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Subject: mixed design

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    Nonparametric Test for Nondecreasing Order Alternatives in Randomized Complete Block and Balanced Incomplete Block Mixed Design
    (North Dakota State University, 2020) Osafo, Mamfe
    Nonparametric tests are used to test hypotheses when the data at hand violate one or more of the assumptions for parametric tests procedures. The test is an ordered alternative (nondecreasing) when there is prior information about the data. It assumes that the underlying distributions are of the same type and therefore differ in location. For example, in dose-response studies, animals are assigned to k groups corresponding to k doses of an experimental drug. The effect of the drug on the animals is likely to increase or decrease with increasing doses. In this case, the ordered alternative is appropriate for the study. In this paper, we propose eight new nonparametric tests useful for testing against nondecreasing order alternatives for a mixed design involving randomized complete block and balanced incomplete block design. These tests involve various modifications of the Jonckheere-Terpstra test (Jonckheere(1952), Terpstra(1954)) and Alvo and Cabilio’s test (1995). Three, four and five treatments were considered with different location parameters under different scenarios. For three and four treatments, 6,12, and 18 blocks were used for the simulation, while 10, 20, and 30 blocks were used for five treatments. Different tests performed best under different block combinations, but overall the standardized last for Alvo outperformed the other test when the number of treatments and number of missing observations per block increases. A simulation study was conducted comparing the powers of the various modification of Jonckheere-Terpstra (Jonckheere(1952), Terpstra(1954)) and Alvo and Cabilio’s (1995) tests under different scenarios. Recommendations are made.
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    Proposed Nonparametric Tests for the Umbrella Alternative in a Mixed Design for Both Known and Unknown Peak
    (North Dakota State University, 2019) Alsuhabi, Hassan Rashed
    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.