K-Sample Rank Tests for Umbrella Alternatives

Abstract

Distribution-free test procedures are proposed for the k -sample problem, where the alternatives of interest are of the form F 1 (x) ≥ ··· ≥ F ℓ (x) ≤ ··· ≤ F k (x) for all x , with at least one strict inequality. These are referred to as umbrella alternatives, and both the ℓ (point of umbrella) known and ℓ unknown settings are considered. Small sample null distributions are discussed, and the results of a Monte Carlo power study are presented. A detailed example illustrating the use of the unknown umbrella point procedure is also given.