A non-parametric test for umbrella alternatives based on ranked-set sampling

A test is proposed that extends the Chen-Wolfe (1990) test for umbrella alternatives with an unknown peak to use with ranked-set samples data. This follows from ideas in Bohn & Wolfe (1992), Magel (1994), and Hartlaub & Wolfe (1999). Critical values are simulated for the proposed test based on ranked-set samples of size 2 for 3, 4 and 5 populations. A power study is conducted comparing the proposed test using ranked-set samples with the Chen-Wolfe and Mack-Wolfe tests using simple random samples. Results are given.