Sample size calculation methods for ordinal logistic regression are proposed to test statistical hypotheses. The author was motivated to do this work by the need for statistical analysis of the red imported fire ants data. The proposed methods use the concept of approximation by the moment-generating function. Some correction methods are also suggested. When a prior data set is available, an empirical method is explored. Application of the proposed methodology to the fire ant mating flight data is demonstrated. The proposed sample size and power calculation methods are applied in the hypothesis testing problems. Simulation studies are also conducted to illustrate their performance and to compare them with existing methods.

In this thesis, we are interested in empirical likelihood (EL) methods for two-sample problems, with focus on the difference of the two population means. A weighted empirical likelihood method (WEL) for two-sample problems is developed. We also consider a scenario where sample data on auxiliary variables are fully observed for both samples but values of the response variable are subject to missingness. We develop an adjusted empirical likelihood method for inference of the difference of the two population means for this scenario where missing values are handled by a regression imputation method. Bootstrap calibration for WEL is also developed. Simulation studies are conducted to evaluate the performance of naive EL, WEL and WEL with bootstrap calibration (BWEL) with comparison to the usual two-sample t-test in terms of power of the tests and coverage accuracies. Simulation for the adjusted EL for the linear regression model with missing data is also conducted.

Sample size calculation methods for ordinal logistic regression are proposed to test statistical hypotheses. The author was motivated to do this work by the need for statistical analysis of the red imported fire ants data. The proposed methods use the concept of approximation by the moment-generating function. Some correction methods are also suggested. When a prior data set is available, an empirical method is explored. Application of the proposed methodology to the fire ant mating flight data is demonstrated. The proposed sample size and power calculation methods are applied in the hypothesis testing problems. Simulation studies are also conducted to illustrate their performance and to compare them with existing methods.

In this report we give a brief introduction to the multilevel models, provide a brief summary of the need for using the multilevel model, discuss the assumptions underlying use of multilevel models, and present by means of example the necessary steps involved in model building. This introduction is followed by a discussion of power and sample size determination in multilevel designs. Some formulae are discussed to provide insight into the design aspects that are most influential in terms of power and calculation of standard errors. Finally we conclude by discussing and reviewing the simulation study performed by Maas and Hox (2005) about the influence of different sample sizes at individual as well as group level on the accuracy of the estimates (regression coefficients and variances) and their standard errors. / text

In this thesis, we are interested in empirical likelihood (EL) methods for two-sample problems, with focus on the difference of the two population means. A weighted empirical likelihood method (WEL) for two-sample problems is developed. We also consider a scenario where sample data on auxiliary variables are fully observed for both samples but values of the response variable are subject to missingness. We develop an adjusted empirical likelihood method for inference of the difference of the two population means for this scenario where missing values are handled by a regression imputation method. Bootstrap calibration for WEL is also developed. Simulation studies are conducted to evaluate the performance of naive EL, WEL and WEL with bootstrap calibration (BWEL) with comparison to the usual two-sample t-test in terms of power of the tests and coverage accuracies. Simulation for the adjusted EL for the linear regression model with missing data is also conducted.

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This thesis demonstrates the possible cutoff sample size point that balances goodness of es-timation and study expenditure by a practical cancer case. As it is crucial to determine the sample size in designing an experiment, researchers attempt to find the suitable sample size that achieves desired power and budget efficiency at the same time. The thesis shows how simulation can be used for sample size and precision calculations with survival data. The pre-sentation concentrates on the simulation involved in carrying out the estimates and precision calculations. The Kaplan-Meier estimator and the Cox regression coefficient are chosen as point estimators, and the precision measurements focus on the mean square error and the stan-dard error.

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The methods available for the calculation of ratios of partition functions for isotopic molecules were examined critically and compared. A number of calculations were made for carbon as well as for selenium systems using the exact method rather than an approximate one. Improvements were made to the sample handling system of the mass spectrometer to prevent sample cross-contamination and to reduce the time needed for sample changeover. Four sets of experiments were performed. The kinetic isotope effects in the reductions to Se° of Se^V1 and Se^1V were studied as were the isotope exchange reactions between Se° and Se^1V and between Se^1V and Se^V1. Estimates were made of the ratios of rate constants and isotope exchange equilibrium constants for 82Se and 76Se in these systems and these were compared with the theoretical values. / Thesis / Doctor of Philosophy (PhD)