Courses for Undergraduates Offered by the Department of Statistics

Last update: July 5, 2006

This document provides some information on courses for undergraduates offered by the Department of Statistics. It should help you decide which first statistics course is right for you and make you aware of the range of courses available for further study. Many of the intermediate classes have only the introductory class (Statistics 22000) as a prerequisite and can be taken by undergraduates. See the program description and the Statistics Department web page for current information on courses and the requirements for a B.A. in statistics. Rules change over time so please ask instructors and advisers to confirm the information presented online.

1. Introductory Courses: Statistics 20000, 22000, 23400.

The Statistics Department offers three distinct courses at the introductory undergraduate level.

Statistics 20000 is the most basic course, does not have a calculus requirement and fulfills one of the general education requirements in the mathematical sciences. Stat 20000 focuses on fundamental ideas of randomization and study design, effective and fallacious presentations and interpretations of statistics, and the concept of statistical inference as illustrated with means, proportions, and linear associations. It is offered Autumn, Winter, and Spring.

Statistics 22000 provides an introduction to how statisticians think about describing data, data collection and research design, probability and randomness, and inference from a sample to a population. This course uses computers and employs more formulas than does Stat 20000. It also provides better preparation than does 20000 for additional methods and theory courses. Examples are taken from the biological, physical, and social sciences - including economics. Additional examples may come from sports, medicine, business, government, and current events. Stat 22000 is offered year round.

Although motivation is hard to quantify, your motivation in your field for further study of statistics is an important factor in both satisfaction and success in statistics. If you are eager to move ahead with research in your field, then statistics is likely to be an essential tool for you, and you will want to learn as much as you can as early as possible. In that case, it may be worthwhile to you to take Stat 22000 (or even 23400) rather than 20000, or even to consider the two-quarter sequence, Stat 24400-24500, in order to have a few more methods in your toolbox for your research and/or to understand some of the mathematical theory behind the methods in order to be better prepared for additional study.

Statistics 23400: Statistical Models and Methods can be a more rigorous alternative to Stat 22000. This course covers essentially the same set of statistical methods as 22000 and, in addtion, includes exposure to probability models and the statistical concepts underlying the methodology. Thus, the pace and depth of the course can be more demanding than for Stat 22000. Univariate calculus and computer simulation are used throughout the course to investigate statistical concepts and their mathematical underpinnings. One full year of univariate calculus is a prerequisite for the course (Math 13300, 15300, or 16300). Familiarity with at least limits, derivatives and integrals of polynomial and exponential functions, change of variable (substitution) in definite integrals, max-min problems, use of summation notation, and sequences and series as well as a willingness to explore ideas mathematically are key to your success in this course. It is offered Autumn, Winter, and Spring.

Stat 23400 takes the mathematical prerequisite quite seriously. Enrolling concurrently in either Math 13300, 15300, or 16300 while taking Stat 23400 is very strongly discouraged. Further, students who do not feel strong mathematically, may want to wait until completing their entire mathematical requirement (e.g., Math 19500-19600 for Economics majors) before enrolling in Stat 23400. Economics majors are strongly encouraged to delay taking Stat 23400 until the quarter just before enrolling in their required econometrics course (Econ 21000), for which Stat 23400 is a prerequisite. Thus, delaying Stat 23400 until at least late in the second year or even early in the third year of the Economics degree program should not be considered unusual.

2. Three Methods Courses: Statistics 22200, 22400, 22600.

Statistics 22000 or equivalent is a prerequisite for Stat 22200 (Linear Models and Experimental Design, Spring), Stat 22400 (Applied Regression Analysis, Autumn), and Stat 22600 (Analysis of Categorical Data, Winter). It would be best, but not essential, to take 22000 during the quarter before taking a course in the 22200/22400/22600 group. More than one of these courses may be taken in any order for credit; they do not overlap very much. Stat 22200/22400/22600, because of their applied focus and detailed attention to the methods they discuss, may be taken after 23400 or 24400-24500 (described in section 3). Additionally, Stat 22200/22400/22600 may be similar to methods classes in other departments, but they might be distinct enough to be taken in addition to those other courses. The combination of a course in statistics and a related but different course in another department could provide excellent coverage of a topic. Please consult with the instructors of the courses and advisers on this issue.

Stat 22200: Linear Models and Experimental Design is taught in Spring. This course focuses on the analysis of quantitative experimental data that might be found in experimental biology, medicine, psychology, industrial process development, and marketing preference data. With a limited budget and resources, how can a study be designed to get as much information as possible about relationships between outcomes of interest and factors under the experimenter's control? Some methods presented in this course have been crucial in advances in medicine, industry, and agriculture. Recently, this course was taken by students from economics, mathematics, statistics, biological sciences, and other majors.

Stat 22400: Applied Regression Analysis is given in Autumn. It focuses on the multiple linear regression model and the method of least squares estimation. Regression is a very popular tool in economics, but also is widely used in the natural and social sciences. How do statisticians compare a model and its predictions to the observed data? How do statisticians examine the appropriateness of model assumptions and develop alternative models? This course provides a mixture of mathematical study of regression and practical advice when using these techniques. Generally, students from economics, mathematics, statistics, psychology, biological sciences, the MPP program, and other majors take Stat 22400.

Stat 22600: Analysis of Categorical Data is offered in the Winter quarter. This course concerns the description, analysis and modeling of data that take the form of counts. What proportion of people have certain complex combinations of attributes and opinions? What behaviors and conditions are associated with outcomes of interest? The methods of this course are particularly relevant for social sciences, biology, and the analysis of survey data. Similar to 22200 and 22400, this course presents models, how to interpret them, and how to assess their fit to the data. Generally, majors from sociology, statistics, economics, biological sciences, and other departments have enrolled in this class.

3. More Advanced Starting Points, Courses for Deeper Study: Statistics 24400-24500-24600, 25100.

Students who want a more mathematical treatment of probability and statistics should consider 24400, or 25100 as an initial course in statistics. Also, students who want a more systematic explanation of probability and statistical inference after 22000 should consider these two courses.

Stat 24400-24500-24600: Statistical Theory and Methods I-II-III are offered in the Autumn, Winter, and Spring, respectively. During the 2006-2007 academic year, a second sequence of Stat 24400-24500 will also be offered Winter-Spring. Stat 24400-24500 is a sequence that provides a more thorough introduction to probability and statistics. Although it has some material in common with Stat 22000/23400, it is presented in a more formal and mathematical manner. It is great as a starting place for learning about probability and statistics. Although there is a high mathematics requirement (Math 19600, 20100, or 20400 - multivariable calculus and some linear algebra), Stat 24400-24500 are not advanced mathematics classes and do involve looking at data and applications, often with use of a computer. Prior experience with a computer is not required. Stat 24600 is designed to build on material from Stat 24400-24500, introducing more complex models and methods of computation.

Statistics 24400-24500-24600 is designed as a sequence, but students often take the pair of classes Stat 24400-24500 or sometimes just Stat 24400. Statistics 22000 is not prerequisite, but could be taken before 24400 in preparation. A wide range of students take Stat 24400 and it is good background for anyone wanting to know more about statistics and probability. Stat 24500 is designed to complete the introduction begun in 24400. It is encouraged that you consider taking the sequence 24400-24500. Even if your department only requires 24400, we believe you should not dismiss 24500. Statistics 24600 was given for the first time in 2000 and is generally taken by master's degree students in statistics, undergraduates in mathematics, statistics, and economics, graduate students in the physical sciences and a few other individuals.

After 24400, the recommended course is 24500. It would also be possible to take 25100 for a more rigorous treatment of probability. It might be possible to take 22200, 22400, or 22600 after just 24400, depending on your background and on the permission of the instructor. After 24400-24500, options include 24600, 25100, 22200, 22400, or 22600, and possibly higher courses.

Stat 23400 is a course that covers some of the topics of Stat 24400-24500, but with a slightly different audience in mind. Although univariate calculus is used, multivariate calculus and linear algebra are not assumed to be familiar as in 24400-24500. Applications and simulations are given at least as much prominence as is theory. Stat majors should take 24400-24500, not 23400.

Stat 25100: Introduction of Mathematical Probability is offered each Spring. Stat 25100 introduces material that is essential for the work of mathematical statisticians and probabilists. It provides a more mathematical introduction to probability than the other 20000-level courses. This course covers fundamentals and axioms; combinatorial probability; conditional probability and independence; some common probability distributions; the law of large numbers and the central limit theorem; and random variables and generating functions. Mathematics, economics, statistics, biochemistry, physics, applied mathematics, and other subjects have been the major areas of students in this class.

You could take one of Stat 22000/23400 before or after Stat 25100. Majors in Statistics are required to take 24400-24500 and 25100 among other courses. Stat 25100 may be taken before 24400-24500, but the recommended sequence is 24400-24500 then 25100. After 25100, if you have sufficient mathematics background, it may be possible to take higher level probability classes in the Department. Ask the instructors for Stat 22200/22400/22600 if you can take their classes after 25100 if 25100 is your only class in the Statistics Department. Mathematical probability and applied statistics can be quite different, and it might be wise to have some background besides 25100 before proceeding with one of 22200/22400/22600.

4. Time Dependent Data Course: Statistics 26100

Statistics 26100 on the analysis of time-dependent data was offered for the first time in Spring, 2006. Watch for this course to return to the schedule again during the 2007-08 academic year. This course considers the modeling and analysis of data that are ordered in time. The main focus will be on quantitative observations taken at evenly spaced intervals and will include both time-domain and spectral approaches. Time permitting, statistical approaches to other data types, such as categorical observations or point processes, will be considered. Students will need some exposure to linear modeling as prerequisite, such as Stat 22400, 23500 (no longer offered), or Stat 24500.

5. Some History: Statistics 26700

Statistics 26700 covers topics in the history of statistics with some focus on major breakthroughs and major misconceptions. Some data are reanalyzed. The Department of Statistics at the University of Chicago is one of the few statistics departments in the country to offer such a course. Stat 22000/23400 would be enough background according to the catalog before taking this course. A methods class 22200/22400/22600, a statistical methods class in another department, or any of the more advanced classes would provide more perspective on statistics. However, the course is designed to be accessible to students with differing degrees of statistical background.

6. Graduate Courses, Survey Research, Master's Degree, Classes in Other Departments and Programs.

Graduate Courses. After Stat 24400-24500 and after Stat 25100 it may be possible to take various graduate level courses in the Department of Statistics. Stat 25100 could lead to advanced probability classes, especially for the mathematically talented and advanced student.

Survey Research. The Department offers a Survey Research class, Statistics 33100, in Autumn. This course could be of interest to students who anticipate a research career that uses and collects survey data. Fields such as sociology, psychology, education, and economics often use survey data in research.

Master's Degree. The Department of Statistics offers a Master's Degree in Statistics. The requirements include nine approved courses and a Master's paper. Students from the college with strong mathematics backgrounds and interest in the use of statistics and probability in an area of research are encouraged to read about the program in the Department admissions page: admissions. Please also see the page that describes the Master's program and discusses requirements.

Statistics Courses in Other Departments. The faculty of the Department of Statistics participate in research and teaching in many other departments and divisions. Links to these programs may be found in the Related Programs section of the Department web page. Two examples are mentioned below. Please see the web page list for more information.

Example 1: The Department of Health Studies offers courses on biostatistics, epidemiology, and other health topics involving statistical methods. Some classes in Health Studies have prerequisites in statistics, which is something for undergraduates interested in health-related fields to consider.

Example 2: The Department of Mathematics at the University of Chicago offers a one-year graduate program leading to the degree of Master of Science in Financial Mathematics. Professors from the Statistics Department teach in the program.

For further information, please consult the the graduate course catalog, the Statistics Department web page (with links to course web pages), instructors and advisors. We hope to see you in some of our classes!