Rankit correlations

The rankit correlation is easily computed in any statistical package using a transform of the two variables being correlated and has been recommended by Bishara and Hittner (2012) when correlating data that is assymmetric or heavy tailed. They conclude that

"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 nonnormal, a permutation test often outperformed other alternatives, including various bootstrap tests."

The rankit transformation for x is of form

rankit(x) = $$\mbox{INV.NORMAL}(\frac{x - 0.5){n})$$

Reference

Bishara AJ and Hittner JB (2012) Testing the Significance of a Correlation With Nonnormal Data: Comparison of Pearson, Spearman, Transformation, and Resampling Approaches. Psychological Methods 17(3) 399-417.