Statistics
James D. Lynch, Chair
Professors
Donald G. Edwards, Ph.D., Ohio State University, 1981, Director for PartTime Students
James D. Lynch, Ph.D., Florida State University, 1974
Director of Center for Reliability and Quality Sciences
Edsel A. Peña, Ph.D., Florida State University, 1986, Graduate Director
Walter W. Piegorsch, Ph.D., Cornell University, 1984
John D. Spurrier, Ph.D., University of Missouri, 1974, Undergraduate Director
Associate Professors
John M. Grego, Ph.D., Pennsylvania State University, 1989, Director of Statistical Laboratory
Peter Waddell, Ph.D., Massey University (New Zealand), 1996
Ronnie W. West, Ph.D., Rice University, 1994
Assistant Professors
Nancy L. Glenn, Ph.D., Rice University, 2002
Brian T. Habing, Ph.D., University of Illinois, UrbanaChampaign, 1998
Kerrie P. Nelson, Ph.D., University of Washington, 2002
Distinguished Professor Emeritus
William J. Padgett, Ph.D., Virginia Polytechnic Institute and State University, 1971
Overview
Statistics plays a vital role in science, industry, business, and government. Competitive starting salaries and a promising job market make a career in statistics an excellent choice for those with mathematical talent, computer skills, and a desire to work with people. The Department of Statistics offers programs of study emphasizing a broad training in both applied and theoretical statistics, including statistical computing and the art of statistical consulting. The department houses the Statistical Laboratory, which offers statistical consulting services to clients throughout the University, government, and industry, as well as the Center for Reliability and Quality Sciences, which helps industry improve the quality of manufactured products and services. The department offers programs of study leading to the Master of Science, Master of Industrial Statistics, and Doctor of Philosophy degrees. It also offers the Certificate of Graduate Study in Applied Statistics. Courses for the C.A.S. and M.I.S. programs are offered in late afternoons, early evenings, and via closedcircuit TV throughout South Carolina.
Admissions
Requirements for admission to all graduate programs conform with general regulations of The Graduate School, including scores on the GRE, two letters of recommendation, and successful academic performance at an accredited baccalaureate institution. The GMAT is acceptable in lieu of the GRE for M.I.S. applicants. At least three semesters of calculus are prerequisite for admission, and for the M.S. and Ph.D. programs an additional semester of advanced calculus and a semester of linear algebra are also required. Applicants for the M.S. and Ph.D. are typically considered for financial support in the form of teaching or research assistantships. To be considered for financial support, it is best to have all application materials submitted at least six months in advance of the target starting date. Applicants whose native language is not English must obtain a TOEFL score of 570 (230 computerbased score) to be considered for admission, with a firstsubscore of at least 57 (22 computerbased score). To be considered for financial support, the TOEFL score should be at least 600 (250 computerbased score), with a firstsubscore of at least 60 (25 computerbased score). Comparable scores on the IELTS may also count toward this admission requirement. For more details, contact the department.
Requests for further information should be addressed to: Graduate Director, Department of Statistics, University of South Carolina, Columbia, SC 29208. Email addresses and more detailed information can be found on the Internet at www.stat.sc.edu.
Degree Requirements
Certificate of Graduate Study in Applied Statistics
The Certificate of Graduate Study in Applied Statistics (C.A.S.) is designed to provide engineers and scientists with the modern data analytic tools needed for effective practice as a specialist in statistical methods.
Admission to the C.A.S. program typically requires a GRE score (verbal plus quantitative) of 950 or more and three semesters of calculus with a 3.00 GPA. Students currently enrolled in other graduate degree programs at USC are automatically eligible to pursue the certificate as long as they have taken the prerequisite calculus courses.
The C.A.S. requires at least 18 semester hours of graduate credits in statistics, at least half of which must be courses at the 700 level or above with the STAT designator, completed within a period of six years before the award of the certificate. The 18 hours must include 6 hours of basic data analysis (STAT 704705 or STAT 700701 or the equivalent) and 3 hours of experimental design (STAT 706 or STAT 506 or the equivalent). At least 9 hours of additional courses must be selected, with the approval of the graduate director or the director for parttime students. Up to 6 semester hours of approved statistics courses may be taken from other departments and/or by transfer credit. With the approval of the department, and subject to the regulations of The Graduate School, courses taken in a certificate program can be applied toward other graduate degrees.
Master of Industrial Statistics
The M.I.S. degree is geared toward persons who are currently working in a business, government, or industrial setting. While some theory is introduced, the focus is on applications of statistics and, in particular, how statistics can be used to improve quality in an organization or process.
Admission to the M.I.S. degree program requires a GRE score (verbal plus quantitative) of at least 1000, or a comparable GMAT score, and at least three semesters of calculus with a 3.00 GPA. The successful applicant must also have two or more years of fulltime work experience in business, industry, government, or the equivalent. The degree requires at least 36 semester hours of approved course work built around a core of seven courses: STAT 525, 702, 703, 704, 705; STAT 506 or 706; and STAT 750 or 761. Additionally, 3 semester hours of independent study (STAT 798) are required. The STAT 798 project will be directed by a faculty member and will ideally involve study of an appropriate application of statistics relevant to the student's work experience or specific to the student's company or agency.
Master of Science
The M.S. degree is designed to provide students with the necessary background for employment as a professional statistician in business, industry, or government and to build a solid foundation for students interested in the Ph.D. program. Considerable flexibility in program emphasis is possible through the selection of elective courses and the thesis topic.
Admission to the M.S. degree program requires a GRE score (verbal plus quantitative) of at least 1050 and an undergraduate GPA of approximately 3.20. The degree requires at least 30 semester hours of approved course work built around a core of five courses: STAT 704, 705, 712, 713, and 714. Also required are 3 semester hours of thesis preparation (STAT 799). In addition to these 30 hours, 2 semester hours of Statistics Seminar (STAT 795) and 1 semester hour each of the consulting seminar (STAT 790) and practicum (STAT 791) are required. Typically, the M.S. requires two full years (four major semesters) of study.
Doctor of Philosophy
The Ph.D. degree is designed to prepare the student to teach statistics at the collegiate level, to do independent research, and/or to work as a lead statistician in business or industry.
Admission to the Ph.D. degree program requires either a master's degree with excellent performance from an accredited institution, or a GRE score (verbal plus quantitative) of approximately 1150 and an undergraduate GPA of approximately 3.50. The Ph.D. requires at least 48 semester hours of regular course work, including the core courses STAT 704, 705, 710, 711, 712, 713, 714, 715, 721, 722, 724, and 740. In addition to these 48 hours, also required are 6 semester hours of Statistics Seminar (STAT 795), 1 semester hour each of the consulting seminar (STAT 790) and practicum (STAT 791) and the 3semesterhour doctoral seminar (STAT 890). The doctoral dissertation is to be written in conjunction with the dissertation research course (STAT 899), for which at least 12 semester hours credit must be earned beyond the courses listed above. The progression through the degree program involves three examinations: the admissiontocandidacy exam, usually taken after the first year of study; the comprehensive exam, taken near the end of required course work; and the dissertation defense.
Course Descriptions (STAT)
 506  Introduction to Experimental Design. (3) (Prereq: MATH 122 or MATH 142 or STAT 201) Techniques of experimentation based on statistical principles with application to quality improvement and other fields. Full and fractional factorial designs for factors at two levels; dispersion effects; related topics.
 509  Statistics for Engineers. (3) (Prereq: MATH 142 or equivalent) Basic probability and statistics with applications and examples in engineering. Elementary probability, random variables and their distributions, random processes, statistical inference, curve fitting, prediction, correlation and application to quality assurance, reliability, and life testing.
 510  Introduction to Applied Probability. (3) (Prereq: MATH 142 with a grade of C or higher) Probability spaces and Markov chains, random variables and expectations, tree measures and transition diagrams, balance equations and limiting distributions, queuing models and Little's Formula, simulation.
 511  Probability. {=MATH 511} (3) (Prereq: MATH 241 with a grade of C or higher) Probability and independence; discrete and continuous random variables; joint, marginal, and conditional densities; moment generating functions; laws of large numbers; binomial, Poisson, gamma, univariate and bivariate normal distributions.
 512  Mathematical Statistics. (3) (Prereq: STAT 511 or MATH 511 with a grade of C or higher) Sampling theory, discrete and continuous transformations, t and F distributions, independence of sample mean and S^{2}; limiting distributions, central limit theorem; quality of estimators, testing statistical hypotheses, confidence intervals, Bayesian estimates.
 513  Theory of Statistical Inference. (3) (Prereq: STAT 512 with a grade of C or higher) Hypothesis testing, NeymanPearson Theorem, best tests, likelihood ratio tests; sufficient statistics, RaoBlackwell theorem, completeness; efficiency, sequential probability ratio test, multiple comparisons.
 515  Statistical Methods I. (3) (Prereq: a grade of C or higher in MATH 111 or equivalent) Applications and principles of descriptive statistics, elementary probability, sampling distributions, estimation, and hypothesis testing. Inference for means, variances, proportions, simple linear regression, and contingency tables. Statistical packages such as SAS.
 516  Statistical Methods II. (3) (Prereq: a grade of C or higher in STAT 515 or STAT 509 or equivalent) Applications and principles of linear models. Simple and multiple linear regression, analysis of variance for basic designs, multiple comparisons, random effects, and analysis of covariance. Statistical packages such as SAS.
 517  Computing in Statistics. (3) (Prereq: STAT 509 or STAT 515 with a grade of C or higher; knowledge of a programming language) Applications of the computer to statistics. Random number generation, efficient design of simulation studies, and advanced statistical computing procedures.
 518  Nonparametric Statistical Methods. (3) (Prereq: A grade of C or higher in STAT 515 or equivalent) Application of nonparametric statistical methods rather than mathematical development. Levels of measurement, comparisons of two independent populations, comparisons of two dependent populations, test of fit, nonparametric analysis of variance, and correlation.
 519  Sampling. (3) (Prereq: STAT 515 or equivalent) Techniques of statistical sampling in finite populations with applications in the analysis of sample survey data. Topics include simple random sampling for means and proportions, stratified sampling, cluster sampling, ratio estimates, and twostage sampling.
 520  Forecasting and Time Series. {=MGSC 520} (3) (Prereq: STAT 516 or MGSC 292) Time series analysis and forecasting using the multiple regression and BoxJenkins approaches.
 525  Statistical Quality Control. {=MGSC 525} (3) (Prereq: STAT 509 or STAT 515 or MGSC 292) Statistical procedures for process control including CUSUM and Shewhart Control Charts, and lotacceptance sampling.
 530  Exploring Multivariate Data. (3) (Prereq: STAT 515 or PSYC 228 or MGSC 292 or equivalent) Introduction to fundamental ideas in multivariate statistics using case studies. Descriptive, exploratory, and graphical techniques; introduction to cluster analysis, principal components, factor analysis, discriminant analysis. Hotelling's T2 and other methods.
 582  Bayesian Networks and Decision Graphs. {=CSCE 582} (3) (Prereq: CSCE 350 and STAT 509) Normative approaches to uncertainty in artificial intelligence. Prababilistic and causal modeling with Bayesian networks and influence diagrams. Applications in decision analysis and support. Algorithms for probability update in graphical models.
 590  Statistics Capstone. (1) (Prereq: STAT 512 and either STAT 509 or STAT 515) Case studies combining applied statistics, mathematical statistics, mathematics, computing, and communications to simulate work experience of a practicing statistician.
 599  Topics in Statistics. (13) Course content varies and will be announced in the schedule of courses by suffix and title.
 700  Applied Statistics I. (3) Introduction to probability and the concepts of estimation and hypothesis testing for use in experimental, social, and professional sciences. One and twosample analyses, nonparametric tests, contingency tables, sample surveys, simple linear regression, various statistical packages. Not to be used for M.S. or Ph.D. credit in statistics or mathematics.
 701  Applied Statistics II. (3) (Prereq: STAT 700 or consent of department) Continuation of STAT 700. Simple linear regression, correlation, multiple regression, fixed and random effects analysis of variance, analysis of covariance, experimental designs, some multivariate methods, various statistical packages. Not to be used for M.S. or Ph.D. credit in statistics or mathematics.
 702  Introduction to Statistical Theory I. (3) (Prereq: MATH 241) Fundamental theory of statistics and how it applies to industrial problems. Topics include probability, random variables and vectors and their distributions, sampling theory, point and interval estimators, and application to the theory of reliability, regression, process control and quality issues. Not to be used for M.S. or Ph.D. credit in statistics.
 703  Introduction to Statistical Theory II. (3) (Prereq: STAT 702) Continuation of STAT 702. Topics include discussion of theoretical properties of point estimators and tests of hypotheses, elements of statistical tests, the NeymanPearson Lemma, UMP tests, likelihood ratio and other types of tests, and Bayes procedures in the decision process. Not to be used for M.S. or Ph.D. credit in statistics.
 704  Data Analysis I. (3) (Prereq: consent of department) Primarily for graduate students in statistics and the mathematical sciences. Probability concepts, inferences for normal parameters, regression, correlation, use of computer statistical packages.
 705  Data Analysis II. (3) (Prereq: STAT 704) Continuation of STAT 704. Analysis of variance (fixed and random effects), analysis of covariance, experimental design, model building, other applied topics, and use of computer statistical packages.
 706  Experimental Design. (3) (Prereq: STAT 701 or STAT 705) Specialized experimental design: 2^{n} and 3^{n} factorials; fractional replication; confounding; incomplete block designs, including splitplot, splitblock, and Latin square designs; general principles of design.
 708  Environmetrics. {=BIOS 808} (3) (Prereq: STAT 701 or 705 or BIOS 757) Statistical methods for environmental and ecological sciences, including nonlinear regression, generalized linear models, spatial analyses/kriging, temporal analyses, metaanalysis, quantitative risk assessment.
 709  Environmetrics II. {=BIOS 809} (3) (Prereq: STAT 708 or BIOS 808; STAT 714) Theoretical underpinnings of environmetrics. Spatial statistics, temporal and longitudinal analysis, hierarchical modeling, and Bayesian inferences for environmental data.
 710  Probability Theory I. {=MATH 710} (3) (Prereq: STAT 511, 512, or MATH 703) Probability spaces, random variables and distributions, expectations, characteristic functions, laws of large numbers, and the central limit theorem.
 711  Probability Theory II. {=MATH 711} (3) (Prereq: MATH 710) More about distributions, limit theorems, Poisson approximations, conditioning, martingales, and random walks.
 712  Mathematical Statistics I. (3) (Prereq: advanced calculus or consent of instructor) Sample spaces, probability and conditional probability, independence, random variables, expectation, distribution theory, sampling distributions, laws of large numbers and asymptotic theory, order statistics, and estimation.
 713  Mathematical Statistics II. (3) (Prereq: STAT 712) Further development of estimation theory and tests of hypotheses, including an introduction to Bayes estimation, sufficiency, minimum variance principles, uniformly most powerful and likelihood ratio tests, and sequential probability ratio tests.
 714  Linear Statistical Models. (3) (Prereq: STAT 513 and MATH 544 or STAT 712 or equivalent) A study of the general linear statistical model and the linear hypothesis. Topics include the multivariate normal distribution, distributions of quadratic forms, and parameter estimation and hypothesis testing for fullrank models, regression models, and less than fullrank models.
 715  Analysis of Variance. (3) (Prereq: STAT 714 or consent of instructor) One way design; multiple comparisons, complete two, three, and higher order designs; Latin squares, incomplete blocks and nested designs; analysis of covariance, random effects models, mixed models; randomization models.
 716  Selected Topics in Probability. {=MATH 716} (3) (Prereq: consent of instructor) Special topics in probability theory and stochastic processes not offered in other courses.
 718  Selected Topics in Statistics. (3) (Prereq: consent of instructor) Special topics in statistics not offered in other courses.
 720  Time Series Analysis. (3) (Prereq: STAT 704 and 512) Stochastic properties, identification, estimation, and forecasting methods for stationary and nonstationary time series models.
 721  Stochastic Processes. (3) (Prereq: STAT 711 or equivalent) Theory of stochastic processes, including branching processes, discrete and continuous time Markov chains, renewal theory, point processes, and Brownian motion.
 722  Advanced Statistical Inference. (3) (Prereq: STAT 713 or consent of instructor) The advanced theory of statistical inference, including the general decision problem; NeymanPearson theory of testing hypotheses; the monotone likelihood ratio property; unbiasedness, efficiency, and other small sample properties of estimators; asymptotic properties of estimators, especially maximum likelihood estimators; and general sequential procedures.
 724  Nonparametric Inference. (3) (Prereq: STAT 713 or consent of instructor) The general theory of nonparametric statistics, including order statistic theory, theory of ranks, Ustatistics in nonparametric estimation and testing, linear rank statistics and their application to location and scale problems, goodnessoffit, and other distributionfree procedures.
 730  Multivariate Analysis. (3) (Prereq: STAT 713) A survey of the theory and applications of the fundamental techniques for analyzing multivariate data.
 740  Statistical Computing. (3) (Prereq: STAT 513 or 712 and knowledge of a computer programming language) A survey of current algorithms and software for solving fundamental problems of statistical computing with emphasis on computer generation of random variates.
 750  Response Surface Methodology. (3) (Prereq: STAT 701 or 705 or consent of department) Methods for fitting (regression) response surfaces and interpreting them subject to random error. Includes designs and industrial process optimization methods.
 761  Reliability and Life Testing. (3) (Prereq: STAT 703 or STAT 713) The various statistical and probability models in reliability and life testing and inference procedures for such models, including life distributions, parametric and nonparametric inference methods, hazard and failure rate functions, plotting methods, analysis of mixtures, censoring.
 770  Categorical Data Analysis. {=BIOS 805} (3) (Prereq: STAT 704 and consent of instructor, or BIOS 759) Advanced methods for analysis of discrete data. Higherorder contingency tables, loglinear and other generalized linear models. Multivariate methods for matched pairs and longitudinal data.
 772  Binary Dose Response Theory and Methods. {=BIOS 850} (3) (Prereq: STAT 512) Threshold, mass action, and target theory; empirical dose response functions; methods in current use among health science researchers.
 775  Generalized Linear Models. {=BIOS 815} (3) (Prereqs: STAT 713 or STAT 513, and STAT 705 or BIOS 757) Statistical theory and applications extending regression and analysis of variance to nonnormal data. Encompasses logistic and other binary regressions, loglinear models, and gamma regression models.
 777  Statistical Phylogenetics and Molecular Evolution. {=BIOL 777} (3) (Prereq: grade of B or better in MATH 241 or STAT 510) Theory and applications of phylogenetics; estimation via Markov models, likelihood, distances and parsimony; hypothesis testing of evolutionary trees and parameters; related topics including molecular divergence time inference.
 778  Item Response Theory. {=EDRM 828} (3) (Prereq: EDRM 711 or PSYC 710 or STAT 701 or STAT 704) Statistical models for item response theory, Rasch and other models for binary and polytomous data, and applications. Use of statistical software.
 790  Seminar in Statistical Consulting. (1) (Prereq: STAT 700 or equivalent) An exposure to the techniques of statistical consulting through discussion and analysis of actual statistical problems which occur in fields of application.
 791  Practicum in Statistical Consulting. (1) (Prereq: STAT 790) Experiences in actual statistical consulting settings; participation and critiques.
 795  Statistics Seminar. (12) Pass/Fail grading.
 798  Independent Study. (16)
 799  Thesis Preparation. (19) For master's candidates.
 890  Doctoral Seminar. (3) For doctoral candidates.
 898  Directed Readings and Research. (112) Restricted to statistics graduate students. (Passfail grading)
 899  Dissertation Preparation. (112) For doctoral candidates.
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