Proposed Nonparametric Tests for the Umbrella Alternative in a Mixed Design for Both Known and Unknown Peak.

다국어 초록 (Multilingual Abstract)

In several situations, and among various treatment effects, researchers might test for an umbrella alternative. The need for an umbrella alternative arises in the evaluation of the reaction to drug dosage. For instance, the reaction might increase as the level of drug dosage increases, where after exceeding the optimal dosage a downturn may occur. A test statistic used for the umbrella alternative was proposed by Mack and Wolfe (1981) using a completely randomized design. Moreover, an extension of the Mack-Wolfe test for the randomized complete block design was proposed by Kim and Kim (1992), where the blocking factor was introduced. This thesis proposes two nonparametric test statistics for mixed design data with k treatments when the peak is known and four statistics when the peak is unknown. The data are a mixture of a CRD and an RCBD.A Monte Carlo simulation is conducted to compare the power of the first two proposed tests when the peak is known, and each one of them has been compared to the tests that were proposed by Magel et al. (2010). Also, it is conducted to compare the power of the last four proposed tests when the peak is unknown. In this study, we consider the simulation from exponential, normal and t distributions with 3 degrees of freedom. For every distribution, equal sample sizes for the CRD portion are selected so that the sample size, n, is 6, 10, 16 and 20. The number of blocks for the RCBD are considered to be half, equal and twice the sample size for each treatment. Furthermore, a variety of location parameter configurations are considered for three, four and five populations. The powers were estimated for both cases, known and unknown peak.In both cases, the results of the simulation study show that the proposed tests, in which we use the method of standardized first, generally perform better than those with standardized second. This thesis also shows that adding the distance modification to the Mack-Wolfe and Kim- Kim statistics provides more power to the proposed test statistics more than those without the application of the distance modification.