Spacing tests for the K-sample problem and random ordering

Distribution-free goodness-of-fit techniques to assess random partitioning of the rank population into disjoint subsets are proposed for analysis with the nonparametric K-sample problem and tests of random ordering for a multisymbol alphabet. Following the approach in Boos (1986) and Kaigh (1996a), linear algebraic mathematical development yields rank spacing and rank indicator orthogonal component procedures for directional and omnibus detection of between-sample differences. Real data sets are used to illustrate the random partition component procedures and Monte Carlo power results to compare spacing and indicator statistics are presented.