Department of Statistics

Kerchof Hall
University of Virginia
P.O. Box 400135
Charlottesville, VA 22904-4135
(434) 924-3222 Fax: (434) 924-3076
www.stat.virginia.edu

Overview Statistics is a means of analyzing data to gain insight into real problems. It is focused on problem solving, rather than on methods that may be useful in specific settings. Statistics is unique in its ability to quantify uncertainty. Thus statistics has become a crucial tool in all aspects of modern society, providing insight in such fields as public policy, law, medicine, the social sciences, and the natural sciences.

The Department of Statistics shares the newly emerged consensus among statisticians that statistical education should focus on data analysis and statistical reasoning rather than the presentation of a coterie of methods. As importantly, the department believes that the mathematical tools underlying statistical inference are significant and necessary for statistics education, but those tools must necessarily remain secondary in the training of statisticians. Because of these views, the statistics program strongly emphasizes its consulting service, which provides statistical consultation to all branches of the University. Through this service, statistics students gain valuable insight into all branches of the field while acquiring practical training in problem solving.

The Department of Statistics offers a broad range of courses covering all areas of applied and theoretical statistics.

Faculty The faculty consist of six full-time, one half-time, and seven adjunct appointments. The half-time faculty has a joint appointment in the department of mathematics, and the adjunct faculty have primary appointments in the departments of biostatistics, economics, and systems engineering. This collection of disciplines, in addition to the interests of the full-time faculty, ensures that the department is able to cater to the interests of diverse students.

Students Students who graduate with in-depth training in statistics enjoy a large range of opportunities. Some pursue employment in the public or private sector, working as actuaries, consultants, data analysts, or teachers, among many fields. Others do graduate study in fields such as economics, finance, mathematics, operations research, psychology, and, of course, statistics.

Interdisciplinary Major in Applied Statistics The Interdisciplinary Major in Applied Statistics provides students with the opportunity to integrate the study of statistics with another quantitatively intensive discipline. Knowledge of statistics is becoming increasingly important in many disciplines, so that students completing this major will have many options available upon graduation.

Students completing this major will be well prepared to design experimental studies and analyze data, in both their emphasis field and other areas. They will also be well prepared for graduate study in statistics, and with a modest amount of advance planning will be able to complete an MS in Statistics at UVa with one additional year of study. Students interested in the 5-year B.A./M.S. program should contact the Department’s major advisor.

The major program has four tracks: Biostatistics, Econometrics, Engineering Statistics, and Mathematical Statistics. The prerequisite for all tracks: Single variable calculus through the second semester, fulfilled by one of Math 122, Math 132, APMA 111.

Track 1: Biostatistics

The Biostatistics track is suitable for students using it as a primary major or a second major in conjunction with a major in Biology. Courses required for this track are:

Track 2: Econometrics

The Econometrics track is suitable for students as a primary major, or will serve well as a second major for students in Economics or Commerce. Courses required for this track are:

Track 3: Engineering Statistics

The engineering statistics track is designed for SEAS students who want to have a second major in the College. However, it is also be possible for a College student to opt for this track. Courses required for this track are:

Track 4: Mathematical Statistics

The target audience for this track are College students who would like an applied quantitative major. Courses required for this track are:

Minor in Statistics and Data Analysis The minor in statistics and data analysis is designed to meet the needs of several types of students: the student interested in applying statistics to some other field, the student interested in exploring a future career in biostatistics or applied statistics, the student interested in a career in actuarial statistics, or the mathematically minded student interested in graduate study in statistics.

Requirements for Minor in Statistics and Data Analysis Five (5) courses selected from: all STAT courses numbered 300 or above, MATH 312 and 511. These five courses must include STAT 512 and, at most, one of MATH 312 or STAT 500.

With consent of the statistics faculty, a student who has had an appropriate introductory statistics course in another department may be exempted from the MATH 312/STAT 500 requirement. Such a student still needs to take five courses from among MATH 511 and all STAT courses numbered 300 or above.

Courses used to satisfy the minor in statistics and data analysis cannot be used to satisfy the requirements of another major. For example, a student who takes MATH 310/312 to satisfy the requirements of the major in mathematics, must take five additional courses from MATH 511 and the STAT courses numbered 300 or above (excluding STAT 500).

Sample Programs The following are examples of programs for a student intending to pursue the minor in statistics and data analysis:

Students should be aware that, except for MATH 312, 511; STAT 500, 512, 513, and 519, all courses for the minor in statistics and data analysis are offered in alternate years. Please consult the department’s Web site for the offering schedule.

Additional Information For more information contact the Department of Statistics, 131 Kerchof Hall, P.O. Box 400135, Charlottesville, Virginia 22904-4135; (434) 924-3222; www.stat.virginia.edu.

Course Descriptions

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Note: The entering College student is encouraged to take the introductory course, STAT 110. This course, entitled Chance, is intended to make students aware of the ubiquity and importance of basic statistics in public policy and everyday life. The course uses a case-study approach based on current chance events reported in daily newspapers and current scientific journals. Credits earned in this course may be counted towards the College’s natural science area requirements. Students are also encouraged to take mathematics courses which serve as prerequisites for higher-level statistics courses.

STAT 110 - (3) (Y)
Chance: An Introduction to Statistics
Studies introductory statistics and probability, visual methods for summarizing quantitative information, basic experimental design and sampling methods, ethics and experimentation, causation, and interpretation of statistical analyzes. Applications use data drawn from current scientific and medical journals, newspaper articles, and the Internet. Students will not receive credit for both STAT 110 and STAT 112.

STAT 112 - (3) (S)
Introduction to Statistics
Includes graphical displays of data, relationships in data, design of experiments, causation, random sampling, probability distributions, inference, confidence intervals, tests of hypotheses, and regression and correlation. Students will not receive credit for both STAT 110 and STAT 112.

STAT 212 - (4) (S)
Introduction to Statistical Analysis
Prerequisite: MATH 121 or equivalent; co-requisite: Concurrent enrollment in a discussion section of STAT 212.
Introduction to the probability and statistical theory underlying the estimation of parameters and testing of statistical hypotheses, including those arising in the context of simple and multiple regression models. Students will use computers and statistical programs to analyze data. Examples and applications are drawn from economics, business, and other fields. Students will not receive credit for both STAT 212 and ECON 371.

STAT 301 - (3) (Y)
Statistical Computing and Graphics
Prerequisite: STAT 110 or 112 or instructor permission.
Introduces statistical computing using S-PLUS. Topics include descriptive statistics for continuous and categorical variables, methods for handling missing data, basics of graphical perception, graphical displays, exploratory data analysis, and the simultaneous display of multiple variables. Students should be experienced with basic text-editing and file manipulation on either a PC or a UNIX system, and with either a programming language (e.g. BASIC) or a spreadsheet program (e.g. MINITAB or EXCEL). Credit earned in this course cannot be applied toward a graduate degree in statistics.

STAT 313 - (3) (O)
Design and Analysis of Sample Surveys
Prerequisite: STAT 110 or 112, MATH 312, or instructor permission.
Discusses the main designs and estimation techniques used in sample surveys; including simple random sampling, stratification, cluster sampling, double sampling, post-stratification, and ratio estimation. Non-response problems and measurement errors are also discussed. Many properties of sample surveys are developed through simulation procedures. The SUDAAN software package for analyzing sample surveys is used.

STAT 500 - (3) (Y)
Introduction to Applied Statistics
Prerequisite: Instructor permission.
Introduces estimation and hypothesis testing in applied statistics, especially the medical sciences. Measurement issues, measures of central tendency and dispersion, probability, discrete probability distributions (binomial and Poisson), continuous probability distributions (normal, t, chi-square, and F), and one- and two-sample inference, power and sample size calculations, introduction to non-parametric methods, one-way ANOVA and multiple comparisons. Students must also enroll in STAT 598 for 1 credit.

STAT 501 - (3) (Y)
Statistical Computing and Graphics
Prerequisite: STAT 110 or 112, and graduate standing or instructor permission. Students who have received credit for STAT 301 may not take STAT 501 for credit.
Introduces statistical computing using S-PLUS. Topics include descriptive statistics for continuous and categorical variables, methods for handling missing data, basics of graphical perception, graphical displays, exploratory data analysis, the simultaneous display of multiple variables. Students should be experienced with basic text-editing and file manipulation on either a PC or a UNIX system, and with either a programming language (e.g. BASIC) or a spreadsheet program (e.g. MINITAB or EXCEL). Credit earned in this course cannot be applied toward a graduate degree in statistics.

STAT 512 - (3) (Y)
Applied Linear Models
Prerequisite: MATH 312 or 510, or instructor permission; corequisite: STAT 598.
Topics include linear regression models, inferences in regression analysis, model validation, selection of independent variables, multicollinearity, influential observations, auto correlation in time series data, polynomial regression, nonlinear regression, and other topics in regression analysis.

STAT 513 - (3) (O)
Applied Multivariate Statistics
Prerequisite: MATH 351 and 312 or 510, or instructor permission; corequisite: STAT 598.
Topics include matrix algebra, random sampling, multivariate normal distributions, multivariate regression, MANOVA, principal components, factor analysis, discriminant analysis. Statistical software is used.

STAT 514 - (3) (Y)
Survival Analysis and Reliability Theory
Prerequisite: MATH 312 or 510, or instructor permission; corequisite: STAT 598.
Topics include lifetime distributions, hazard functions, competing-risks, proportional hazards, censored data, accelerated-life models, Kaplan-Meier estimator, stochastic models, renewal processes, and Bayesian methods for lifetime and reliability data analysis.

STAT 515 - (3) (SI)
Actuarial Statistics
Prerequisite: MATH 312 or 510, or instructor permission.
Covers the main topics required by students preparing for the examinations in Actuarial Statistics, set by the American Society of Actuaries. Topics include life tables, life insurance and annuities, survival distributions, net premiums and premium reserves, multiple life functions and decrement models, valuation of pension plans, insurance models, and benefits and dividends.

STAT 516 - (3) (E)
Experimental Design
Prerequisite: MATH 312 or 510, or instructor permission; corequisite: STAT 598.
Introduces the basic concepts in experimental design. Topics include analysis of variance, multiple comparison tests, completely randomized design, general linear model approach to analysis of variance, randomized block designs, Latin square and related designs, completely randomized factorial design with two or more treatments, hierarchical designs, split-plot and confounded factorial designs, and analysis of covariance.

STAT 517 - (3) (O)
Applied Time Series
Prerequisite: MATH 312 or 510, or instructor permission; corequisite: STAT 598.
Studies the basic time series models in both the time domain (ARMA models) and the frequency domain (spectral models). Emphasizes application to real data sets.

STAT 518 - (3) (SI)
Numerical Methods in Statistics
Prerequisite: MATH 351 and knowledge of a programming language suitable for scientific computation, or instructor permission.
Studies selected topics in linear algebra and related numerical algorithms of special importance in statistics, including linear least-squares, eigenvalues and eigenvectors, QR decomposition, singular value decomposition, and generalized matrix inverses.

STAT 519 - (3) (Y)
Introduction to Mathematical Statistics
Prerequisite: MATH 312 or 510, or instructor permission.
Studies the fundamentals of statistical distribution theory, moments, transformations of random variables, point estimation, hypothesis testing, confidence regions.

STAT 520 - (3) (O)
Design and Analysis of Sample Surveys
Prerequisite: STAT 112 or MATH 312, and graduate standing or instructor permission.
Discusses the main designs and estimation techniques used in sample surveys, including simple random sampling, stratification, cluster sampling, double sampling, post-stratification, ratio estimation. Non-response problems and measurement errors are also discussed. Many properties of sample surveys are developed through simulation procedures. The SUDAAN computer package for analyzing sample surveys is used. Students who have received credit for STAT 313 may not take STAT 520 for credit.

STAT 531 - (3) (Y)
Clinical Trials Methodology
Prerequisite: A basic statistics course (MATH 312/510), or instructor permission.
Studies experimental designs for randomized clinical trials, sources of bias in clinical studies, informed consent, logistics, and interim monitoring procedures (group sequential and Bayesian methods).

STAT 598 - (1) (Y)
Applied Statistics Laboratory
Corequisite: A 500-level STAT applied statistics course.
This course, the laboratory component of the department’s applied statistics program, deals with the use of computer packages in data analysis. Enrollment in STAT 598 is required for all students in the department’s 500-level applied statistics courses (STAT 501, 512, 513, 514, 516, 517, 520). STAT 598 may be taken repeatedly provided that a student is enrolled in at least one of these 500-level applied courses. However, no more than one unit of STAT 598 may be taken in any semester.

STAT 599 - (3) (IR)
Topics in Statistics
Prerequisite: Instructor permission.
Studies topics in statistics that are not part of the regular course offerings.