Statistics

Head:
John Boyer

Director of graduate studies:
James Neill

Graduate faculty:

John Boyer, Ph.D., Michigan State University.

Suzanne Dubnicka, Ph.D., Pennsylvania State University.

James Higgins, Ph.D., University of Missouri-Columbia.

Dallas Johnson, Emeritus, Ph.D., Colorado State University.

Kenneth Kemp, Emeritus, Ph.D., Michigan State University.

George Milliken, Emeritus, Ph.D., Colorado State University.

James Neill, Ph.D., Kansas State University.

Paul Nelson, Ph.D., Rutgers University.

Weixing Song, Ph.D., Michigan State University.

Haiyan Wang, Ph.D., The Pennsylvania State University.

Winston Yang, Ph.D., Iowa State University.

Careers

To solve problems we need information. But, what kind? How much? And after we get it, what do we do with it? Statisticians deal with numerical information usually called data. Their job is to match the data with the problem, and to figure out what to collect and how to make the numbers manageable so that other people can understand them. All areas that involve the collection and analysis of data can benefit from the skills of a statistician. Monitoring the environment, developing new vaccines, making more reliable products, growing crops more efficiently, and setting insurance rates are just some endeavors in which statisticians have had a significant impact. Statistics is a field in which experts have virtually unlimited opportunities.

Perhaps the most recognizable careers in statistics are those in the state and federal governments. Professionals are not only hired into such areas as the Bureau of Labor Statistics and the Bureau of the Census, but are in demand in many service agencies.

Universities hire statisticians in many academic departments, including mathematics, management sciences, economics, genetics, history, and psychology, and at the administrative and service levels, including business affairs, research support, and personnel.

Private industry is a heavy user of the skills of the statistician. For example, the pharmaceutical industry employs many statisticians to design studies and analyze data to show the safety and effectiveness of new drug compounds. Manufacturing industries are increasingly using statisticians to help them improve quality and productivity. Private consulting can be lucrative for the experienced statistician who works with both private industry and government. Companies of all sizes employ staff statisticians to keep the business progressing and competitive.

Preparation

The Department of Statistics accepts students from many different disciplines. Students entering the M.S. program should have a background of calculus, matrix algebra, computer programming, and introductory statistics. Students entering the Ph.D. program should have additional course work in statistics and mathematics.

Programs

The Department of Statistics offers studies leading to a master of science or a doctor of philosophy degree. A master's degree is recommended for a career in industry or government. The Ph.D. degree is usually required for post-secondary teaching and higher level positions. The department offers concentration in applied and mathematical probability and statistics.

Master's degree

Two master's degree options are available: the master's report options and the nonreport option.

For the master's report options, the student must take 30 hours of coursework and write a reoprt for 2 additional hours of credit.
For the nonreport option, the student must take 35 hours of coursework and pass a comprehensive exam approved by the supervisory committee.

The master's report option is strongly recommended for all students, especially those for whom the master's degree will be the terminal degree.

In either case, the coursework must include STAT 713, STAT 770, STAT 771, STAT 860, at least one of STAT 710, STAT 720, or STAT 722, and at least one credit of STAT 945.

Ph.D. degree

Students are required to have 90 credit hours. A typical program consists of 30 hours from the master's program, 30 hours of additional course work and 30 hours of research. Students are required to pass a qualifying exam, which is given in January and August each year. The qualifying exam consists of material from STAT 720, STAT 770, STAT 771, STAT 860, and STAT 861. It will test your knowledge of basic methods and introductory theory. Students who fail the exam may, upon recommendation of the faculty, be allowed to take it a second time, but approval of a second opportunity is not automatic.

Upon completion of course work, normally in the third year of Ph.D. study, students who have passed the qualifying exam must take a preliminary exam. This exam is required by the university and is intended to test the student's breadth and depth of knowledge in the chosen field of study. The exam is prepared in consultation with the student's major professor and advisory committee. It consists of two parts: (1) a statistical foundations exam; (2) an integrated topics exam over the student's area of specialization. Students are also required to present a seminar on a topic approved by the major professor and advisory committee in which the student is to demonstrate an ability to read and communicate information in the research literature.

Graduate certificate in applied statistics

The department offers the Graduate Certificate in Applied Statistics to recognize the preparation and proficiency of non-majors in data analysis in a wide variety of subject matter areas. Graduate students in a variety of academic disciplines are conducting research that requires knowledge in applied statistics. Such students may wish to demonstrate proficiency in applied statistics as it may be useful when looking for meaningful employment opporutnities, in addition to helping them become better researchers in their chosen fields. In order to strengthen their educational programs and the quality of graduate education, a Graduate Certificate in Applied Statistics has been developed.

Consulting opportunities

The department does a tremendous amount of consulting work for researchers and students on campus and for individuals and agencies off campus. Projects vary in length of time and sophistication of methods needed to complete them. Students may contact the department head to find out what is available. Those who wish to do consulting will be assigned a faculty member to direct the work. At the student's discretion, up to 2 hours credit may be earned for consulting by registering for STAT 945.

Statistics courses

Undergraduate and graduate credit in minor field

STAT 510. Introductory Probability and Statistics I. (3) I, II. Descriptive statistics, probability concepts and laws, sample spaces; random variables; binomial, uniform, normal, and Poisson; two-dimensional variates; expected values; confidence intervals; binomial parameter, median, mean, and variance; testing simple hypotheses using CIs and X²; goodness of fit. Numerous applications. Pr.: MATH 221.

STAT 511. Introductory Probability and Statistics II. (3) I, II. Law of Large Numbers, Chebycheff's Inequality; continuation of study of continuous variates; uniform, exponential, gamma, and beta distribution; Central Limit Theorem; distributions from normal sampling; introduction to statistical inference. Pr.: STAT 510.

Undergraduate and graduate credit

STAT 702. Statistical Methods for Social Sciences. (3) I, II. Statistical methods applied to experimental and survey data from social sciences; test of hypotheses concerning treatment means; linear regression; product-moment, rank, and bi-serial correlations; contingency tables and chi-square tests. Pr.: MATH 100.

STAT 703. Statistical Methods for Natural Scientists. (3) I, II, S. Statistical concepts and methods basic to experimental research in the natural sciences; hypothetical populations; estimation of parameters; confidence intervals; parametric and nonparametric tests of hypotheses; linear regression; correlation; one-way analysis of variance; t-test; chi-square test. Pr.: Junior standing and equiv. of college algebra.

STAT 704. Analysis of Variance. (2) I, II, S. Computation and interpretation for two- and three-way analyses of variance; multiple comparisons; applications including use of computers. Meets four times a week during first half of semester. Pr.: One previous statistics course.

STAT 705. Regression and Correlation Analyses. (2) I, II, S. Multiple regression and correlation concepts and methods; curvilinear regression; applications including use of computers. Meets four times a week during second half of semester. Pr.: One previous statistics course.

STAT 706. Basic Elements of Statistical Theory. (3) I. The mathematical representation of frequency distributions, their properties, and the theory of estimation and hypothesis testing. Elementary mathematical functions are used to illustrate theory. Pr.: MATH 205, 210 or 220 and STAT 320.

STAT 710. Sample Survey Methods. (2) I, in even years. Design, conduct, and interpretation of sample surveys. Pr.: STAT 702 or 703. Meets four times a week during first half of semester.

STAT 713. Applied Linear Statistical Models. (4) I. Matrix-based regression and analysis of variance procedures at a mathematical level appropriate for a first-year graduate statistics major. Topics include simple linear regression, linear models in matrix form, multiple linear regression, model building and diagnostics, analysis of covariance, multiple comparison methods, contrasts, multifactor studies, blocking, subsampling, and split-plot designs. Pr.: Prior knowledge of matrix or linear algebra and one prior course in statistics. A student may not receive credit for both the STAT 704/705 sequence and STAT 713.

STAT 716. Nonparametric Statistics. (2) I, in odd years. Hypothesis testing when form of population sampled is unknown: rank, sign, chi-square, and slippage tests; Kolmogorov and Smirnov type tests; confidence intervals and bands. Meets four times a week during second half of semester. Pr.: One previous course in statistics.

STAT 717. Categorical Data Analysis (3) II. Analysis of categorical count and proportion data. Topics include tests of association in two-way tables; measures of association; Cochran-Mantel-Haenzel tests for 3-way tables; generalized linear models; logistic regression; loglinear models. Pr.: STAT 704, 705

STAT 720. Design of Experiments. (3) II, S. Planning experiments so as to minimize error variance and avoid bias; Latin squares; split-plot designs; switch-back or reversal designs; incomplete block designs; efficiency. Pr.: STAT 704 and 705.

STAT 722. Statistical Designs for Product Development and Process Improvement. (3) II. A study of statistically designed experiments which have proven useful in product development and process improvement. Topics include randomization, blocking, factorial treatment structures, fractional factorial designs, screening designs, Taguchi methods, response surface methods. Pr.: STAT 511 or STAT 704 and 705.

STAT 725. Introduction to the SAS Computing. (1) I. Topics may include basic environment and syntax, reading and importing data from files, writing and exporting data to files, data manipulation, basic graphics, and built-in and user-defined functions. Pr.: one graduate level course in statistics.

STAT 726. Introduction to Splus/R Computing. (1) II. Topics may include basic environment and syntax, reading and importing data from files, data manipulation, basic graphics, and built-in and user-defined functions. Pr.: one graduate level course in statistics.

STAT 730. Multivariate Statistical Methods. (3) I. Multivariate analysis of variance and covariance; classification and discrimination; principal components and introductory factor analysis; canonical correlation; digital computing procedures applied to data from natural and social sciences. Pr.: STAT 704, 705.

STAT 735. Statistics in Health Related Industries. (2) I, in odd years. Case studies and selected literature of applications of statistics to problems in the pharmaceutical and health-related industries are discussed. Topics include pharmacokinetic analysis, covariance analysis, crossover studies, bioequivalence. Meets four times a week during first half of semester. Pr.: STAT 704, 705, 720.

STAT 736. Bioassay. (2) II, in odd years. Direct assays; quantitative dose-response models; parallel line assays; slope ratio assays; experimental designs for bioassay; covariance adjustment; weighted estimates; assays based on quantal responses. Meets four times a week during second half of semester. Pr.: STAT 704 and 705.

STAT 740. Nonlinear Models. (3) S, in even years. Methods of estimating parameters of nonlinear models; procedures for testing hypotheses; construction of confidence intervals and regions; nonlinear analysis of covariance; quantal dose response and probabilistic choice models. Pr.: MATH 222, STAT 720.

STAT 745. Statistical Graphics (3) II, in even years. Visual display of quantitative information. Statistical graphics topics to include visual perception, basic graphics construction, quantitative univariate to multivariate statistical graphics, trellis displays, introduction to smoothing and graphics, introduction to density estimation and graphics, and categorical graphics. Modern graphics software will be used. Pr.: STAT 705 or equivalent.

STAT 770. Theory of Statistics I. (3) I. Probability models, concepts of probability, random discrete variables, moments and moment generating functions, bivariate distributions, continuous random variables, sampling. Central Limit Theorem, characteristic functions. More emphasis on rigor and proofs than in STAT 510 and 511. Pr.: MATH 222.

STAT 771. Theory of Statistics II. (3) II. Introduction to multivariate distributions; sampling distributions, derivation, and use; estimation of parameters, testing hypothesis; multiple regression and correlation; simple experimental designs; introduction to nonparametric statistics; discrimination. Pr.: STAT 770.

STAT 799. Topics in Statistics. (Var.) I, II, S. Pr.: STAT 703 or 770 and consent of instructor.

STAT 810. Seminar in Probability and Statistics. (1) I, II. Discussion and lectures on topics in probability and statistics; one seminar talk by each student registered for credit. Pr.: Graduate standing and at least two graduate courses in statistics.

STAT 818. Theory of Life-Data Analysis. (3) II, in odd years. A study of models and inferential procedures important to life-data analysis. Comparison of estimators (MLE, BLUE, etc.). Pivotal quantities. Design and regression models for non-normal distributions. Analysis of censored data. Pr.: STAT 771.

STAT 825. Numerical Methods of Statistics. (3) II, in odd years. Topics may include efficient programming echniques, generating data from non-standard distributions, simulation techniques,resampling methods, optimization techniques, smoothing, and imputation. Pr.: STAT 725, STAT 726, STAT 771.

STAT 850. Stochastic Processes I. (3) II. Generating functions; conditional probability and conditional expectations; normal processes and covariance stationary processes; Poisson processes; renewal processes; Markov chains, discrete time. Pr.: STAT 770.

STAT 851. Stochastic Processes II. (3) I. Markov chains, discrete time; Markov chains continuous time; birth-death processes; Kolmogorov differential equations; diffusion processes, foward and backward Kolmogorov equations; applications. Pr.: STAT 850.

STAT 860. Linear Models I. (3) I. Subspaces, projections, and generalized inverses; multivariate normal distribution, distribution of quadratic forms; optimal estimation and hypothesis testing procedures for the general linear model; application to regression models, correlation model. Pr.: STAT 704, 705, 771; course in matrices.

STAT 861. Linear Models II. (3) II. Continued application of optimal inference procedures for the general linear model to multifactor analysis of variance, experimental design models, analysis of covariance, split-plot models, repeated measures models, mixed models, and variance component models; multiple comparison procedures. Pr.: STAT 860.

STAT 870. Analysis of Messy Data. (3) I. Design structures; treatment structures; equal and unequal variances; multiple comparisons; unequal subclass numbers; missing cells; interpretation of interaction; variance components; mixed models; split-plot and repeated measures; analysis of covariance; cross-over designs. Pr.: STAT 720.

STAT 880. Time Series Analysis. (3) I, in odd years. Autocorrelation function; spectral density; autoregressive integrated moving average processes; seasonal time series; transfer function model; intervention analysis; regression model with time series error. Pr.: STAT 705 and 770.

STAT 898. Master's Report. (2) I, II, S. Pr.: Consent of instructor.

STAT 899. Master's Thesis Research. (Var.) I, II, S. Pr.: Consent of instructor.

STAT 901. Rank and Robustness. (2) I, in even years. A study of robust and rank-based procedures for estimation and testing in one-and two-sample location problems and linear models. Topics may include; norm-based inference; asymptotic theory; asymptotic relative efficiency; evaluating robustness via the influence function and breakdown; R-estimates, M-estimates, U-statistics. Pr.: STAT 771, STAT 860.

STAT 902. Generalized Linear Models. (2) II, in odd years. Statistical models based on the exponential family of distributions where a function of the mean response is linear in the covariates. Applications to non-normal and discrete data, including binary, Poisson and gamma regression, and log-linear models. Topics include likelihood-based estimation and testing, model-fitting, residual analysis, over-dispersed models, quasi-liklihood, and the use of computer packages. Pr.: STAT 717, STAT 771, STAT 860.

STAT 903. Spatial and Longitudinal Data. (2) I, in odd years. Statistical analysis of spatially and temporally correlated data, including inference for continuous and discrete data based on linear, nonlinear and generalized linear models and methods. Inferential objectives include prediction of response and estimation of correlation/covariance structures. Pr.: STAT 720, STAT 771, STAT 861.

STAT 904. Resampling Methods. (2) II, in even years. Application, theory, and computational aspects of resampling methods. Topics include parametric, nonparametric, jackknife, and finite-population resampling; bootstrap confidence intervals and hypothesis tests; randomization theory and permutation tests; applications to regression; implementation using statistical software. Additional topics may include double bootstrap, dependent data, efficient resampling. Pr.: STAT 771, STAT 860.

STAT 920. Experimental Design Theory. (3) II, in odd years. Incomplete block designs; theory of the construction and analysis of experimental designs. Pr.: STAT 720 and 861.

STAT 930. Theory of Multivariate Analysis. (3) II, in even years. The multivariate normal distribution, the Wishart distribution, Jacobians of vector and matrix transformations, Hotelling's T2-statistic, the union-intersection principle, tests on mean vectors and covariance matrices, Box's approximations to critical points, the multivariate general linear model, discriminant analysis, and principal component analysis. Pr.: STAT 730 and 861.

STAT 945. Problems in Statistical Consulting. (Var.) I, II, S. Principles and practices of statistical consulting. Supervised experience in consultation and consequent research concerning applied statistics and probability associated with on-campus investigations. Pr.: STAT 704, 705, and 771.

STAT 950. Advanced Studies in Probability and Statistics. (Var.) I, II, S. Theoretical studies of advanced topics in probability, decision theory, Markov processes, experimental design, stochastic processes, or advanced topics. May be repeated. Pr.: STAT 771.

STAT 980. Probability and Asymptotics. (3) I. Probability theory, including independence, conditioning, modes of stochastic convergence, laws of large numbers, central limit theory, martingales. Statistical applications to asymptotic approximations and efficiency for inference in parametric and nonparametric models based on likelihood methods and statistical functionals. Pr.: Math through at least two semesters of advanced calculus and STAT 771.

STAT 981. Advanced Inference. (3) II. Foundations and methods of statistical inference including invariance, likelihood and Bayesian inference, decision theory, estimating equations and prediction. Additional topics may include E-M algorithm, Hasings-Metrolopis algorithm, exponential families, order restricted inference, density estimation, sequential methods, other likelihoods, large sample and conditional inference. Pr.: STAT 980.

STAT 999. Research in Statistics. (Var.) I, II, S. Pr.: Consent of instructor.

For more information

For additional information and application materials please contact:
Department of Statistics
Kansas State University
101 Dickens Hall
Manhattan, KS 66506-0802
Phone: 785-532-6883
FAX: 785-532-7736
E-mail: gradrec@stat.ksu.edu
Home Page: http://www.ksu.edu/stats/