Statistics and Probability Commons^™

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.

Remarks On A Paper Of Ahmad, Ahmad And Ahmed, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Ahmad et al. (2015) consider a Transmuted Kumaraswamy distribution and study certain properties of their distribution. In the title of their paper they mention characterization of this distribution, but no characterization are presented in their paper. In the present short note, we establish certain characterizations of the Transmuted Kumaraswamy distribution in three directions.

The Transmuted Weibull-Pareto Distribution, Ahmed Z. Afify, Haitham M. Yousof, Nadeem Shafique Butt, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

A new generalization of the Weibull-Pareto distribution called the transmuted Weibull-Pareto distribution is proposed and studied. Various mathematical properties of this distribution including ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves and order statistics are derived. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new lifetime model is illustrated by means of an application to a real data set.

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 …

Development Of Efficient Simultaneous Confidence Bounds For Linear Mixed Models With Applications In Alcohol Research, Emmanuel Joseph Sequeira

Open Access Theses & Dissertations

Multiplicity corrections are necessary to ensure the accuracy of conclusions made in studies that carry out multiple inferences simultaneously. This Thesis uses the methodology derived by Hunter and Worsley to obtain improved simultaneous confidence bounds (SCBs) that are less conservative than the highly used Bonferroni SCBs, for studies using linear mixed modeling. Empirical coverage rates were obtained for data that was generated using simulations, to compare the accuracy of the Hunter-Worsley SCBs with that of the Bonferroni SCBs. The bounds were also applied to data in the field of alcohol research, where comparisons were made to determine the moderating effect …

Pre-Tuned Principal Component Regression And Several Variants, Pei Wang

Open Access Theses & Dissertations

The regression coecient estimates from ordinary least squares (OLS) have a low probability of being close to the real value when there is a multicollinearity problem in the design matrix. In order to combat this problem, many regularized methods have been introduced. Principal components regression (PCR) is an important analysis tool for dealing with multicollinearity and high-dimensionality. In conventional PCR, the rst step is to change the original predictors to orthogonal principal components (PC's) by a linear transformation. These PC's correspond to the eigenvalues which are sorted in a decreasing order. The next step is to regress the response on …

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 …

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 …

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.

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 …

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 …