Statistics and Probability Commons^™

A Saddlepoint Approximation To Left-Tailed Hypothesis Tests Of Variance For Non-Normal Populations, Tyler L. Grimes

UNF Graduate Theses and Dissertations

When the variance of a single population needs to be assessed, the well-known chi-squared test of variance is often used but relies heavily on its normality assumption. For non-normal populations, few alternative tests have been developed to conduct left tailed hypothesis tests of variance. This thesis outlines a method for generating new test statistics using a saddlepoint approximation. Several novel test statistics are proposed. The type-I error rates and power of each test are evaluated using a Monte Carlo simulation study. One of the proposed test statistics, R_gamma2, controls type-I error rates better than existing tests, while having comparable power. …

Space-Time Modelling Of Emerging Infectious Diseases: Assessing Leptospirosis Risk In Sri Lanka, Cameron C F Plouffe

Theses and Dissertations (Comprehensive)

In this research, models were developed to analyze leptospirosis incidence in Sri Lanka and its relation to rainfall. Before any leptospirosis risk models were developed, rainfall data were evaluated from an agro-ecological monitoring network for producing maps of total monthly rainfall in Sri Lanka. Four spatial interpolation techniques were compared: inverse distance weighting, thin-plate splines, ordinary kriging, and Bayesian kriging. Error metrics were used to validate interpolations against independent data. Satellite data were used to assess the spatial pattern of rainfall. Results indicated that Bayesian kriging and splines performed best in low and high rainfall, respectively. Rainfall maps generated from …

Student Performance In Curricula Centered On Simulation-Based Inference: A Preliminary Report, Beth Chance, Jimmy Wong, Nathan L. Tintle

Faculty Work Comprehensive List

"Simulation-based inference"(e.g., bootstrapping and randomization tests) has been advocated recently with the goal of improving student understanding of statistical inference, as well as the statistical investigative process as a whole. Preliminary assessment data have been largely positive. This article describes the analysis of the first year of data from a multi-institution assessment effort by instructors using such an approach in a college-level introductory statistics course, some for the first time. We examine several pre-/post-measures of student attitudes and conceptual understanding of several topics in the introductory course. We highlight some patterns in the data, focusing on student level and instructor …

Resolving Gnetum Evolutionary History, Angela Mcfadden

All Master's Theses

Gnetum are non-flowering seed plants of the tropics, indigenous to South America, Africa, and Asia. This group of about 40 species is fascinating to botanists because it shares distinctive morphological characteristics with flowering plants, such as broad leaves, woody stems, and flower-like strobili. There are still questions surrounding the relationships within the genus of Gnetum. With that in mind, I focused my work on generating phylogenetic hypotheses, using two molecular data sets: a concatenation of over 60 different chloroplast genes (66,815 base pairs), and the whole chloroplast genome (128,772 base pairs). This allowed me to compare the two phylogenies …

Garch(1,1) With Sifted Gamma-Distributed Errors, Alan C. Budd

College of Graduate Studies: Theses & Dissertations

Typical General Autoregressive Conditional Heteroskedastic (GARCH) processes involve normally-distributed errors, and they model strictly-positive error processes poorly. This thesis will present a method for estimating the parameters of a GARCH(1,1) process with shifted Gamma-distributed errors, conduct a simulation study to test the method, and apply the method to real time series data.

Data, Data, Data, Mary Whisner

Librarians' Articles

The legal profession often requires extensive data for everything from simple statistical questions to large-scale empirical research projects. Ms. Whisner discusses some of her favorite sources for finding and evaluating statistics.

Empirical Likelihood And Differentiable Functionals, Zhiyuan Shen

Theses and Dissertations--Statistics

Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. It has been shown by Owen (1988,1990) and many others that empirical likelihood ratio (ELR) method can be used to produce nice confidence intervals or regions. Owen (1988) shows that -2logELR converges to a chi-square distribution with one degree of freedom subject to a linear statistical functional in terms of distribution functions. However, a generalization of Owen's result to the right censored data setting is difficult since no explicit maximization can be obtained under constraint in terms of distribution functions. Pan and Zhou (2002), instead, study the …

Continuous Time Multi-State Models For Interval Censored Data, Lijie Wan

Theses and Dissertations--Statistics

Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models.

Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was …

Aggregated Quantitative Multifactor Dimensionality Reduction, Rebecca E. Crouch

Theses and Dissertations--Statistics

We consider the problem of making predictions for quantitative phenotypes based on gene-to-gene interactions among selected Single Nucleotide Polymorphisms (SNPs). Previously, Quantitative Multifactor Dimensionality Reduction (QMDR) has been applied to detect gene-to-gene interactions associated with elevated quantitative phenotypes, by creating a dichotomous predictor from one interaction which has been deemed optimal. We propose an Aggregated Quantitative Multifactor Dimensionality Reduction (AQMDR), which exhaustively considers all k-way interactions among a set of SNPs and replaces the dichotomous predictor from QMDR with a continuous aggregated score. We evaluate this new AQMDR method in a series of simulations for two-way and three-way interactions, …

Challenges In Developing Applications For Aging Populations, Drew Marie Williams, Md O. Gani, Ivor D. Addo, Akm Jahangir Alam Majumder, Chandana Tamma, Mong-Te Wang, Chih-Hung Chang, Sheikh Iqbal Ahamed, Cheng-Chung Chu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Elderly individuals can greatly benefit from the use of computer applications, which can assist in monitoring health conditions, staying in contact with friends and family, and even learning new things. However, developing accessible applications for an elderly user can be a daunting task for developers. Since the advent of the personal computer, the benefits and challenges of developing applications for older adults have been a hot topic of discussion. In this chapter, the authors discuss the various challenges developers who wish to create applications for the elderly computer user face, including age-related impairments, generational differences in computer use, and the …

Improved Parameter Estimation Of The Log-Logistic Distribution With Applications, Joseph Reath

Dissertations, Master's Theses and Master's Reports

In this report, we work with parameter estimation of the log-logistic distribution. We first consider one of the most common methods encountered in the literature, the maximum likelihood (ML) method. However, it is widely known that the maximum likelihood estimators (MLEs) are usually biased with a finite sample size. This motivates a study of obtaining unbiased or nearly unbiased estimators for this distribution. Specifically, we consider a certain `corrective' approach and Efron's bootstrap resampling method, which both can reduce the biases of the MLEs to the second order of magnitude. As a comparison, we also consider the generalized moments (GM) …

Comparison Of Option Price From Black-Scholes Model To Actual Values, Matthew J. Krznaric

Williams Honors College, Honors Research Projects

The Black-Scholes model is a widely used method for pricing European-style options in a straightforward way, through the use of calculations and ideal market assumptions. Due to certain unrealistic ideal conditions exercised by the model, The Black-Scholes technique of pricing options may not be entirely accurate in implementation. This paper addresses these problems due to the model limitations, determining how The Black-Scholes method compares to the results when using the actual data. Using a mix of historical S&P500 data and generated normal distributions, we first calculated and graphed option prices through the Black-Scholes formulas. With the help of R, we …

Two Combinatorial Proofs Of Identities Involving Sums Of Powers Of Binomial Coefficients, John Engbers, Christopher Stocker

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Learning About Modeling In Teacher Preparation Programs, Hyunyi Jung, Eryn Stehr, Jia He, Sharon L. Senk

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study explores opportunities that secondary mathematics teacher preparation programs provide to learn about modeling in algebra. Forty-eight course instructors and ten focus groups at five universities were interviewed to answer questions related to modeling. With the analysis of the interview transcripts and related course materials, we found few opportunities for PSTs to engage with the full modeling cycle. Examples of opportunities to learn about algebraic modeling and the participants’ perspectives on the opportunities can contribute to the study of modeling and algebra in teacher education.

Diversification And Market Neutral Portfolios In S&P500, Alan S. Agnew

Williams Honors College, Honors Research Projects

Our goal is to investigate strategies to deal with the risks associated with holding asset in the stock market. We first deal with risk of holding a specific stock, by the use of diversification. Later, we’ll attempt to deal with the market risk, which is the risk of entire market going up and down. Data used in this project comes from daily adjusted closing price of stocks listed in the S&P500 index ranging from January 3^rd, 2000 to December 31^st, 2015 and the data is processed using statistical software R.

Sections 2 through 4 of this …

Black Cloud Randomization Test, Nicholas S. Vanni

Williams Honors College, Honors Research Projects

The Black Cloud Randomization Test looks at a nontraditional question and attempts to answer the question using unique statistics. The purpose of this paper is to apply what has been learned throughout the years and apply this knowledge to a final project. Data for this project follows an emergency room’s on call schedule, as well as the number of traumas that came in during each day shift. The project builds on what has been already learned and helps to open a different way of working with statistics. The project was coded in the R software. With different restrictions, there are …

Distribution-Free Trends Test To Determine The Construct Validity Of An Anti-Social Criminal Attitudes Scale, Holly Ann Child

Wayne State University Dissertations

The Sawilosky's I-Test was developed to as an alternative method to evaluate construct validity, more specifically, in regards to the Multitrait-Multimethod Matrix designed by Campbell and Fiske (1959). Typically, researchers use a method by Campbell and Fiske that involves a subjective “physical” look at the matrix to determine validity. Sawilowsky’s I-Test offers a statistical approach that incorporates the current practice but removes the subjectivity involved in this process.

There are only two existing studies that look at the I-Test, Sawilowsky in 2002 and Cuzzocrea in 2007. Both studies found that although the I-Test is not a perfect statistic, it provides …

The Impact Of Multiple Imputation On The Type Ii Error Rate Of The T Test, Tammy A. Grace

Wayne State University Dissertations

ABSTRACT

THE IMPACT OF MULTIPLE IMPUTATION ON THE TYPE II ERROR RATE OF

THE T TEST

by

TAMMY A. GRACE

August 2016

Advisor: Shlomo Sawilowsky, PhD

Major: Evaluation and Research

Degree: Doctor of Philosophy

The National Academy of Science identified numerous high priority areas for missing data research. This study addresses several of those areas by systematically investigating the impact of multiple imputation on the rejection rate of the independent samples t test under varying conditions of sample size, effect size, fraction of missing data, distribution shape, and alpha. In addition to addressing gaps in the missing data literature, this …

Doing Qualitative Research Online Book Review, Donna M. Busarow

Journal of Social, Behavioral, and Health Sciences

A recent addition to qualitative instruction is Salmon's (2016) book, Doing Qualitative Research Online. This book review examines the book as an educational tool for student researchers.

Consistency Of Cheeger And Ratio Graph Cuts, Nicolas Garcia Trillos, Dejan Slepcev, James Von Brecht, Thomas Laurent, Xavier Bresson

Mathematics, Statistics and Data Science Faculty Works

This paper establishes the consistency of a family of graph-cut- based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based on graph cuts like the Cheeger and ratio cuts. We show that minimizers of these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut (which partitions the ground truth measure). Moreover, we obtain sharp conditions on how the connectivity radius can be …

Non-Conventional Approaches To Syntheses Of Ferromagnetic Nanomaterials, Dustin M. Clifford

Theses and Dissertations

The work of this dissertation is centered on two non-conventional synthetic approaches to ferromagnetic nanomaterials: high-throughput experimentation (HTE) (polyol process) and continuous flow (CF) synthesis (aqueous reduction and the polyol process). HTE was performed to investigate phase control between Fe_xCo_1-x and Co_3-xFe_xO_y. Exploration of synthesis limitations based on magnetic properties was achieved by reproducing M_s=210 emu/g. Morphological control of Fe_xCo_1-x alloy was achieved by formation of linear chains using an H_ext. The final study of the Fe_xCo_1-x chains used DoE to …

Finding The Cutpoint Of A Continuous Covariate In A Parametric Survival Analysis Model, Kabita Joshi

Theses and Dissertations

In many clinical studies, continuous variables such as age, blood pressure and cholesterol are measured and analyzed. Often clinicians prefer to categorize these continuous variables into different groups, such as low and high risk groups. The goal of this work is to find the cutpoint of a continuous variable where the transition occurs from low to high risk group. Different methods have been published in literature to find such a cutpoint. We extended the methods of Contal and O’Quigley (1999) which was based on the log-rank test and the methods of Klein and Wu (2004) which was based on the …

Powerful Association Test Combining Rare Variant And Gene Expression Using Family Data From Genetic Analysis Workshop 19, Yen Yi Ho, Weihua Guan, Michael O'Connell, Saonli Basu

Faculty Publications

Background: Genetic association studies aim to test for disease or trait association with genetic variants, either throughout the human genome or in regions of interest. However, for most diseases and traits, the combined effects of associated genetic variants explain only a small proportion of the genetic variation. This "missing heritability" may be a result of the small effects of common variants considered in the genetic association studies. Rare variants may also play an important role in understanding the missing heritability of complex traits. Method: We propose a novel weight-adjustment approach to combine gene expression into rare variant analysis. Results from …

Sample Size Calculation For Ph Mixture Cure Model, Yihong Zhan

Theses and Dissertations

With the development of advanced medical technology, a significant proportion of patients can be cured of many chronic diseases. Because a substantial fraction of patients have censored information, the standard survival model, such as the proportional hazards (PH) model cannot capture the cured information of patients. Thus PH mixture cure model is developed to handle the survival data with potential cured information. A corresponding sample size formula based on log rank test has been proposed by Wang et al. (2012) and the probability of death in their formula is only contributed by the control arm. However, to calculate the sample …

Parametric Reversed Hazards Model For Left Censored Data With Application To Hiv, Farahnaz Islam

Theses and Dissertations

Left censoring is generally a rare type of censoring in time-to-event data, however there are some fields such as HIV related studies where it commonly occurs. Currently, there is no clear recommendation in the literature on the optimal model and distribution to analyze left-censored data. Recommendations can help researchers apply more accurate models for this type of censoring. This study derives the Parametric Reversed Hazards (PRH) Model for a variety of distributions which may be appropriate for left censored data. The performance of these derived PRH models to analyze HIV viral load data are compared using extensive simulations and a …

Modeling Spatially Varying Effects Of Chemical Mixtures, Jenna Czarnota

Theses and Dissertations

Cancer incidence is associated with exposures to multiple environmental chemicals, and geographic variation in cancer rates suggests the importance of accommodating spatially varying effects in the analysis of environmental chemical mixtures and disease risk. Traditional regression methods are challenged by the complex correlation patterns inherent among co-occurring chemicals, and the applicability of geographically weighted regression models is limited in the setting of environmental chemical risk analysis. In comparison to traditional methods, weighted quantile sum (WQS) regression performs well in the identification of important environmental exposures, but is limited by the assumption that effects are fixed over space. We present an …

Effect Of An Interactive Component On Students' Conceptual Understanding Of Hypothesis Testing, Sarah Anne Inkpen

Walden Dissertations and Doctoral Studies

The Premier Technical College of Qatar (PTC-Q) has seen high failure rates among students taking a college statistics course. The students are English as a foreign language (EFL) learners in business studies and health sciences. Course delivery has involved conventional content/curriculum-centered instruction with minimal to no interactive components. The purpose of this quasi-experimental study was to assess the effectiveness of an interactive approach to teaching and learning statistics used in North America and the United Kingdom when used with EFL students in the Middle East. Guided by von Glasersfeld's constructivist framework, this study compared conceptual understanding between a convenience sample …

Early Sex Work Initiation And Condom Use Among Alcohol-Using Female Sex Workers In Mombasa, Kenya: A Cross-Sectional Analysis, A. M. Parcesepe, Kelly L'Engle, S. L. Martin, S. Green, C. Suchindran, P. Mwarogo

Nursing and Health Professions Faculty Research and Publications

Objectives Early initiation of sex work is prevalent among female sex workers (FSWs) worldwide. The objectives of this study were to investigate if early initiation of sex work was associated with: (1) consistent condom use, (2) condom negotiation self-efficacy or (3) condom use norms among alcohol-using FSWs in Mombasa, Kenya.

Methods In-person interviews were conducted with 816 FSWs in Mombasa, Kenya. Sample participants were: recruited from HIV prevention drop-in centres, 18 years or older and moderate risk drinkers. Early initiation was defined as first engaging in sex work at 17 years or younger. Logistic regression modelled outcomes as a function …

The Relationship Between Exercise And Depression And Anxiety In College Students, Joshua Frank, Dr. Amy Adkins, Nathan Thomas, Dr. Danielle Dick

UROP Posters

The literature shows an inverse association between exercise and mental disorders. The aim of this study is to further elaborate on this association with regards to exercise and its relationship with anxiety and depression in a college sample. The subject group focused on seniors in the Spit for Science data set which incorporated a total of 821 students. Physical activity was assessed using the International Physical Activity Questionnaire (IPAQ) to estimate the overall metabolic equivalents (MET’s) each student spent in walking, moderate, or vigorous activity levels in the previous week. Sum scores were used to measure depression and anxiety. Overall,the …

An Analysis Of Accuracy Using Logistic Regression And Time Series, Edwin Baidoo, Jennifer L. Priestley

Published and Grey Literature from PhD Candidates

This paper analyzes the accuracy rates for logistic regression and time series models. It also examines a relatively new performance index that takes into consideration the business assumptions of credit markets. Although prior research has focused on evaluation metrics, such as AUC and Gini index, this new measure has a more intuitive interpretation for various managers and decision makers and can be applied to both Logistic and Time Series models.