Proposed Nonparametric Tests for the Simple Tree Alternative in a Mixed Design

• Main Author: Olet, Susan
• Format: Others
• Published: North Dakota State University 2018
• Online Access: https://hdl.handle.net/10365/27365

For the general alternative, many test statistics exist for the dependent and independent variables. However, no documented test statistics exist for simple tree alternative for the dependent variables, independent variables, and mixed designs that consider both dependent and independent variables. This research proposes six nonparametric test statistics when we have a mixed design that consists of observations from a Randomized Complete Block Design (RCBD) and a Completely Randomized Design (CRD). A simulation was conducted to compare the proposed test statistics under five conditions: changing number of treatments, varying the underlying distribution, increasing the variance between the RCBD and CRD, changing the proportions of the RCBD portion to the CRD, and changing the shifts configurations for the treatment effects. The simulation results indicate that Approach II and Approach VI had the highest powers overall. Approach II is when equal weight √ is assigned to the standardized modified Fligner-Wolfe and standardized modified Page’s test statistic. While, Approach VI is when more weight, attributed to the sample size is assigned to the standardized modified Fligner-Wolfe, the CRD portion and less weight attributed to small number of blocks is assigned to the standardized modified Page’s test statistic, which is the RCBD portion of the mixed design. It was noted that, when the sample size was greater than the number of blocks and the RCBD and CRD variances are equal, Approach VI had the highest powers. On the other hand, when the variance in the CRD was greater than the variance of RCBD, Approach II had the highest powers. Also, when the number of blocks for the RCBD portion is greater than the sample size for the CRD portion in the mixed design, Approach II had the highest powers when the variance in the CRD portion was equal to the variance in the RCBD portion. On the other hand, when the variance in the CRD portion was greater than the variance in the RCBD portion Approach VI had the highest powers.