Abstract
Abstract Distribution-free test procedures are proposed for the k-sample problem, where the alternatives of interest are of the form F 1 (x) ≥ ··· ≥ Fl(x) ≤ ··· ≤ Fk (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.
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