| dc.description.abstract | Researchers sometimes use the umbrella alternative when testing for differences in treatment effects, where the parameters increase up to a point and decrease after that point. Sometimes different treatment effects may result in changes to location parameters only, to scale parameters only, or to both. In this study, we considered tests for three distinct scenarios; the tests in each scenario were compared based on estimated power for the different underlying distributions and on different known umbrella peaks that were based on 3, 4, or 5 populations. For all three scenarios, recommendations for which test was better will be given in a variety of cases.
In scenario one, this research investigates existing test statistics proposed by Magel et al. (2010) for detecting umbrella alternatives when the peak is known, and the underlying design consists of a completely randomized design (CRD) and randomized complete block design (RCBD). We investigate the powers of the tests compared to each other when testing for location in this design when the variance of the CRD portion is 2, 4, and 9 times larger than the variance of the RCBD portion. Three underlying distributions, a variety of location shifts, and different ratios between the sample size in the CRD portion compared to the number of blocks in the RCBD portion are considered.
In the second scenario, three nonparametric tests are proposed for a CRD design with k populations to test for the umbrella alternative with known peak, p, for both location and scale parameters. A simulation study was implemented to see if the proposed tests maintained their significance levels. Also, the tests proposed were compared based on estimated powers for sample sizes of 15 and a variety of location and scale shifts.
In the third scenario, we proposed nonparametric test statistics to test for an umbrella pattern testing for location and scale for a mixed design. Powers were estimated for different ratios of sample size in the CRD to the number of blocks in the RCBD and equal variance ratios between a CRD and a RCBD, as well as changes in the location and scale parameters. | en_US |
