Proposed Nonparametric Tests for the Umbrella Alternative in a Mixed Design for Location and Scale

Aims: To develop and compare tests for a mixed design of a Randomized Complete Block Design (RCBD) with a Completely Randomized Design (CRD) with k populations in testing for the umbrella alternative with known peak, p, for both location and scale parameters. These tests were combinations of the Mack-Wolfe test, the Kim-Kim test, and both the Mack-Wolfe test, and the Kim-Kim test using the Moses technique.

Study Design: Monte Carlo Simulation Study.

Place and Duration of Study: North Dakota State University, Department of Statistics, August 2020-December 2021.

Methodology: A simulation study was conducted to see how well the proposed tests maintained their significant levels. Powers were also estimated for different ratios of sample size in the CRD to the number of blocks in the RCBD; we assumed equal variance ratios between the CRD and the RCBD. Different parameter changes were considered to see if they would impact which test statistics had greater power. In all cases, it was assumed three observations per treatment, per block in the RCBD portion.

Conclusion: All proposed tests maintained their significance levels. An overall test is recommended if both location and scale parameters change.