Browsing by Author "Ndungu, Alfred Mungai"

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    A Nonparametric Test for the Non-Decreasing Alternative in an Incomplete Block Design
    (North Dakota State University, 2011) Ndungu, Alfred Mungai
    The purpose of this paper is to present a new nonparametric test statistic for testing against ordered alternatives in a Balanced Incomplete Block Design (BIBD). This test will then be compared with the Durbin test which tests for differences between treatments in a BIBD but without regard to order. For the comparison, Monte Carlo simulations were used to generate the BIBD. Random samples were simulated from: Normal Distribution; Exponential Distribution; T distribution with three degrees of freedom. The number of treatments considered was three, four and five with all the possible combinations necessary for a BIBD. Small sample sizes were 20 or less and large sample sizes were 30 or more. The powers and alpha values were then estimated after 10,000 repetitions.The results of the study show that the new test proposed is more powerful than the Durbin test. Regardless of the distribution, sample size or number of treatments, the new test tended to have higher powers than the Durbin test.
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    Nonparametric Tests for the Non-Decreasing and Alternative Hypotheses for the Incomplete Block and Completely Randomized Mixed Design
    (North Dakota State University, 2014) Ndungu, Alfred Mungai
    This research study proposes a solution to deal with missing observations which is a common problem in real world datasets. A nonparametric approach is used because of its ease of use relative to the parametric approach that beleaguer the user with firm assumptions. The study assumes data is in an Incomplete Block (IBD) and Completely Randomized (CRD) Mixed Design. The scope of this research was limited to three, four and five treatments. Mersenne - Twister (2014) simulations were used to vary the design and to estimate the test statistic powers. Two test statistics are proposed if the user expects a non – decreasing order of differences in treatment means. They are both applicable in the cited mixed design. The tests combine Alvo and Cabilio (1995) and Jonckheere – Terpstra ((Jonckheere (1954), Terpstra (1952)) in two ways: standardizing the sum of the standardized statistics and standardizing the sum of the unstandardized statistics. Results showed that the former is better. Three tests are proposed for the umbrella alternative. The first, Mungai’s test, is only applicable in an IBD. The other two tests combine Mungai’s and Mack – Wolfe (1981) using the same methods described in the previous paragraph. The same conclusion holds except when the size of the IBD’s sample was equal to or greater than a quarter that of the CRD.