Monotonicity of Rank Statistics in some Non–parametric: Testing Problems

B.F. Schriever

Statistica Neerlandica, 1987, vol. 41, issue 2, 99-109

Abstract: For some non–parametric testing problems (one–sided two–sample problem, k–sample trend problem, testing independence against positive dependence) a partial ordering, denoted by ≥, over the alternatives is defined. This partial ordering expresses the strength of the deviation from the null–hypothesis. All familiar rank tests turn out to become more powerful under “increasing” alternatives; that is, all familiar rank statistics preserve the ordering stochastically in samples whenever it is present between underlying distributions. As a tool, the sample equivalence of ≥ is introduced as a partial ordering over pairs of permutations. Functions, defined on pairs of permutations, which preserve this ordering are studied.

Date: 1987
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