rank test, and is often described as a test for comparing medians of two marginal distributions when the distributions of the paired differences is non-normal and asymmetric. What is often overlooked in this setting is that there is an additional set of assumptions needed when utilizing the sign-test in this manner. If these assumptions are not met one may potentially declare two identical marginal distributions different when in fact they are identical, something we term the false-interpretation probability. We illustrate the false-interpretation concept via theory, a simulation study and through a real-world example from the Cancer Genome Atlas (TCGA) breast cancer RNA sequencing data.
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