Return to Table of Contents

Go to Program of Study

Go to bottom of document

Courses

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 Common Core sequences in the biological, physical, or social sciences. This course fulfills one of the Common Core 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 Common Core 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 in the autumn 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. 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 Qualitative 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.

227. Biostatistical Methods. PQ: Stat 220 or 244, MedBio 315, or consent of instructor. This course builds on the statistical methods introduced in Stat 220 and deals with methods frequently required in biology and medicine. Topics include an overview of biostatistics, linear regression and correlation, adjustment for covariates, contingency table analysis emphasizing 2-by-2 tables, logistic regression, and survival data analysis. Additional topics may include Poisson regression and statistical methods in epidemiology, such as relative risk, attributable risk, and assessment of screening and diagnostic tests. Staff. Autumn.

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. M. Stein. Spring.

242. Applied Probability and Elementary Stochastic Models. PQ: Math 133, 153, or consent of instructor. This course is an introduction to probability and stochastic processes at an elementary level. Emphasis is on topics that have applications in the natural and social sciences. Topics include conditional probability, independence, random variables and expectations, standard distributions such as the binomial and Poisson distributions, and random processes, including Poisson processes and Markov chains. This course covers more material but in considerably less depth than Stat 230, with more emphasis on applications and less on rigorous proofs. Not offered 1996-97; will be offered 1997-98.

244-245. 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, 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.

299. 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. Students may take this course 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.

The 300-level courses are currently being restructured. For more information, consult the departmental counselor. Updated departmental and course information can also be found electronically on the Department of Statistics home page on the World Wide Web (http://galton.uchicago.edu/).

301-302. Mathematical Statistics. PQ: Math 205, and Stat 245, 251, and 304; or equivalent. 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.

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

321. Applied Multivariate Analysis (=Bus 423). 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. The techniques discussed are illustrated by real examples involving both physical and social sciences data. Staff. Autumn.

381-382. Measure-Theoretic Probability I, II. PQ: Stat 312 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. Winter, Spring.

Go to top of document