Running Head: CORRELATION WITH NON-NORMAL DATA 1 Testing the Significance of a Correlation with Non-normal Data: Comparison of Pearson, Spearman, Transformation, and Resampling Approaches

It is well known that when data are non-normally distributed, a test of the significance of Pearson's r may inflate Type I error rates and reduce power. Statistics textbooks and the simulation literature provide several alternatives to Pearson’s correlation. However, the relative performance of these alternatives has been unclear. Two simulation studies were conducted to compare 12 methods, including Pearson, Spearman's rank-order, transformation, and resampling approaches. With most sample sizes (N ≥ 20), Type I and Type II error rates were minimized by transforming the data to a normal shape prior to assessing the Pearson correlation. Among transformation approaches, a general purpose Rank-Based Inverse Normal transformation (i.e., transformation to rankit scores) was most beneficial. However, when samples were both small (N ≤ 10) and extremely non-normal, the permutation test often outperformed other alternatives, including various bootstrap tests.