Publications by Colleges and Departments (MSU - Bozeman)
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Item The Development and Evolution of an Introductory Statistics Course for In-Service Middle-Level Mathematics Teachers(2014-11) Schmid, Kendra K.; Blankenship, Erin E.; Kerby, April T.; Green, Jennifer L.; Smith, Wendy M.The statistical preparation of in-service teachers, particularly middle school teachers, has been an area of concern for several years. This paper discusses the creation and delivery of an introductory statistics course as part of a master’s degree program for in-service mathematics teachers. The initial course development took place before the advent of the Common Core State Standards for Mathematics (CCSSM) and the Mathematics Education of Teachers (MET II) Reports, and even before the GAISE Pre-K-12 Report. Since then, even with the recommendations of MET II and the wide-spread implementation of the CCSSM, the guidance available to faculty wishing to develop a statistics course for professional development of inservice teachers remains scarce. We give an overview of the master’s degree program and discuss aspects of the course, including the goals for the course, course planning and development, the instructional team, course delivery and modifications, and lessons learned through five offerings. With this paper, we share our experiences developing such a course, the evolution of the course over multiple iterations, and what we have learned about its value to the middle-level teachers who have participated. As more and more universities are being asked to develop courses specifically for in-service teachers, we wrote thisItem Using Quantile Regression to Measure the Differential Impact of Economic and Demographic Variables on Obesity(2012-09) Belasco, Eric J.; Chidmi, B.; Lyford, C. P.; Funtanilla, M.The fight against obesity in the U.S. has become a pressing priority for policy makers due to many undesirable outcomes including escalating health care costs, reduced quality of life and increased mortality. This analysis uses data from the 2007 Behavioral Risk Factor Surveillance System (BRFSS) to evaluate the relationship between behavioral, economic, and demographic factors with BMI while explicitly accounting for systematic heterogeneity using a quantile regression. Results suggest that the effect of exercise, smoking, occupation, and race vary by sizeable amounts from high to low BMI-quantiles. This strongly indicates that future research efforts and policy responses to obesity need to account for these differences in order to develop more effective policies.Item Functional Analysis of Variance for Association Studies(Public Library of Science, 2014) Greenwood, Mark C.; Vsevolozhskaya, Olga; Zaykin, Dmitri; Wei, Changshuai; Lu, QingWhile progress has been made in identifying common genetic variants associated with human diseases, for most of common complex diseases, the identified genetic variants only account for a small proportion of heritability. Challenges remain in finding additional unknown genetic variants predisposing to complex diseases. With the advance in next-generation sequencing technologies, sequencing studies have become commonplace in genetic research. The ongoing exome-sequencing and whole-genome-sequencing studies generate a massive amount of sequencing variants and allow researchers to comprehensively investigate their role in human diseases. The discovery of new disease-associated variants can be enhanced by utilizing powerful and computationally efficient statistical methods. In this paper, we propose a functional analysis of variance (FANOVA) method for testing an association of sequence variants in a genomic region with a qualitative trait. The FANOVA has a number of advantages: (1) it tests for a joint effect of gene variants, including both common and rare; (2) it fully utilizes linkage disequilibrium and genetic position information; and (3) allows for either protective or risk-increasing causal variants. Through simulations, we show that FANOVA outperform two popularly used methods – SKAT and a previously proposed method based on functional linear models (FLM), – especially if a sample size of a study is small and/or sequence variants have low to moderate effects. We conduct an empirical study by applying three methods (FANOVA, SKAT and FLM) to sequencing data from Dallas Heart Study. While SKAT and FLM respectively detected ANGPTL 4 and ANGPTL 3 associated with obesity, FANOVA was able to identify both genes associated with obesity.Item Intermediate Statistics with R(2014-01) Greenwood, Mark C.Introductory statistics courses prepare students to think statistically but cover relatively few statistical methods. Building on the basic statistical thinking emphasized in an introductory course, a second course in statistics at the undergraduate level can explore a large number of statistical methods. This text covers more advanced graphical summaries, One-Way ANOVA with pair-wise comparisons, Two-Way ANOVA, Chi-square testing, and simple and multiple linear regression models. Models with interactions are discussed in the Two-Way ANOVA and multiple linear regression setting with categorical explanatory variables. Randomization-based inferences are used to introduce new parametric distributions and to enhance understanding of what evidence against the null hypothesis “looks like”. Throughout, the use of the statistical software R via Rstudio is emphasized with all useful code and data sets provided within the text. This is Version 3.1 of the book.Item Focused Group Interviews as an Innovative Quanti-qualitative Methodology (QQM): Integrating Quantitative Elements into a Qualitative Methodology(Nova Southeastern University, Inc., 2006) Grim, Brian; Gromis, Judy; Harmon, Alison H.There is a sharp divide between quantitative and qualitative methodologies in the social sciences. We investigate an innovative way to bridge this gap that incorporates quantitative techniques into a qualitative method, the “quanti-qualitative method” (QQM). Specifically, our research utilized small survey questionnaires and experiment-like activities as part of the question route in a series of five focused group interviews on nutrition education. We show how these quantitative-type activities fit naturally with our question route and contributed to testing the hypotheses within the context of the five important characteristics of focused group interviews. The innovative use of QQM in focused group interviews makes data analysis easier and more transparent and permits collection of richer, more multifaceted data in a cost-effective fashion. Key Words: Focus Groups, Qualitative-Quantitative Methodology, QQM, and Qualitative Hypothesis Testing.Item Multi-scale clustering of functional data with application to hydraulic gradients in wetlands(Columbia University, New York, 2011) Greenwood, Mark C.; Soida, Richard S.; Sharp, Julia L.; Peck, Rory G.; Rosenberry, Donald O.A new set of methods are developed to perform cluster analysis of functions, motivated by a data set consisting of hydraulic gradients at several locations distributed across a wetland complex. The methods build on previous work on clustering of functions, such as Tarpey and Kinateder (2003) and Hitchcock et al. (2007), but explore functions generated from an additive model decomposition (Wood, 2006) of the original time se- ries. Our decomposition targets two aspects of the series, using an adaptive smoother for the trend and circular spline for the diurnal variation in the series. Different measures for comparing locations are discussed, including a method for efficiently clustering time series that are of different lengths using a functional data approach. The complicated nature of these wetlands are highlighted by the shifting group memberships depending on which scale of variation and year of the study are considered.