Correlation analysis: Exact permutation paradigm

Abstract

For a general class of problems, the permutation of observations isthe only possible method of truly constructing exact tests ofsignificance. The exact sampling distribution of a test statisticfor an experiment compiled by the permutation approach requires noreference to a population distribution and therefore no requirementthat it should conform to a mathematically definable frequencydistribution. Algorithms for the exact permutation distribution ofcorrelation coefficients is presented and implemented. As anillustrative example, critical values for Pearson's product momentand Spearman's rank correlation coefficients are produced forCharles Darwin's data on the heights of cross and self fertilized plants.