For a general class of problems, the permutation of observations is the only possible method of truly constructing exact tests of significance. The exact sampling distribution of a test statistic for an experiment compiled by the permutation approach requires no reference to a population distribution and therefore no requirement that it should conform to a mathematically definable frequency distribution. Algorithms for the exact permutation distribution of correlation coefficients is presented and implemented. As an illustrative example, critical values for Pearson's product moment and Spearman's rank correlation coefficients are produced for Charles Darwin's data on the heights of cross and self fertilized plants.