Statistics

###### http://wp.stolaf.edu/mscs/

**Director, 2014-15****:** Paul Roback (MSCS), multilevel models, GLM, classification methods

**Faculty, 2014-15:** Anthony Becker (Economics), microeconomics, public policy, econometrics, statistics; Laura Boehm Vock (MSCS), spatial data analysis, Bayesian methods; Sharon Lane-Getaz (MSCS), statistics education; Julie Legler (MSCS), biostatistics, GLM, correlated data; Jessica Musselman (MSCS), biostatistics, epidemiology; Matthew Richey (MSCS), computational mathematics and software design; Katherine Ziegler-Graham (MSCS), biostatistics

With the growing abundance of data gathered in nearly every field, statistical methods have become invaluable for transforming data into useful information. As a subject, statistics is interdisciplinary, spanning the sciences (natural and social), the humanities, and even the arts. Examples of areas of applications include economics, biology, health, education, actuarial sciences, and law. An increasing number of majors and concentrations require or recommend a statistics course.

OVERVIEW OF THE CONCENTRATION

At St. Olaf, students can combine their interests in statistics with any major and acquire a background that leads to graduate study and abundant career opportunities. To find out more about the statistics concentration, visit the Statistics program.

##### INTENDED LEARNING OUTCOMES FOR THE CONCENTRATION

##### REQUIREMENTS FOR THE CONCENTRATION

Four courses: two required foundation courses in statistical modeling (plus a prerequisite of introductory statistics), and two electives (as described below). Concentrators are encouraged to participate in an experiential learning opportunity, such as those available with the Center for Interdisciplinary Research.

1. Required Foundation

Statistics 272: *Statistical Modeling*

Statistics 316: *Advanced Statistical Modeling*

In addition, a prerequisite for the required foundation: either AP Statistics, Statistics 110, Statistics 212, Statistics 214, or Economics 263 (or permission of instructor)

Math-Economics double majors can substitute Economics 385: *Econometrics* for Statistics 316: *Advanced Statistical Modeling*.

2. Electives (Students choose at least two of the following courses):

Computer Science 125: *Computer Science for Scientists and Mathematicians* (taken Spring 2013 or later)

Economics 385: *Econometrics*

Mathematics 262: *Probability Theory* (strongly recommended for mathematics majors)

Psychology 230: *Research Methods* * in Psychology*

Sociology/Anthropology 371:* Foundations of Social Science Research: Quantitative Methods *

Statistics 270: *Intermediate Statistics for Social Science Research *

Statistics 282: *Topics in Statistics*

Statistics 302: *Biostatistics:* *Design and Analysis*

Statistics 322: *Statistical Theory* (strongly recommended for mathematics majors)

3. An Experiential Learning Component (Optional)

Each concentrator is encouraged to participate in experientially-based research or employment that takes statistical methods beyond the traditional classroom. This can occur on or off campus. Prior approval by the director of Statistics Program and a letter after the fact from a supervisor are required to earn credit. Excellent opportunities for experiential learning in statistics are available through academic internships (Statistics 294), the mathematics practicum (Mathematics 390), and the Center for Interdisciplinary Research (CIR) (Mathematics, Statistics, Computer Science 389). As a CIR fellow, students can work during the academic year or summer with faculty on research from a variety of disciplines.

Note: For students considering graduate school in statistics or a closely related field, the following courses are recommended: Mathematics 126 or 128: *Calculus II*, Mathematics 220: *Elementary Linear Algebra*, Mathematics 226: *Multivariable Calculus*, Mathematics 230: *Differential Equations I*, Mathematics 242: *Modern Computational Mathematics*, Mathematics 244 and 344: *Real Analysis I and II*, Computer Science 251-252:* Software Design and Implementation*.

Statistics 110, Statistics 212, and Economics 263 all provide an introduction to statistics, and students should not take more than one; they can all serve as a prerequisite for further courses, although Economics 263 is geared toward majors in economics. Statistics 214 is also an introductory course that assumes no background in statistics, but it can also be taken by students coming from Statistics 110, Economics 263 or AP Statistics who would like a transition into the statistics concentration.

##### COURSES

This is an introductory course for the liberal arts. Students learn study design principles and
develop statistical literacy and reasoning. They learn to describe distributions, assess if known
distributions fit their data, estimate population values with confidence intervals, and assess
statistical significance with hypothesis tests (e.g., chi-square, *z-*, and *t-*tests,
ANOVA, correlation, and regression). In addition to lectures, there is a weekly computer lab. Not
recommended for students who have completed a term of calculus. STAT 110, STAT 212,
and ECON 263 all provide an introduction to statistics, and students should not take more
than one; they all can serve as a prerequisite for further courses. Offered each semester.

212 Statistics for the Sciences

A first course in statistical methods for scientists, this course addresses issues for proposing/designing an experiment, as well as exploratory and inferential techniques for analyzing and modeling scientific data. Topics include probability models, exploratory graphics, descriptive techniques, statistical designs, hypothesis testing, confidence intervals, and simple/multiple regression. Prerequisite: MATH 119 or MATH 120 or equivalent. Offered each semester. Enrollment limited for seniors. STAT 110, STAT 212, and ECON 263 all provide an introduction to statistics and students should not take more than one; they all can serve as a prerequisite for further courses. Counts toward the mathematical biology concentration.

214 Honors Statistics for the Sciences

This course engages students with the material in STAT 212 in greater depth and breadth. Topics such as bootstrapping and multiple regression will be introduced in addition to core material from STAT 212. No previous experiences with statistics is assumed; this course provides an introduction to statistics, but it can also be taken by students coming from STAT 110, ECON 263, or AP Statistics who would like a transition into the statistics concentration. Prerequisites: MATH 119 or MATH 120 or equivalent, or CSCI 125, or some previous statistics (e.g., AP Statistics or STAT 110 or ECON 263). Counts toward mathematical biology concentration.

270 Intermediate Statistics for Social Science Research

This course focuses on the use of statistics in a social science context. Students investigate three essential questions: How can one reliably measure something? How does one design valid research? How does one analyze research results? Topics include ANOVA designs (for example, one-way and two-way with interaction), data reduction methods, and principles of measurement. Interdisciplinary groups work together on case studies throughout the term. Prerequisites: STAT 110, STAT 212, or STAT 214, or ECON 263, or equivalent preparation, or permission of the instructor. Offered fall 2013-14 and alternate years.

This course takes a case-study approach to the fitting and assessment of statistical models with application to real data. Specific topics include multiple regression, model diagnostics, and logistic regression. The approach focuses on problem-solving tools, interpretation, mathematical models underlying analysis methods, and written statistical reports. Prerequisite: STAT 110, STAT 212, or STAT 214, or ECON 263, or equivalent preparation, or permission of instructor. Offered each semester. Counts toward mathematical biology concentration.

Students explore special topics in statistics. Topics vary from year to year. May be repeated if topics are different. Offered periodically.

294 Internship

298 Independent Study

302 Biostatistics: Design and Analysis

The course investigates issues in health-related settings using a quantitative, research-oriented perspective. Course material focuses on global and public health issues, study design, methods for analyzing health data, and communication of research findings. Design topics include controlled trials, case-control, cohort and other observational studies. Methods include survival analysis and casual inference for observational studies. Communication emphasizes writing up findings and interpreting published research. Prerequisite: completion of STAT 272 or permission of the instructor. Counts toward mathematical biology concentration. Offered during fall semester 2014-15 and alternate years.

316 Advanced Statistical Modeling

This course extends and generalizes methods introduced in STAT 272 by introducing generalized linear models (GLMs) and correlated data methods. GLMs cover logistic and Poisson regression, and more. Correlated data methods include longitudinal data analysis and multilevel models. Applications are drawn from across the disciplines. Prerequisite: STAT 272. Offered annually in the spring semester. Counts toward neuroscience concentration.

This course is an investigation of modern statistical theory along with classical mathematical statistics topics such as properties of estimators, likelihood ratio tests, and distribution theory. Additional topics include Bayesian analysis, bootstrapping, Markov Chain Monte Carlo, and other computationally intensive methods. Prerequisite: STAT 272 and MATH 262. Offered annually in the fall semester. Counts toward neuroscience concentration.

Mathematics, Statistics, and Computer Science 389 Research Methods (0.5 credit)

Students focus on writing scientific papers, preparing scientific posters, and giving presentations in the context of a specific, year-long, interdisciplinary research project. In addition, this weekly seminar series builds collaborative research skills such as working in teams, performing reviews of math, statistics, and computer science literature, consulting effectively, and communicating proficiently. Exposure to post-graduate opportunities in math, statistics, and computer science disciplines is also provided. Open to students accepted into the Center for Interdisciplinary Research

394 Internship

396 Directed Undergraduate Research: "Topic Description"

This course provides a comprehensive research opportunity, including an introduction to relevant background material, technical instruction, identification of a meaningful project, and data collection. The topic is determined by the faculty member in charge of the course and may relate to his/her research interests. Prerequisite: Determined by individual instructor. Offered based on department decision. May be offered as a 1.00 credit course or .50 credit course.

398 Independent Research

related courses

125 Computer Science for Scientists and Mathematicians

This course focuses on handling data: visualization, finding patterns, and communicating with data. The primary tools are Python (for transforming data) and R (for visualization and classification). Students work individually and in teams to apply basic principles and explore real-world datasets with a sustainability theme. Prerequisite: calculus or consent of the instructor. Counts toward statistics and mathematical biology concentrations. One of CSCI 121, CSCI 125, CSCI 251counts toward linguistic studies concentration. Offered each semester.

Economics 263 Statistics for Economics

This course emphasizes skills necessary to understand and analyze economic data. Topics include descriptive statistics, probability and random variables, sampling theory, estimation and hypothesis testing, and practical and theoretical understanding of simple and multiple regression analysis. Applications to economic and business problems use real data, realistic applications, and econometric/statistical software. Prerequisite: MATH 119 or MATH 120 and one of Economics 110-121, or consent of the instructor. Offered each semester. STAT 110, STAT 212, and ECON 263 all provide an introduction to statistics. ECON 263 is recommended for economics majors who do not plan to take both STAT 272 and ECON 385. Credit will not be given for more than one of STAT 110, STAT 212, or ECON 263; credit will not be given for STAT 110, STAT 212, or ECON 263 following completion of STAT 272.

Economics 385 Econometrics

Ideal for students interested in applying statistical models to economic problems, this course emphasizes theoretical foundations, mathematical structure and applications of major econometric techniques, including ordinary least squares, generalized least squares, dummy variables, non-linear transformations, instrumental variables, simultaneous equation modeling, and time series models. Students in the class complete a sophisticated economic research project of their choice. Prerequisites: ECON 261 and either ECON 263 or STAT 272 or permission of instructor. Offered annually.

Mathematics 262 Probability Theory

This course is an introduction to the the mathematics of randomness. Topics include probabilities on discrete and continuous sample spaces, conditional probability and Bayes' Theorem, random variables, expectation and variance, distributions (including binomial, Poisson, geometric, normal, exponential, and gamma) and the Central Limit Theorem. Students use computers in the exploration of these topics. Prerequisite: MATH 126 or MATH 128. Offered each semester.

Mathematics 390 Mathematics Practicum

Students work in groups on substantial problems posed by and of current interest to area businesses and government agencies. The student groups decide on promising approaches to their problem and carry out the necessary investigations with minimal faculty involvement. Each group reports the results of its investigations with a paper and an hour-long presentation to the sponsoring organization. Prerequisite: Permission of instructor. Offered annually during Interim.

Psychology 230 Research Methods in Psychology

This course prepares the student with tools for understanding how research studies in psychology are conceptualized, designed, carried out, interpreted, and disseminated to the public. Use of library and Internet resources, ethical guidelines in the conduct of research and the skills of good scientific writing are emphasized. Students work independently and in small groups to design and conduct their own research projects. Prerequisites: PSYCH 125; STAT 110, STAT 212, STAT 214, or ECON 263. Offered each semester.

Sociology/Anthropology 371 Foundations of Social Science Research: Quantitative Methods

Students gain the skills necessary to conduct and critically evaluate quantitative research. Students learn the underlying theoretical assumptions and orientations of quantitative research, including research design, sampling techniques, strategies for data collection, and approaches to analysis. Students gain practice in data analysis by conducting a research project and using the Statistical Package for the Social Sciences (SPSS), a standard in sociology. Open to sociology/anthropology majors only. Prerequisite: STAT 110 or STAT 212 or STAT 214. Offered annually in the fall semester. Counts toward environmental studies major (social science track).