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STA STATISTICSOn this page: Introduction | Faculty Members | Programs | Courses See also: Course Summer Timetable | Course Winter Timetable | Secondary School Information | More on Department IntroductionStatistical theory and methodology have applications in almost all areas of science, engineering, business, government, and industry. The practising statistician is involved in such diverse projects as designing clinical trials to test a new drug, economic model-building to evaluate the costs of a guaranteed-income scheme, predicting the outcome of a national election, planning a survey of television viewing habits, and estimating animal populations. Today's consumer is bombarded with the results of so many quantitative studies using statistical methodology that it is necessary for a person to know something about Statistics in order to be properly critical. A basic knowledge of Statistics should be an integral part of everyone's general education. Advanced probability theory is used to analyse the changing balance among the age-groups in a population as the birth rate changes, the control force needed to keep an aircraft on course through gusts of wind, the chance that the demand for electricity by all the customers served by a substation will exceed its capacity. These are just three of many phenomena that can only be analysed properly in terms of randomness and probability. The course offerings are intended not only for specialists in the theory of the subject but also to serve the needs of the many other disciplines that use statistical methods, e.g. in sample survey design and experimental design. Students following the Specialist Program are encouraged to include courses in major fields of application in their overall program. The Major Program can be profitably combined with specialization in another discipline. Both applied and theoretical courses are offered in Statistics and Probability. The foundation courses STA 220H, 221H, 250H, 255H, 257H, and JBS 229H are distinguished primarily by their mathematical demands, as indicated by the prerequisites. Students interested in the Biological or Social Sciences will generally find the most relevant courses of the more advanced courses to be STA 302H, 322H, 332H, and 429H. Furthermore, the probability course STA 347H will be of interest to those whose field of application includes model building. Undergraduate Studies Coordinator: A.M. Vukov Enquiries: 100 St. George Street, Sidney Smith Hall, Room 6018 (978-3452/5136)
STATISTICS PROGRAMSEnrolment in these programs requires completion of four courses; no minimum GPA is required. Enrolment forms may be obtained at your College Registrar's Office. STATISTICS AND MATHEMATICS (Hon.B.Sc.)Consult Professor J.S. Rosenthal, Department of Statistics.Specialist program: S12891 (10 full courses or their equivalent, including at least one 400-series course)
NOTE: The Department recommends that PHY 150Y be taken in first year, and that CSC 148H/260H be taken during the program STATISTICS (B.Sc.)Specialist program (Hon.B.Sc): S22891
(11.5 full courses or their equivalent, including at least one 400-series course)
APM 441H, 446H, 456H, 461H, CSC 318H, 354H
NOTES:
Major program (B.Sc.): M22891 (6.5 full courses or their equivalent)
ECO 227Y/(ECO 220Y, STA 257H) (MAT 223H/240H recommended in First Year)
NOTE: Suggested combinations for the four STA half courses are as follows:
Minor program (B.Sc.): R22891 (4 full courses or their equivalent)
STATISTICS AND COMPUTER SCIENCE — See COMPUTER SCIENCE AND STATISTICS
STATISTICS AND ECONOMICS — See ECONOMICS
STATISTICS COURSES(see Section 4 for Key to Course Descriptions)For Distribution Requirement purposes STA 220H, 221H, 250H, 255H, 257H and JBS 229H have NO distribution requirement status; STA 429H is a SCIENCE or SOCIAL SCIENCE course; all other STA courses are classified as SCIENCE courses.
SCI199Y Undergraduate seminar that focuses on specific ideas, questions, phenomena or controversies, taught by a regular Faculty member deeply engaged in the discipline. Open only to newly admitted first year students. It may serve as a breadth requirement course; see First Year Seminars: 199Y.
STA107H Introduction to the theory of probability, with emphasis on the construction of discrete probability models for applications. After this course, students are expected to understand the concept of randomness and aspects of its mathematical representation. Topics include random variables, Venn diagrams, discrete probability distributions, expectation and variance, independence, conditional probability, the central limit theorem, applications to the analysis of algorithms and simulating systems such as queues.
STA220H An introductory course in statistical concepts and methods, emphasizing exploratory data analysis for univariate and bivariate data, sampling and experimental designs, basic probability models, estimation and tests of hypothesis in one-sample and comparative two-sample studies. A statistical computing package is used but no prior computing experience is assumed.
STA221H Continuation of STA220H, emphasizing major methods of data analysis such as analysis of variance for one factor and multiple factor designs, regression models, categorical and non-parametric methods.
JBS229H Continuation of STA220H, jointly taught by Statistics and Biology faculty, emphasizing methods and case studies relevant to biologists including experimental design and analysis of variance, regression models, categorical and non-parametric methods.
STA250H A survey of statistical methodology with emphasis on data analysis and applications. The topics covered include descriptive statistics, basic probability, simulation, data collection and the design of experiments, tests of significance and confidence intervals, power, multiple regression and the analysis of variance, and count data. Students learn to use a statistical computer package as part of the course.
STA255H This courses deals with the mathematical aspects of some of the topics discussed in STA250H. Topics include discrete and continuous probability distributions, conditional probability, expectation, sampling distributions, estimation and testing, the linear model.
STA257H This course is concerned with the development of the probability model. Topics include probability measures, distribution functions, probability and density functions, random variables, conditional probability, expectation, convergence in distribution, the Weak and Strong Laws of Large Numbers, the Central Limit Theorem, some Normal distribution theory and applications.
STA299Y Credit course for supervised participation in faculty research project. See Research Opportunity Program for details.
STA302H Analysis of the multiple regression model by least squares; statistical properties of the least square analysis, including the Gauss Markov theorem; estimate of error; residual and regression sums of squares; distribution theory under normality of the observations; confidence regions and intervals; tests for normality; variance stabilizing transformations, multicollinearity, variable search method.
STA322H Designing samples for valid inferences about populations at reasonable cost: stratification, cluster/multi-stage sampling, unequal probability selection, ratio estimation, control of non-sampling errors (e.g. non-response, sensitive questions, interviewer bias).
STA221H
STA332H Design and analysis of experiments; randomization; analysis of variance; incomplete block designs; Latin squares; orthogonal polynomials; factorial and fractional designs; response surface methodology.
STA347H Review of basic probability and expectations including independence and its consequences, fundamental limit theorems, Markov Processes including branching processes and birth and death processes, Poisson point process and extensions, some renewal theory and simple Gaussian processes.
STA348H A continuation of STA347H. Further limit theorems, martingales, Markov processes, queues, probability and expectation spaces, stochastic processes and inference.
STA352Y An introduction to the theory of mathematical statistics. The topics include: a review of some relevant concepts from the theory of probability, the theory of optimal estimators, tests and confidence regions, large sample theory, likelihood theory, distribution-free methods, Bayesian inference.
STA422H The course discusses foundational aspects of various theories of statistics. Specific topics covered include: likelihood based inference, decision theory, fiducial and structural inference, Bayesian inference.
STA429H For life and social science students. The course discusses many advanced statistical methods used in the life and social sciences. Emphasis is on learning how to become a critical interpreter of these methodologies while keeping mathematical requirements low. Topics covered include multiple regression, logistic regression, discriminant and cluster analysis, principal components and factor analysis. Does not count towards any STA programs.
STA437H Practical techniques for the analysis of multivariate data; fundamental methods of data reduction with an introduction to underlying distribution theory; basic estimation and hypothesis testing for multivariate means and variances; regression coefficients; principal components and the partial, multiple and canonical correlations; multivariate analysis of variance; profile analysis and curve fitting for repeated measurements; classification and the linear discriminant function.
STA438H An introductory survey of current multivariate analysis, multivariate normal distributions, distribution of multiple and partial correlations, Wishart distributions, distribution of Hotelling's T2, testing and estimation of regression parameters, classification and discrimination.
STA442H Advanced topics in statistics and data analysis with emphasis on applications. Diagnostics and residuals in linear models, introductions to generalized linear models, graphical methods, additional topics such as random effects models, split plot designs, smoothing and density estimation, analysis of censored data, introduced as needed in the context of case studies.
STA450H Topics of current research interest are covered. Topics change from year to year, and students should consult the department for information on material presented in a given year. (Not offered in 1998-99)
STA457H An overview of methods and problems in the analysis of time series data. Topics include: descriptive methods, filtering and smoothing time series, theory of stationary processes, identification and estimation of time series models, forecasting, seasonal adjustment, spectral estimation, bivariate time series models.
STA496H/497H Independent study under the direction of a faculty member. Persons wishing to take this course must have the permission of the Undergraduate Secretary and of the prospective supervisor.
STA498Y/499Y Independent study under the direction of a faculty member. Persons wishing to take this course must have the permission of the Undergraduate Secretary and of the prospective supervisor. 
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