All Times ET
Keywords: Randomized complete block design; completely randomized block design; incomplete block design; Mack-Wolfe test; Kim-Kim test; Magel-Ndungu test; peak known; modification test.
Aims: Introducing and comparing six different tests for the umbrella alternative in a mixed design for a known peak.
Study Design: Simulation study consisting of a randomized complete block design, a completely randomized design, and a balanced incomplete block design portions for various underlying distributions.
Place and Duration of Study: Simulation study was conducted at North Dakota State University from June 2018 through May 2020.
Methodology: This paper proposes six nonparametric tests for testing the umbrella alternative with known peak when the data are mixtures of a randomized complete block design, a completely randomized design, and a balanced incomplete block design. The proposed tests consist of various combinations of the usual and modified Mack-Wolfe test, the usual and modified Kim-Kim test, and the usual and modified Magel-Ndungu test respectively. The tests consist of the following combinations. a.Nonmodification Mack-Wolfe test, nonmodification Kim-Kim test, and nonmodification Magel-Ndungu test b.Distance (modified) Mack-Wolfe test, distance Kim-Kim test, and distance Magel-Ndungu test, c.Squared distance (modified) Mack-Wolfe test, squared distance Kim-Kim test, and squared distance Magel-Ndungu test. The proposed test statistics are standardized. There are two types of standardized tests. These are standardized first and standardized last. Results of these standardized tests are compared to each other. Results: When there were 3 populations, the standardized first versions of the test statistics was seen to have performed better. Results were seen to vary when the population parameters were 4 and 5.
Conclusion: The standardized first versions of the test generally was seen to perform better that the standardized last versions of the test statistics.