Nonparametric test for the umbrella alternative with known peak in a mixed design

Abstract

This paper proposes test statistics for detecting umbrella alternative with known peak when the data are a mixture of a randomized complete block and a completely randomized design. Modifications of the Mack-Wolfe and Kim-Kim test are proposed to develop the two statistics for a mixed design. The exact mean and variance of the modified versions of Mack-Wolfe and Kim-Kim test statistic under the null distribution are derived. The proposed test statistics are compared, through a simulation study, to each other and with some of the existing tests in terms of assessing the power and the type I error. Results are given.