which is distributed approximately as Student's t distribution with n − 2 degrees of freedom under the null hypothesis.[9] A justification for this result relies on a permutation argument.[10]
pvrank[11] is a very recent R package that computes rank correlations and their p-values with various options for tied ranks. It is possible to compute exact Spearman coefficient test p-values for n ≤ 26.
A generalization of the Spearman coefficient is useful in the situation where there are three or more conditions, a number of subjects are all observed in each of them, and it is predicted that the observations will have a particular order. For example, a number of subjects might each be given three trials at the same task, and it is predicted that performance will improve from trial to trial. A test of the significance of the trend between conditions in this situation was developed by E. B. Page[12] and is usually referred to as Page's trend test for ordered alternatives.