A robust Spearman correlation coefficient permutation test

In this work, we show that Spearman’s correlation coefficient test about (Formula presented.) found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about (Formula presented.) are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis (Formula presented.) based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples.