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Nonparametric statistics are commonly used in the field of statistics due to their robustness when the underlying assumptions are violated for the usual parametric statistics. In this dissertation, we proposed eight nonparametric methods to test for nondecreasing ordered alternative for a mixed design consisting of a combination of completely randomized design (CRD) and randomized complete block design (RCBD). There were four nonparametric tests, based on the Jonckheere-Terpstra test and modifications of it, employed to propose these nonparametric methods. A Monte Carlo simulation study was conducted using SAS program to investigate the performance of the proposed tests under a variety of nondecreasing location shifts among three, four and five populations and then compare these powers to each other and with the powers of the test statistics introduced by Magel et al. (2009). Three underlying distributions are used in the study including the standard normal distribution, the standard exponential distribution and student's t-distribution (3 degrees of freedom). We considered three scenarios of proportions of the number of blocks in the RCBD portion to the sample size in the CRD portion, namely, assuming that the portion of the number of blocks in RCBD is larger, equal, and smaller than the portion of the sample size in the CRD. Moreover, equal and unequal sample sizes were both considered for the CRD portion. The results of the simulation study indicate that all the proposed methods maintain their type one error and also indicate that at least one of the proposed methods did better compared to the tests of Magel et al. (2009) in terms of the estimated powers. In general, situations are found in which the proposed methods have higher powers and situations are found in which tests in Magel et al. (2009) have higher powers. |
