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Course Criteria
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3.00 Credits
This course meets one of the general education requirements in the mathematical sciences. STAT 20000 may not be used in the statistics major. It is recommended for students who do not plan to take advanced statistics courses. Not open to students with credit for STAT 22000 or 23400 who matriculated in the College after August, 2008. This course introduces 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. Autumn, Winter, Spring.
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2.00 Credits
PQ: MATH 15200 or equivalent. Students who matriculate in the College after August, 2008, may count either STAT 22000 or 23400, but not both, toward the forty-two credits required for graduation. This course introduces 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. Autumn, Winter, Spring.
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3.00 Credits
PQ: STAT 22000 or equivalent. This course covers principles and techniques for the analysis of experimental data and the planning of the statistical aspects of experiments. Topics include linear models; analysis of variance; randomization, blocking, factorial designs; confounding; and incorporation of covariate information. Spring.
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3.00 Credits
PQ: STAT 22000 or equivalent. This course introduces 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 natural and social sciences. Matrix notation is introduced as needed. Autumn.
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3.00 Credits
PQ: STAT 22000 or equivalent. This course covers statistical methods for the analysis of structured, counted data. Topics 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. Winter.
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3.00 Credits
PQ: STAT 22400 or 24500 or equivalent, or consent of instructor. This course is designed to provide students with tools for analyzing categorical, count, and time-to-event data frequently encountered in medicine, public health, and related biological and social sciences. This course emphasizes application of the methodology rather than statistical theory (e.g., recognition of the appropriate methods, interpretation and presentation of results). Methods covered include contingency table analysis, Kaplan-Meier survival analysis, Cox proportional-hazards survival analysis, logistic regression, and Poisson regression. Winter.
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2.00 Credits
PQ: MATH 13300, 15300, or 16300. Students who matriculate in the College after August, 2008, may count either STAT 22000 or 23400, but not both, toward the forty-two credits required for graduation. This course is recommended for students throughout the natural and social sciences who want a broad background in statistical methodology and exposure to probability models and the statistical concepts underlying the methodology. Probability is developed for the purpose of modeling outcomes of random phenomena. Random variables and their expectations are studied; including means and variances of linear combinations and an introduction to conditional expectation. Binomial, Poisson, normal and other standard probability distributions are considered. Some probability models are studied mathematically, and others are studied via simulation on a computer. Sampling distributions and related statistical methods are explored mathematically, studied via simulation and illustrated on data. Methods include, but are not limited to, inference for means and variances for one- and two-sample problems, correlation, and simple linear regression. Graphical and numerical data description are used for exploration, communication of results, and comparing mathematical consequences of probability models and data. Mathematics employed is to the level of univariate calculus, but is less demanding than that required by STAT 24400. Summer, Autumn, Winter, Spring.
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3.00 Credits
PQ: Multivariate calculus (MATH 19520 or 20000 or equivalent.) This course covers linear algebra, with special attention to topics useful in statistical applications. In addition to addressing theoretical and algorithmic aspects of solving systems of linear equations, topics may include, but are not limited to, least squares, orthogonal projections, positive-definite matrices, quadratic forms, matrix decompositions, and an introduction to vector spaces. The computer is used to study some computational issues and mathematical explorations. Winter.
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3.00 Credits
PQ: Multivariate Calculus (MATH 19520 or 20000 or equivalent) and Linear Algebra (MATH 19620, 25500 or STAT 24300 or equivalent). Some previous experience with statistics helpful but not required. This course is a systematic introduction to the principles and techniques of statistics, with emphasis on the analysis of experimental data. The first quarter covers tools from probability and the elements of statistical theory. Topics include the definitions of probability and random variables, binomial and other discrete probability distributions, normal and other continuous probability distributions, joint probability distributions and the transformation of random variables, principles of inference (including Bayesian inference), maximum likelihood estimation, hypothesis testing and confidence intervals, likelihood ratio tests, multinomial distributions, and chi-square tests. Examples are drawn from the social, physical, and biological sciences. The coverage of topics in probability is limited and brief, so those who have taken a course in probability find reinforcement rather than redundancy. The second quarter covers statistical methodology, including the analysis of variance, regression, correlation, and some multivariate analysis. Some principles of data analysis are introduced, and an attempt is made to present the analysis of variance and regression in a unified framework. The computer is used in the second quarter. Autumn, Winter; Winter, Spring. (Note that the Autumn/Winter sequence tends to be slightly more advanced than the Winter/Spring sequence.)
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3.00 Credits
PQ: STAT 24400-24500, or equivalent. Knowledge of probability distributions, random variables, and estimation techniques (e.g., maximum likelihood at the level of STAT 24400-24500). Topics vary from year to year. The course recently has treated the impact of missing data on statistical analyses (e.g., probability models and methods of estimation and inference); algorithms for iterative maximum likelihood estimation (e.g., the Expectation-Maximization [EM] and Newton-Raphson algorithms); and Bayesian computation (e.g., Data Augmentation and Monte Carlo Markov Chain methods). Spring.
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