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The major end-points arising from cancer clinical trials are reviewed. These are: tumour response, treatment morbidity, survival with related data, and quality of life. A survey of tumour response data from 81 published clinical trials found the most common statistical test in use to be a Chi squared test of the total response rate, but a total of 21 different statistical methods were used. The various statistical tests available are reviewed, including the Mann-Whitney test and the Chi squared test for trend which make use of all the categories of response and their intrinsic order. The assumptions underlying the tests are described. Theoretical considerations support the Mann-Whitney test as the optimum choice for the analysis of tumour response data. Methods for comparing alternative statistical tests are summarised, and a new method is described which uses a number of typical sets of data to estimate the relative efficiency of two statistical tests by the median value of the square of the ratio of the z-values. Using this technique, and data from the 81 trials, the Mann-Whitney test is found to be around 40% more efficient than the Chi squared test of the total response rate (this increased efficiency is equivalent to increasing the recruitment to the trial by 40%).This practical result is confirmed by mathematical modelling of tumour response using the power relation of the Mann-Whitney test for ordered categorical data, which is derived. Clinical data is found to fit best a shift model which assumes homogeneity of treatment effect across the different grades of response. On the basis of this model, the Mann-Whitney test is found to be 30% to 110% more efficient than a Chi squared test of the total response rate. The similarities of acute morbidity data to tumour response data lead to similar general conclusions on the optimum method of statistical analysis. In a survey of 36 published clinical trials, the most common method of statistical analysis was again a Chi squared test of a dichotomy (such as no morbidity versus morbidity of any grade). Analysis of data from these trials shows the Mann-Whitney test to be more efficient by around 30%.A survey of 81 papers reporting tumour response in clinical trials found that few of them used methods of estimation of the difference between the treatments, or derived confidence intervals of the size of such a difference. Methods of estimation and calculation of confidence intervals were found even less often in a survey of methods of presentation of morbidity results. The possible reasons for this are discussed. It is concluded that the current methods of analysis of tumour response data and many sets of acute treatment morbidity data are not optimum, and a change should be made from the Chi squared test to the Mann-Whitney test. Such a change could be equivalent to an increase in recruitment into many cancer clinical trials of around 40%.

The classic nonparametric confidence intervals for a difference or ratio of medians assume that the distributions of the response variable or the log-transformed response variable have identical shapes in each population. Asymptotic distribution-free confidence intervals for a difference and ratio of medians are proposed which do not require identically shaped distributions. The new asymptotic methods are easy to compute and simulation results show that they perform well in small samples.

It is a well documented fact that primary teachers as a group are quite lacking in their enthusiasm for science, a subject of constant concern for those committed to its role as a component of the primary school curriculum. In order to test the effects of various treatments on groups of teachers and pre-service trainees, a 21 item questionnaire was developed to measure attitudes towards science in the primary school curriculum, towards improving expertise in the area, and in the traditional &quotescientific attitudes and values&quote. A new group of pre-service students provided one group and the pilot population, students in their final semester of a Diploma in Teaching programme another group, and teachers attending residential schools for UG2 conversion and PGl teacher education courses provided several other groups based on teaching location. Items were selected from the pilot instrument on their ability to discriminate between high scoring and low scoring groups measured with the Mann-Whitney U test. Analyses in the main survey between groups, were carried out using Mann-Whitney U test and Kruskal-Wallis one way analysis of variance, and between items, using Wilcoxon matched-pairs signed-ranks test. All manipulation and analysis of data was carried out with the assistance of two computer programs, written in PASCAL by the author specifically for this study � one for item analysis, the other, a statistical package for analysing the main survey data. Findings include 'support for prediction in the literature that change in education is a slow process, demanding ongoing support by the system and teacher education institutions, for teachers committed to the change. Also, the value of computer support, and advantages of tailoring a statistical package to the study, rather than the study to analyses readily accessible, are clearly demonstrated.

The purpose of this thesis is to compare rank-based tests of bivariate stochastic order. Given two bivariate distributions $F$ and $G$, the general problem we are dealing with is to test $H_0: F=G$ against $H_1:F<G$, where $F$ and $G$ are independent continuous distributions on $\Re ^2$. (``$F<G$" means that $F(x)\leq G(x)~\forall x\in \Re^2$, and $\exists x\in \Re^2$ such that $F(x)< G(x)$.). In particular, we will analyze three analogues of the one-dimensional Mann-Whitney-Wilcoxon test in two dimensions. Two of the test statistics are new; we call them the Kendall and Spearman statistics. We will then show the asymptotic distributions and carry out empirical comparisons of the Kendall, Spearman and the third two-dimensional Mann-Whitney-Wilcoxon statistics.

The purpose of this thesis is to compare rank-based tests of bivariate stochastic order. Given two bivariate distributions $F$ and $G$, the general problem we are dealing with is to test $H_0: F=G$ against $H_1:F<G$, where $F$ and $G$ are independent continuous distributions on $\Re ^2$. (``$F<G$" means that $F(x)\leq G(x)~\forall x\in \Re^2$, and $\exists x\in \Re^2$ such that $F(x)< G(x)$.). In particular, we will analyze three analogues of the one-dimensional Mann-Whitney-Wilcoxon test in two dimensions. Two of the test statistics are new; we call them the Kendall and Spearman statistics. We will then show the asymptotic distributions and carry out empirical comparisons of the Kendall, Spearman and the third two-dimensional Mann-Whitney-Wilcoxon statistics.

The purpose of this thesis is to compare rank-based tests of bivariate stochastic order. Given two bivariate distributions $F$ and $G$, the general problem we are dealing with is to test $H_0: F=G$ against $H_1:F<G$, where $F$ and $G$ are independent continuous distributions on $\Re ^2$. (``$F<G$" means that $F(x)\leq G(x)~\forall x\in \Re^2$, and $\exists x\in \Re^2$ such that $F(x)< G(x)$.). In particular, we will analyze three analogues of the one-dimensional Mann-Whitney-Wilcoxon test in two dimensions. Two of the test statistics are new; we call them the Kendall and Spearman statistics. We will then show the asymptotic distributions and carry out empirical comparisons of the Kendall, Spearman and the third two-dimensional Mann-Whitney-Wilcoxon statistics.

The purpose of this thesis is to compare rank-based tests of bivariate stochastic order. Given two bivariate distributions $F$ and $G$, the general problem we are dealing with is to test $H_0: F=G$ against $H_1:F<G$, where $F$ and $G$ are independent continuous distributions on $\Re ^2$. (``$F<G$" means that $F(x)\leq G(x)~\forall x\in \Re^2$, and $\exists x\in \Re^2$ such that $F(x)< G(x)$.). In particular, we will analyze three analogues of the one-dimensional Mann-Whitney-Wilcoxon test in two dimensions. Two of the test statistics are new; we call them the Kendall and Spearman statistics. We will then show the asymptotic distributions and carry out empirical comparisons of the Kendall, Spearman and the third two-dimensional Mann-Whitney-Wilcoxon statistics.

Recent inspections conducted on levee safety in the U.S. that participate in the United States Army Corps of Engineers (USACE) Levee Safety Program under Public-Law 84-99 have shown that the overwhelming majority (>95%) of these levees have at least some deficiency associated with them, and many being identified as having an unacceptable safety rating (≈30%). In the U.S., many levees were constructed using funding from the federal government, but the responsibility of operation and maintenance of the levees were turned over to local government bodies. Given the local funding of levee maintenance, the socioeconomic characteristics of these levee-protected communities may be useful in identifying which communities may not have the economic, social, and / or political capital to maintain their levees to an acceptable safety standard. Using the lens of socio-hydrology, this study examines the socioeconomic and demographic characteristics of levee-protected communities and their relationship to the safety rating of their levee system. Using GIS, socioeconomic data were compiled for each of the evaluated Illinois levee systems from the US Census and the USACE’s National Levee Database (NLD). In addition to socioeconomic data, the NLD contained information on a levee’s age, protection level, estimated value of structures within the levee-protected area, ownership, inspection status, safety rating, and other structural details. The value of levee-protected agricultural lands was also assessed using a soil productivity index used by the state of Illinois to assess taxes on farmland. This information was compiled to investigate the potential differences of socioeconomic characteristics of communities with unacceptable to those with an acceptable levee rating. To assess the differences between the compiled socioeconomic information, the Independent Samples U-Test was implemented to quantify differences between communities with an acceptable verse unacceptable safety rating. In this study, 71 levee systems were identified with a levee safety rating and socioeconomic data from which to perform the statistical comparison between levee systems with an acceptable versus unacceptable safety rating. Of these 71 levees systems, 28 had an unacceptable and 43 had an at least minimally acceptable safety rating. The results from the Independent Samples U-Test showed that five variables with substantial variance (α ≤ 0.2, 80% CI) between the levee safety ratings were, the age of the levee, property value per structure, the average soil productivity index, per capita income, and the percentage of population being black. Using these substantial variables, a binary logistic regression model was created to see if they could be used to realistically predict the levee system’s safety rating. The regression model was able to accurately predict 84% of the ‘acceptable’ group while only correctly predicting 25% of the ‘unacceptable’ group resulting in an overall accuracy of 61%. The inability of this model to predict a levee system’s safety rating underscores the complexities in trying to determine which socioeconomic factors are important for identifying a given levee system’s safety rating. This finding also suggests there are potentially other variables which may be more robust predictors of a community’s ability to adequately maintain their levee. Future research should investigate these complexities in identifying which communities can adequately maintain their levee system.

Microarray technology enables simultaneous gene expression level monitoring for thousands of genes. While this technology has now been recognized as a powerful and cost-effective tool for large-scale analysis, the many systematic sources of experimental variations introduce inherent errors in the extracted data. Data is gathered by processing scanned images of microarray slides. Therefore robust image processing is particularly important and has a large impact on downstream analysis. The processing of the scanned images can be subdivided in three phases: gridding, segmentation and data extraction. To measure the gene expression levels, the processing of cDNA microarray images must overcome a large set of issues in these three phases that motivates this study. This study presents automatic gridding methods and compares their performances. Two segmentation techniques already used, the Seeded Region Growing Algorithm and the Mann-Whitney Test, are examined. We present limitations of these techniques. Finally, we studied the data extraction method used in MicroArray Suite (MS), a microarray analysis software, via synthetic images and explain its intricacies. / Master of Science