Physical Sciences and Mathematics Commons^™

Statistical Graphics: Applications To The R And Gr Methods In Linear Models, Mei Huang Wang

Dissertations

Statistical graphics combine statistics and graphics together to visually display analytical statistical results. They present information in a way that is very easy to understand and, furthermore, they frequently reveal information that is hidden from numerical summaries. Our purpose of this study is to explore the field of statistical graphics by investigating their application to statistical methods in the context of the R and GR methods in linear models. We consider the problems of score selection, R-diagnostics, and comparison of the R- and GR-fits.

We have developed a user friendly program which uses dynamic graphics and a user interface to …

A New Soft Tissue Analysis : To Establish Facial Esthetic Norms In Young Adult Females, Anne Béress

Loma Linda University Electronic Theses, Dissertations & Projects

Two hundred and fifty-five articles, books, and masters theses were reviewed for the most frequently applied soft tissue measurements in the literature in order to develop a new soft tissue analysis computer program that includes established soft tissue measurements and the newly developed globe analysis. A meta analysis of 20 normal occlusion studies, was performed to obtain mean values and standard deviations to form a large sample size. Inclusion criteria for articles in the meta analysis were normal occlusion, no orthodontic treatment, pleasing faces, statement on age, race, and lip position of the population. For the lateral view, angular and …

Optimality And Construction Of Designs With Generalized Group Divisible Structure, Sudesh K. Srivastav

Mathematics & Statistics Theses & Dissertations

This thesis is an investigation of the optimality and construction problems attendant to the assignment of v treatments to experimental units in b blocks of size k, paying special attention to settings for which equal replication of the treatments is not possible. The model is that of one way elimination of heterogeneity, in which the expectation of an observation on treatment i in block j is T_i + βj (treatment effect + block effect), where T_i and βj are unknown constants, 1 ≤ i ≤ v and 1 ≤ j ≤ b. All observations are assumed to …

Random Cayley Maps, Michelle Schultz

Dissertations

Determining the orientable surfaces on which a given graph can be imbedded is the central problem of topological graph theory. The natural setting for studying this problem is random topological graph theory, where a probability model is defined on the space of all labeled 2-cell imbeddings of a connected graph. The major focus of this dissertation is the study of Cayley maps in the setting of random topological graph theory.

A Cayley graph provides a representation of a finite group and a fixed generating set for the group. A Cayley map is an imbedding of a Cayley graph whose vertex …

Adaptive Density Estimation Based On The Mode Existence Test, Nizar Sami Jawhar

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The kernel persists as the most useful tool for density estimation. Although, in general, fixed kernel estimates have proven superior to results of available variable kernel estimators, Minnotte's mode tree and mode existence test give us newfound hope of producing a useful adaptive kernel estimator that triumphs when the fixed kernel methods fail. It improves on the fixed kernel in multimodal distributions where the size of modes is unequal, and where the degree of separation of modes varies. When these latter conditions exist, they present a serious challenge to the best of fixed kernel density estimators. Capitalizing on the work …

Linear Models For Multivariate Repeated Measures Data, Shantha S. Rao

Mathematics & Statistics Theses & Dissertations

In this dissertation we focus mainly on the analysis of continuous multivariate repeated measurements data based on the assumption of multivariate normality. However certain aspects of the analysis of univariate repeated measures data are also considered. Typically, we have measurements on p variables (possibly correlated) in the form of px1 vectors y_ijk observed at k = 1,2, ...,t_ij occasions on j = 1,2, ..., n_i individuals from i = 1,2, ..., g groups. We assume a naturally occurring covariance structure V_ij ⊗ ∑ among the p variables on the j^th individual from i^th group …

Association Between Nutrient Intake And Risk Of Coronary Heart Disease In California Seventh-Day Adventists, Peter Pribiš

Loma Linda University Electronic Theses, Dissertations & Projects

Dietary habits are believed to be major determinants of risk of coronary heart disease (CHD). Studies of high and low risk populations have suggested several nutrients to be protective or hazardous against CHD. Most published work since 1984 on diet and CHD in the Adventist Health Study (AHS) population examined either foods or food groups. This study investigated ten nutrients as exposure variables and their relationship to CHD risk. A cohort of 23,616 nonsmoking, non-Hispanic white California Seventh-day Adventists was followed for six years beginning in 1976. Extensive dietary information was collected at baseline, as well as values of traditional …

Federal Legislation Needed To Improve Towing Vessel Safety, Paul J. Keenan Jr.

Theses and Major Papers

To the casual observer, towing vessels and barges, with their low profile and unassuming presence, may seem to be an uninspiring and small part of the shipping scene. However, tank and dry cargo barges actually carry sixty-nine percent of our nation's domestic waterborne commerce. Regulations for large ships, especially oil tankers, have touched every aspect of the shipping industry, including naval architecture, engineering, damage control, manning, training, licensing, etc. Towing vessels and barges however, have largely managed to escape the proliferation of regulation. Current legislation does not provide for the inspection of sea-going towing vessels under three hundred gross tons …

Power Analysis For The Mixed Linear Model, Cheryl Annette Dixon

Theses and Dissertations

Power analysis is becoming standard in inference based research proposals and is used to support the proposed design and sample size. The choice of an appropriate power analysis depends on the choice of the research question, measurement procedures, design, and analysis plan. The "best" power analysis, however, will have many features of a sound data analysis. First, it addresses the study hypothesis, and second, it yields a credible answer.

Power calculations for standard statistical hypotheses based on normal theory have been defined for t-tests through the univariate and multivariate general linear models. For these statistical methods, the approaches to power …