Permutation is an attractive approach to assess association between two vectors x and y, by comparing the observed statistic to the distribution induced by random permutation of one of the vectors. For a number of “standard” statistics, equivalent testing can be performed by using the sample Pearson correlation. Applications include the standard tests applied in the two-sample problem, simple linear regression, several generalized linear models, linear categorical trend tests, and rank-based association. We describe a simple approximation to the distribution of the correlation under permutation, providing accurate p-values that can be quickly computed for a variety of data types. The approximation may be especially useful in high-throughput applications in which a series of x-vectors is compared to one or more y-vectors.
Zhou, Yi-Hui and Wright, Fred A., "Simple and accurate trend tests using a permutation approximation" (October 2012). The University of North Carolina at Chapel Hill Department of Biostatistics Technical Report Series. Working Paper 31.