On rank statistics: An approach via metrics on the permutation group
This paper gives a general method to generate rank test statistics for two-sample or multisample problems using different metrics on the permutation group w.r.t. which rank tests are invariant. Some well-known tests such as Kendall's tau, Spearman's rho and Spearman's footrule are already well-known but use of the Hamming distance and the Ulam distance is a novel one. This method is applied systematically to: (i) the location problem --- one-sample, two-sample and multisample situation, (ii) the two-sample dispersion problem with equal medians, (iii) the two-way layout problem and (iv) the problem of testing for trend. The paper also derives some combinatorial and group theoretic properties of the above metrics that play a key role in the computation of the corresponding test statistics.
two-sample dispersion problem with equal medians
scientific article; zbMATH DE number 95636
scientific article