Nonparametric Methods for the Nondecreasing Ordered Hypothesis in a Mixed Design

Aims: Introduce two new test statistics in testing for the nondecreasing alternative in a mixed design consisting of a Completely Randomized Portion and a Randomized Complete Block Portion.

Study Design: Simulation study comparing four test statistics for the nondecreasing alternative in a mixed design consisting of a CRD and an RCBD portion. The test statistics included two new test statistics and two existing test statistics. Random samples were taken from three different types of underlying distributions. Different percentages of the CRD portion will be considered as well as different sample sizes. Powers were estimated based on a variety location parameter shifts. Three, four, and five populations were considered.

Place and Duration of Study: The simulation study took place on the campus of North Dakota State University during the calendar year 2019.

Methodology: Levels of significance for each of the three types of underlying distributions, when the RCBD portion was larger than the CRD portion, when the CRD portion was larger than the RCBD portion, and when the CRD portion was equal to the RCBD portion, and when the number of populations were 3, 4, and 5.

Results: Regardless of the underlying population types, the proposed test statistics did better than the existing test statistics when the difference between the last two parameters is large. This was true for 3, 4, and 5 populations.

Conclusion: When the differences between the last two parameters is large, the two new test statistics performed better. Otherwise, the existing test statistics are better. In both cases, it is better to use the combined test statistic that first standardizes the individual test statistics for the CRD and RCBD portions before adding them together.