published_or_final_version / Applied Statistics / Master / Master of Social Sciences

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In a field study of irrigated chile (Capsicum annum L.) production in southeastern Arizona and southwestern New Mexico from 2008 through 2009, soil and tissue test samples were analyzed for a full spectrum of nutrients at 16 different sites, including nitrogen (N) phosphorus (P), potassium (K), zinc (Zn), iron (Fe), and boron (B), with the objective of evaluating soil and tissue nutrient testing procedures and establishing basic testing guidelines and recommendations with respect to yield potentials. Results for soil and tissue analysis were correlated to yield results. The results provide estimates for baselines which can be tested through subsequent calibration experiments for the development of recommendations for critical soil and tissue test values. These soil test and plant nutrients values will be evaluated in subsequent experiments in an effort to better define fertilizer nutrient inputs in order to gain better nutrient management efficiencies in irrigated chile production systems.

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A wide array of procedures have been proposed for testing correlation pattern. Many, but not all, of the statistical techniques available for testing correlation pattern are derived under the distributional condition of multivariate normality which does not always hold in the behavioral, educational and social sciences. Though a number of studies have explored the performance of structure analysis techniques under conditions of multivariate nonnormality, very little is known about the actual performance of many correlation structure analysis techniques under conditions of multivariate nonnormality. In addition, very little is known about the actual concurrent performance of tests of multivariate normality. The present investigation ascertains how tests of correlation pattern hypotheses and indicators of multivariate normality perform when data are from multivariate normal or nonnormal parent populations. This paper reviews and examines, using a Monte Carlo simulation study, the concurrent performance of different approaches to testing (1) correlation pattern hypotheses, including, (i) normal theory (NT) and asymptotically distribution free (ADF) covariance structure analysis techniques, (ii) NT and ADF correlation structure analysis techniques, (iii) correlation pattern specific techniques; (2) the distributional assumption of multivariate normality using statistics based on Mardia's measures of multivariate skewness and kurtosis. This paper also examines the performance characteristics of test procedures based on joint consideration of tests of multivariate normality and structure analysis techniques. Performance of the covariance and correlation structure analysis techniques, tests of multivariate normality, and joint test procedures was assessed across different types of correlation pattern models, numbers of variables, levels of skew and kurtosis, sample sizes, and nominal alpha levels, on the primary Neyman-Pearson criterion for an optimal test, according to which an optimal procedure (1) controls experimentwise Type I error rate at or below the nominal level, (2) maximizes power.

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Suppose two treatments are being compared in a clinical trial with a fixed number of subjects. Half the subjects receive treatment 1, while the other half receive treatment 2. Measurements of some relevant response variable are made on each subject at equally spaced time points. This thesis proposes a procedure for testing at each time point the null hypothesis H₀ of no treatment differences, while controlling the overall probability of type I error. Chapter 1 describes alternative methods for estimating the unknown parameters of models generating short series of measurements. Maximum likelihood estimation, and modified variance based estimation, are considered in 1.1 and 1.2 respectively. A 4 parameter model is described in 1.3. This allows for increasing or decreasing variances of measurements within subjects. In 1.4, maximum likelihood estimation is used in fitting the 4 parameter model to two data sets. In Chapter 2, attention focuses on sequential testing, with data arising from the 4 parameter model. The possibility of using stopping rules based on posterior probabilities, rather than sequentially adjusted P values, is considered briefly in 2.1. Two methods for determining appropriate nominal significance levels for successive tests, when the model for data is assumed known, are described in 2.2. An algorithm for integrating quickly a special case of the multivariate normal density, in high dimensions, presented in 2.3, facilitates implementation of the two methods. In 2.4, test procedures based on the methods of 2.2 are described, in which model parameters are (re-) estimated at each time point, as data accumulate. Test statistics and z-values are adjusted for each test, according to the updated parameter estimates. Simulations show that these procedures give overall significance levels close to those required. One of the two procedures is preferred on the basis of power to detect deviations from H₀.

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Typescript / 192 leaves / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematics, 1965