The modern science of statistics involves the invention, study, and development of principles and methods for modeling uncertainty through mathematical probability; for designing experiments, surveys, and observational programs; and for analyzing and interpreting empirical data. Mathematics plays a major role in all statistical activity, whether of an abstract nature or dealing with specific techniques for analyzing data. Statistics is an excellent field for students with strong mathematical skills and an interest in applying these skills to problems in the natural and social sciences. A program leading to the Bachelor of Arts degree in statistics offers excellent coverage of the principles and methods of statistics in combination with a solid training in mathematics. In addition, there is considerable elective freedom enabling interested students to examine those areas of knowledge in the biological, physical, and social sciences that are often subjected to detailed statistical analysis. The concentration provides a base for graduate study in statistics or in other subjects with strong quantitative components. An honors program is available. Students considering graduate study in statistics or related fields are encouraged to discuss their programs with the departmental counselor at an early stage, whether or not they plan to receive an undergraduate degree in statistics.

During 1999-2000 returning students may choose whether to fulfill their requirements for physical, biological, and mathematical sciences according to the new rules or according to those in force prior to this year. To satisfy the old requirements, students must take two quarters of an approved mathematical sciences sequence. If they elect to take the new curriculum, they must take one quarter of an approved mathematical sciences course. In addition, a sixth quarter of an approved course in physical, biological, or mathematical sciences must be taken to complete the general education requirements. NOTE: In order to get general education credit for calculus, two quarters must be taken. This will count as two quarters toward fulfilling the science general education requirement.

Statistics Courses for Students in Other Concentrations. Courses at the 200 level are designed to provide instruction in statistics, probability, and statistical computation for students from all parts of the University. These courses differ in emphasis on theory or methods, on the mathematical level, and in the direction of applications. Most of the introductory courses make serious use of high-speed computers to exemplify and explore statistical concepts and methods. The nature and extent of computer work varies according to the course and instructor. No previous experience with computers is expected for any first course. Statistics courses are not mathematics courses, but the mathematics prerequisites provide a useful guide to the level of a statistics course. In general, students are advised to take the course with the highest prerequisites that they can meet and, when possible, to take a two- or three-quarter sequence rather than a one-quarter course. In particular, students who have taken calculus should not take Statistics 200 but, rather, should take Statistics 220, 244-245-246, or 251.

Introductory Courses and Sequences. Statistics 220 is the usual first course in statistics, providing a general introduction to statistical concepts, techniques, and applications to data analysis and to problems in the design, analysis, and interpretation of experiments and observational programs. Computers are used throughout the course. One or two sections of Statistics 220 in the autumn, winter, and spring quarters use examples drawn from economics and business and a selection of texts and topics that are more appropriate for concentrators in economics. Statistics 200 is an alternative that has no calculus prerequisite and places less emphasis on exploring statistical techniques. Statistics 251 is an introductory course in probability.

Statistics 244-245-246 is recommended for students who want a thorough introduction to statistical theory and methodology. No prior training in statistics or probability is required for Statistics 244-245-246. However, Statistics 200 or 220 would provide a helpful background; students who have taken one of these are encouraged to take Statistics 244-245-246 if they want more extensive training in the basis of statistical methods.

Statistics 244-245 and 251 form the core of the statistics concentration: this is recommended as a cognate sequence to concentrators in the quantitative sciences and mathematics. It would be preferable, but not mandatory, to take Statistics 251 after 244-245; accordingly, 251 is now offered in the spring quarter to create a three-quarter sequence.

For students more interested in exploring methods and their applications, Statistics 222, 224, and 226 are recommended. These are complementary second courses that emphasize some class of methods for the analysis of data. They may be taken in any order. Each presumes a previous course in statistics (Statistics 220 or equivalent) and experience using computers in data analysis (as in Statistics 220). The emphasis is on linear models and experimental design in Statistics 222, multiple regression and least squares in Statistics 224, and counted data in Statistics 226.

For students who have completed Statistics 245, many graduate courses in statistics offer opportunities for further study of statistical theory, methods, and applications. The introductory probability course (Statistics 251) may be taken separately from any statistics courses. Statistics 251 can be supplemented with more advanced probability courses, such as Statistics 312, 313 or 381-383. NOTE: College students may register for a number of other 300-level courses in statistics. For further information, consult the instructor, the departmental counselor, or the Department of Statistics Web site (http://galton.uchicago.edu/).

Degree Programs. Students in the statistics program should meet the general education requirements in the mathematical sciences with courses in calculus. Concentration requirements include four additional prescribed mathematics courses and five prescribed statistics courses; the four mathematics courses should be completed by the end of the third year. Additional requirements include one course in computer science and two more courses in mathematics, statistics, or computer science. The five required statistics courses must include Statistics 244-245 and Statistics 251; and either 224 or 343. The fifth required statistics course may be either Statistics 220 or another course such as Statistics 222, 226, 240, 246, 301, 312, or 321. If Statistics 220 is included as part of the program, it should be taken before Statistics 244 is taken. Candidates should be sure their course program has the approval of the departmental counselor. NOTE: Students completing concentrations in both statistics and economics may replace Mathematics 200-201 and Mathematics 250/255 with Mathematics 195-196 and Mathematics 203.

Summary of Requirements

† Credit may be granted by examination.

Grading. Subject to College and divisional regulations, and with the consent of the instructor, all students except concentrators in statistics may register for regular letter grades or P/F grades in any 200-level statistics course. A grade of P is given only for work of C- quality or higher. Incompletes are allowed only in cases of serious emergency. To meet the concentration requirement in statistics, a grade of at least C- must be earned in each of the twelve courses; a grade of P is not acceptable for meeting these concentration requirements.

Honors. The B.A. with honors is awarded to students who have a grade point average of 3.0 or better overall and 3.25 or better in the twelve required courses in the concentration and who, in addition to these courses, complete an approved honors paper (Statistics 299). Interested students who meet the program requirements should see the departmental counselor before the end of their third year in the College.

PETER MCCULLAGH, Ralph and Mary Otis Isham Professor, Department of Statistics and the College

200. Elementary Statistics. PQ: Math 102, 106, placement into 131 or higher, or satisfactory performance on a special elementary diagnostic mathematics examination, and completion of one of the general education sequences in the biological, physical, or social sciences. This course meets one of the general education requirements in the mathematical sciences. This course is an introduction to statistical concepts and methods for the collection, presentation, analysis, and interpretation of data. Elements of sampling, simple techniques for analysis of means, proportions, and linear association are used to illustrate both effective and fallacious uses of statistics. Staff. Autumn, Winter, Spring.

220. Statistical Methods and Their Applications. PQ: Math 152 or equivalent and completion of one of the general education sequences in the biological, physical, or social sciences. This is an introduction to statistical techniques and methods of data analysis, including the use of computers. Examples are drawn from the biological, physical, and social sciences. Students are required to apply the techniques discussed to data drawn from actual research. Topics include data description, graphical techniques, exploratory data analyses, random variation and sampling, one- and two-sample problems, the analysis of variance, linear regression, and analysis of discrete data. One or more sections of Stat 220 use examples drawn from economics and business and a selection of texts and topics that are more appropriate for concentrators in economics. Staff. Summer, Autumn, Winter, Spring.

222. Linear Models and Experimental Design. PQ: Stat 220 or equivalent. This course covers principles and techniques for the analysis of experimental data and the planning of the statistical aspects of experiments, surveys, and observational programs. Topics may include linear and nonlinear models; analysis of variance and response surface analysis; randomization, blocking, and factorial designs; fractional replication and confounding; incorporation of covariate information; design and analysis of sample surveys; designs subject to constraints; split-plot and nested experiments; and components of variance. Staff. Spring.

224. Applied Regression Analysis. PQ: Stat 220 or equivalent. This course is an introduction to the methods and applications of fitting and interpreting multiple regression models. The primary emphasis is on the method of least squares and its many varieties. Topics include the examination of residuals, the transformation of data, strategies and criteria for the selection of a regression equation, the use of dummy variables, tests of fit, nonlinear models, biases due to excluded variables and measurement error, and the use and interpretation of computer package regression programs. The techniques discussed are illustrated by many real examples involving data from both the physical and social sciences. Matrix notation is introduced as needed. Staff. Autumn.

226. Analysis of Categorical Data. PQ: Stat 220 or equivalent. This course covers statistical methods for the analysis of structured, counted data. Topics discussed may include Poisson, multinomial, and product-multinomial sampling models; chi-square and likelihood ratio tests; log-linear models for cross-classified counted data, including models for data with ordinal categories and log-multiplicative models; logistic regression and logit linear models; and measures of association. Applications in the social and biological sciences are considered, and the interpretation of models and fits, rather than mathematical details of computational procedures, is emphasized. The computer is used throughout the course. Staff. Winter.

240. Probability and Statistics for the Natural Sciences. PQ: Math 201 or 196; and Chem 113 or 123, or Phys 123, 133, or 143. This course is an introduction to those topics in probability and statistics most relevant to experimental sciences, particularly the physical sciences. Probability topics include the central limit theorem and rules of probability, random variables, means, variances, and correlations. Statistics topics include propagation of errors, inference for means, and regression analysis for experimental data. In addition, topics in linear algebra such as vector spaces, projection and eigenvalues and eigenvectors are studied within the context of regression. Connections of statistical methods to Fourier series and other mathematical methods commonly used in the physical sciences may also be made. Staff. Spring.

241. Probability and Statistics for the Natural Sciences. PQ: Math 201 or 196; and Chem 113 or 123 or Phys 123, 133, or 143. The first five weeks of Stat 240 (50 units credit). Staff. Spring.

244-245-246. Statistical Theory and Methods. PQ: Math 153 or equivalent. A systematic introduction to the principles and techniques of statistics, with emphasis on the analysis of experimental data. Topics include theoretical and empirical frequency distributions; binomial, Poisson, normal, and other standard distributions; random variables and probability distributions; principles of inference including Bayesian inference, maximum likelihood estimation, hypothesis testing, and confidence intervals; and analysis of counted data, analysis of variance, least squares, and multiple and logistic regression. Computers are used throughout the sequence. Staff. Autumn, Winter.

251. Introduction to Mathematical Probability. PQ: Math 200 or 203, or consent of instructor. This course, which was previously Stat 230, covers fundamentals and axioms; combinatorial probability; conditional probability and independence; binomial, Poisson, and normal distributions; the law of large numbers and the central limit theorem; and random variables and generating functions. Staff. Spring.

267. History of Statistics (=CFS 329, HiPSS 256, Stat 267). PQ: Prior statistics course. This course covers topics in the history of statistics, from the eleventh century to the middle of the twentieth century. The emphasis is on the period 1650 to 1950, and on the mathematical developments in the theory of probability and how they came to be used in the sciences, both to quantify uncertainty in observational data and as a conceptual framework for scientific theories. The course includes broad views of the development of the subject, and closer looks at specific people and investigations, including reanalyses of historical data. S. Stigler. Spring.

297. Undergraduate Research. PQ: Consent of faculty adviser and departmental counselor. Students are required to submit the College Reading and Research Course Form. Open to students concentrating in statistics and to nonconcentrators. May be taken either for a P/F grade or for a quality grade. This course consists of reading and research in an area of statistics or probability under the guidance of a faculty member. A written report must be submitted at the end of the quarter. Staff. Autumn, Winter, Spring.

299. Bachelor's Paper. PQ: Consent of faculty adviser and departmental counselor. Students are required to submit the College Reading and Research Course Form. Open to students concentrating in statistics. May be taken P/N or P/F. This course consists of reading and research in an area of statistics or probability under the guidance of a faculty member, leading to a bachelor's paper. The paper must be submitted at the end of the quarter. Staff. Autumn, Winter, Spring.

301-302. Mathematical Statistics. PQ: Stat 304 or consent of instructor. This course surveys the mathematical structure of modern statistics. Topics include statistical models, methods for parameter estimation, comparison of estimators, efficiency, confidence sets, theory of hypothesis tests, elements of linear hypothesis theory, analysis of discrete data, and an introduction to Bayesian analysis. Staff. Winter, Spring.

304. Distribution Theory. PQ: Stat 245 and Math 205, or consent of instructor. This course covers methods of deriving, characterizing, displaying, approximating, and comparing distributions. Topics include algebra by computer (Maple and Macsyma), standard distributions (uniform, normal, beta, gamma, F, t, Cauchy, Poisson, binomial, and hypergeometric), moments and cumulants, characteristic functions, exponential families, the Pearson system, Edgeworth and saddlepoint approximations, and Laplace's method. Staff. Autumn.

312. Introduction to Stochastic Processes I. PQ: Stat 251, and Math 201 or 204. This course is an introduction to stochastic processes not requiring measure theory. Topics include branching processes, recurrent events, renewal theory, random walks, Markov chains, Poisson, and birth-and-death processes. Staff. Winter.

313. Introduction to Stochastic Processes II. PQ: Stat 312 or consent of instructor. This course is a sequel to Stat 312. Topics covered include continuous time Markov chains: birth and death processes and queues, introduction to discrete time martingales, Brownian motion and diffusions. Time permitting: stochastic ordering, Poisson approximations. The emphasis is on defining the processes and calculating or approximating various related probabilities. The measure theoretic aspects of these processes is not covered rigorously. Staff. Spring.

329. Applied Multivariate Analysis (=Bus 424, Stat 329). PQ: Stat 220 or equivalent. This course is an introduction to multivariate analysis. Topics include principal component analysis, multidimensional scaling, discriminant analysis, canonical correlation analysis, and cluster analysis. Staff. Spring.

343. Applied Linear Statistical Methods. PQ: Stat 245 and Math 250, or equivalents. This course is an introduction to the theory, methods, and applications of fitting and interpreting multiple regression models. Topics include the examination of residuals, the transformation of data, strategies and criteria for the selection of a regression equation, nonlinear models, biases due to excluded variables and measurement error, and the use and interpretation of computer package regression programs. The theoretical basis of the methods, the relation to linear algebra, and the effects of violations of assumptions are studied. Techniques discussed are illustrated by examples involving both physical and social sciences data. Staff. Autumn.

350-351. Epidemiology (=HlthSt 310-311, Stat 350-351). PQ: Consent of instructor. The quantitative study of the spread of diseases in a population. Staff. Autumn, Spring.

356. Introduction to Survival Analysis (=HlthSt 331, Stat 356). PQ: Consent of instructor. The analysis of longitudinal data on patients. Staff. Winter.

381. Measure-Theoretic Probability I. PQ: Stat 313 or consent of instructor. A detailed, rigorous treatment of probability from the point of view of measure theory, as well as existence theorems, integration and expected values, characteristic functions, moment problems, limit laws, Radon-Nikodym derivatives, and conditional probabilities. Staff. Autumn.