| dc.description.abstract | 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. | en_US |
