rank correlation coefficient

Spearman's rank correlation coefficient is the product moment correlation applied to the ranks. In the case of where there are no tied ranks, this is algebraically equivalent to computing the value of

where di = difference in ranks of the ith pair and n is the number of data pairs. When n is reasonably small, this computation is very quick. When there are tied ranks the above formula is not algebraically equivalent to the pmcc applied to the ranks but is often used as a reasonable approximation.

Kendall's rank correlation coefficient: Sir Maurice Kendall proposed a measure of rank correlation based on the number of neighbour-swaps needed to move from one rank ordering to another. If Q is the minimum number of neighbour swaps needed in a set of data with n values then Kendall's coefficient is given by

Significance tests can then be carried out using critical values from books of statistical tables.

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