Courses in Statistics

This is a basic course in statistics. The topics covered are the nature of statistical reasoning, graphical and descriptive statistical methods, design of experiments, sampling methods, probability, probability distributions, sampling distributions, estimation and statistical inference. Confidence intervals and hypothesis tests for means and proportions are studied in the one- and two-sample settings. The course concludes with inference-regarding correlation, linear regression, chi-square tests for two-way tables and one-way ANOVA. Statistical software is used throughout the course, and students engage in a wide variety of hands-on projects. This counts toward the core course requirement for the major. Students with credit for STAT 116 cannot take STAT 106 for credit. No prerequisite. Offered every semester.

Appropriate applications of statistical methods have changed the way some Major League Baseball teams manage the game. (See "Moneyball: The Art of Winning an Unfair Game.") Statistics are used in other sports to evaluate the performance of individual players or teams. The focus of this course is on the proper application of statistical models in sports. Students use appropriate methods to examine interesting questions such as: Are there unusual patterns in the performance statistics of "steroid sluggers" such as Barry Bonds and Mark McGwire or pitchers such as Roger Clemens? Other possible topics include the impact of a penalty kick in soccer, home-field advantage in football, technological improvements in golf or cycling, and of training methods in marathon running. Although the sport and question of interest change, the focus on proper applications of appropriate statistical methods remains the same. Students analyze data and present their results to the class. Oral and written reports are expected. This counts toward the core course requirement for the major. Students with credit for STAT 106 cannot take STAT 116 for credit. No prerequisite. Offered occasionally.

This course focuses on choosing, fitting, assessing and using statistical models. Simple linear regression, multiple regression, analysis of variance, general linear models, logistic regression and discrete data analysis provide the foundation for the course. Classical interference methods that rely on the normality of the error terms are thoroughly discussed, and general approaches for dealing with data where such conditions are not met are provided. For example, distribution-free techniques and computer-intensive methods, such as bootstrapping and permutation tests, are presented. Students use statistical software throughout the course to write and present statistical reports. The culminating project is a complete data analysis report for a real problem chosen by the student. The MATH 106–206 sequence provides a thorough foundation for statistical work in economics, psychology, biology, political science and many other fields. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: STAT 106 or 116, or a score of 4 or 5 on the AP statistics exam. Offered every semester.

This course focuses on nonparametric and distribution-free statistical procedures. These procedures rely heavily on counting and ranking techniques. In the one- and two-sample settings, the sign, signed-rank and Mann-Whitney-Wilcoxon procedures are discussed. Correlation and one-way analysis of variance techniques also are investigated. A variety of special topics are used to wrap up the course, including bootstrapping, censored data, contingency tables and the two-way layout. The primary emphasis is on data analysis and the intuitive nature of nonparametric statistics. Illustrations come from real data sets, and students are asked to locate an interesting data set and prepare a report detailing an appropriate nonparametric analysis. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: STAT 106 or 116, or a score of 4 or 5 on the AP statistics exam. Offered every other year.

This course provides a mathematical introduction to probability and statistics using R statistical software. The primary goal of the course is to learn and apply Monte-Carlo simulation techniques to a wide variety of problems. We focus on solving problems from a numerical point of view, with methods to complete numerical integration, root finding, curve fitting, variance reduction and optimization. Core knowledge of R and basic programming concepts are introduced. Case studies and projects are independently completed throughout the semester. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: STAT 106 or STAT 116. Offered every other year.

Each offering of this course approaches the study of variability using a particular set of statistical tools (such as Bayesian Analysis, biostatistics, sports analytics, experimental design or statistical machine learning). Specific statistical methodology within a subfield of the discipline is examined. A large component of each offering involves intensive projects in which students are expected to determine which statistical methods are appropriate for a given setting before analyzing data. As part of these projects and daily activities, students use R to analyze data to make inferences about the population characteristics of interest. Additionally, written and oral communication are a regular part of the course. The course may be repeated for credit as long as the subfield is different. That is, students may receive credit for each specific subfield only once. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: any STAT course at the 200 level or higher. Offered every spring.

Additional information for different subfields: https://www.kenyon.edu/academics/departments-and-majors/mathematics-statistics/academic-program-requirements/courses-in-statistics/stat-306-topics/

This course focuses on linear regression models. Simple linear regression with one predictor variable serves as the starting point. Models, inferences, diagnostics and remedial measures for dealing with invalid assumptions are examined. The matrix approach to simple linear regression is presented and used to develop more general multiple regression models. Building and evaluating models for real data are the ultimate goals of the course. Time series models, nonlinear regression models and logistic regression models also may be studied if time permits. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: STAT 106 or 116, and MATH 224. Offered every other spring.

This course follows MATH 336 and introduces the mathematical theory of statistics. Topics include sampling distributions, order statistics, point estimation, maximum likelihood estimation, methods for comparing estimators, interval estimation, moment-generating functions, bivariate transformations, likelihood ratio tests and hypothesis testing. Computer simulations accompany and corroborate many of the theoretical results. Course methods often are applied to real data sets. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: MATH 336. Offered every other spring.

Individual study is a privilege reserved for students who want to pursue a course of reading or complete a research project on a topic not regularly offered in the curriculum. It is intended to supplement, not take the place of, coursework. Individual study cannot be used to fulfill requirements for the major. Individual studies will earn 0.25-0.5 units of credit. To qualify, a student must identify a member of the mathematics department willing to direct the project. The professor, in consultation with the student, creates a tentative syllabus (including a list of readings and/or problems, goals and tasks) and describes in some detail the methods of assessment (e.g., problem sets to be submitted for evaluation biweekly; a 20-page research paper submitted at the course's end, with rough drafts due at given intervals; and so on). The department expects the student to meet regularly with the instructor for at least one hour per week. All standard enrollment/registration deadlines for regular college courses apply. Because students must enroll for individual studies by the end of the seventh class day of each semester, they should begin discussion of the proposed individual study by the semester before, so that there is time to devise the proposal and seek departmental approval. Permission of instructor and department chair required. Individual study courses may be counted as electives in the major, subject to consultation with and approval by the Department of Mathematics and Statistics. No prerequisite.