Multi-sample rank tests for location against Lehmann-type alternatives

TL;DR

This paper introduces new rank tests for comparing multiple distributions under stochastic ordering, extending Lehmann's two-sample approach, and demonstrates their distribution-free property and power comparison with existing tests.

Contribution

It proposes two classes of rank tests for multiple samples against Lehmann-type alternatives, extending existing methods and establishing their distribution-free nature.

Findings

The new tests are distribution free under Lehmann-type alternatives.

Power of the proposed tests is compared favorably to the Jonckheere-Terpstra test.

The tests extend two-sample rank methods to multiple samples.

Abstract

This paper deals with testing the equality of $k$ ($k\ge 2$) distribution functions against possible stochastic ordering among them. Two classes of rank tests are proposed for this testing problem. The statistics of the tests under study are based on precedence and exceedance statistics and are natural extension of corresponding statistics for the two-sample testing problem. Furthermore, as an extension of the Lehmann alternative for the two-sample location problem, we propose a new subclass of the general alternative for the stochastic order of multiple samples. We show that under the new Lehmann-type alternative any rank test statistics is distribution free. The power functions of the two new families of rank tests are compared to the power performance of the Jonckheere-Terpstra rank test.