College of Letters & Science
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The College of Letters and Science, the largest center for learning, teaching and research at Montana State University, offers students an excellent liberal arts and sciences education in nearly 50 majors, 25 minors and over 25 graduate degrees within the four areas of the humanities, natural sciences, mathematics and social sciences.
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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 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 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.