A method for generating permutation distribution of ranks in a k-sample experiment.

Abstract

A method for generating exhaustive permutation distribution of the ranks in a k-sample experiment is presented. This provides a methodology for constructing exact test of significance of a rank statistic. The proposed method is linked to the partition of integers and in a combinatorial sense the distribution of the ranks is obtained via its generating function. The formulas are defined recursively to speed up computations using the computer algebra system Mathematica.

Key words: Partitions, generating functions, combinatorics, permutation test, exact tests, computer algebra, k-sample, rank statistics.