Arts & Science Calendar 1998-99: Table of Contents: Programs and Courses
[Calendar: Contents | Calendar: Search | Programs & Courses |  Queries & Comments]


On this page: Introduction | Faculty Members | Programs | Courses
See also: Course Summer Timetable | Course Winter Timetable | Secondary School Information | More on Department


Statistical 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)

Faculty Members

Professor Emeritus
D.A.S. Fraser, BA, Ph D, FRSC W.A.O'N. Waugh, MA, D Phil
I. Guttman, MA, Ph D

Professor and Acting Chair of the Department
N.M. Reid, M Sc, Ph D

D.F. Andrews, M Sc, Ph D P. McDunnough, M Sc, Ph D
M.J. Evans, MA, Ph D M.S. Srivastava, M Sc, Ph D
A. Feuerverger, B Sc, Ph D R. Tibshirani, M Sc, Ph D

Associate Professors
D. Brenner, M Sc, Ph D B. Chan, MA, Ph D, ASA
L.J. Brunner, MA, Ph D (E) K. Knight, MS, Ph D
S. Broverman, M Sc, Ph D, ASA J.S. Rosenthal, MA, Ph D

Assistant Professors
S. Jain, M Sc, Ph D X. Lin, MA, Ph D
R. Neal, B Sc, Ph D

Senior Tutors
O. Fraser, B Com, M Sc (E) A.M. Vukov, MA, ASA


Enrolment in these programs requires completion of four courses; no minimum GPA is required. Enrolment forms may be obtained at your College Registrar's Office.


Consult Professor J.S. Rosenthal, Department of Statistics.

Specialist program: S12891 (10 full courses or their equivalent, including at least one 400-series course)
First Year: MAT 157Y
Second Year: MAT 240H, 247H, 257Y, 267H, STA 257H (MAT 240H recommended in First Year)
Third and Fourth Years:
1. MAT 357Y, STA 352Y, 347H, 348H
2. At least 2 half-courses from STA 302H, 332H, 437H, 442H, 450H
3. At least 2 half-courses from STA 422H, 438H, 457H
4. At least one 300+ level f.c.e. from APM, CSC, MAT

NOTE: The Department recommends that PHY 150Y be taken in first year, and that CSC 148H/260H be taken during the program


Specialist program (Hon.B.Sc): S22891 (11.5 full courses or their equivalent, including at least one 400-series course)
First Year: CSC 148H/260H (may be taken in 2nd year; CSC 108H recommend preparation); MAT 137Y/157Y (STA 107H recommended)
Second Year: MAT 223H/240H, 224H/247H, MAT 237Y/239Y/257Y, STA (250H, 257H)/(220H, 221H, 257H)/ECO 227Y/(ECO 220Y, STA 257H) (MAT 223H/240H recommended in First Year)
Higher Years:
1. STA 302H, 347H, 352Y, 442H
2. Three of STA 332H, 348H, 422H, 437H, 438H, 450H, 457H
3. MAT 357Y/two of MAT 301H, 302H, 323H, 334H, 335H, 338H, 344H, 363H
4. Two of: ACT 335H/CSC 336H/350H/351H, APM 346H, 336H/366H, 351Y, 361H/ACT 330H,

APM 441H, 446H, 456H, 461H, CSC 318H, 354H
5. Two additional half courses at the 300+ level from ACT/APM/CSC/MAT/STA

1. At least one of MAT 257Y/338H/357Y is strongly recommended.
2. Some 300-level MAT courses which have MAT 246Y as a prerequisite are recommended.

Major program (B.Sc.): M22891 (6.5 full courses or their equivalent)
First Year: CSC 108H/148H/260H (may be taken in 2nd year); MAT 135Y/137Y/157Y
Second Year: MAT 223H/240H, 235Y/237Y/239Y/257Y; STA (250H, 257H)/(220H, 221H, 257H)/

ECO 227Y/(ECO 220Y, STA 257H) (MAT 223H/240H recommended in First Year)
Higher Years:
1. STA 302H
2. A selection of four STA half-courses from STA 322H, 332H, 347H, 348H, 352Y, 422H, 437H, 438H, 442H, 457H

NOTE: Suggested combinations for the four STA half courses are as follows:
1. STA 347H, 348H, 352Y,
2. Four of: STA 322H, 332H, 437H, 442H, 457H
3. STA 332H, 347H, 437H, 442H/422H

Minor program (B.Sc.): R22891 (4 full courses or their equivalent)
1. MAT 133Y/135Y/137Y
2. MAT 223H/240H; (STA 250H/ (220H, 221H), 255H/257H)/ECO 220Y/227Y
3. STA (302H, 352Y)/three STA half-courses at the 300/400-level




(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.

First Year Seminar 52T

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.

An Introduction to Probability and Modelling 39L, 13T

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.
Exclusion: ECO227Y/STA255H/257H Co-requisite: MAT135Y/137Y/157Y(MAT137Y/157Y is strongly recommended; MAT133Y is not acceptable)

The Practice of Statistics I 39L, 13T

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.
Exclusion: ECO220Y/227Y/GGR270Y/PSY201H/SOC300Y/STA250H/255H
Prerequisite: Grade 12 Mathematics and one University course in the physical, social, or life sciences
STA220H does not count as a distribution requirement course.

The Practice of Statistics II 39L, 13T

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.
Prerequisite: STA220H
STA221H does not count as a distribution requirement course.

Statistics for Biologists 39L, 13T

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.
Exclusion: ECO220Y/227Y/GGR270Y/PSY202H/SOC300Y/STA221H/250H/255H/257H
Prerequisite: BIO150Y, STA220H
JBS229H does not count as a distribution requirement course.

Statistical Concepts 39L, 13T

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.
Exclusion: ECO220Y/227Y/GGR270Y/PSY201H/SOC300Y/STA220H/221H
Prerequisite: MAT133Y/135Y/137Y/157Y
STA250H does not count as a distribution requirement course

Statistical Theory 39L, 13T

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.
Exclusion: ECO220Y/227Y/STA257H
Prerequisite: STA250H/221H/JBS229H, MAT133Y/135Y/137Y/157Y
STA255H does not count as a distribution requirement course.

Probability with Statistical Applications 39L, 13T

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.
Exclusion: ECO227Y/STA255H
Prerequisite: STA107H/250H/221H/JBS229H/ECO220Y, MAT135Y/137Y/157Y (MAT137Y/157Y is strongly recommended)
Co-requisite: MAT235Y/237Y/239Y/257Y (All prerequisites are waived if enroled in MAT257Y)
STA257H does not count as a distribution requirement course.

Research Opportunity Program

Credit course for supervised participation in faculty research project. See Research Opportunity Program for details.

Regression Analysis 39L

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.
Exclusion: ECO327Y, 357Y
Prerequisite: STA255H/(250H, 257H)/ECO220Y(70%)/227Y
Recommended preparation: APM233Y/MAT223H/240H

Design of Sample Surveys 39L

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).
Prerequisite: ECO220Y/227Y/GGR270Y/JBS229H/PSY202H/SOC300Y/


Experimental Design (formerly STA402H) 39L

Design and analysis of experiments; randomization; analysis of variance; incomplete block designs; Latin squares; orthogonal polynomials; factorial and fractional designs; response surface methodology.
Prerequisite: STA302H/352Y/ECO327Y/357Y

Probability I 39L

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.
Prerequisite: MAT235Y/239Y/257Y, ECO227Y/STA257H/255H(80%)

Probability II (formerly STA447H) 39L

A continuation of STA347H. Further limit theorems, martingales, Markov processes, queues, probability and expectation spaces, stochastic processes and inference.
Exclusion: STA466H
Prerequisite: STA347H/352Y

Introduction to Mathematical Statistics 78L

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.
Prerequisite: MAT235Y/239Y/257Y, ECO227Y/STA257H/255H(80%)

Theory of Statistical Inference 39L

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.
Prerequisite: STA352Y

Advanced Statistics for the Life and Social Sciences 39L

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.
Exclusion: All 300+ level STA courses except STA322H
Prerequisite: ECO220Y/227Y/GGR270Y/JBS229H/PSY202H/SOC300Y/STA221H/250H

Applied Multivariate Statistics 26L, 13P

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.
Prerequisite: ECO327Y/357Y/STA302H/352Y
Recommended preparation: APM233YMAT223H/240H

Theoretical Multivariate Statistics 39L

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.
Prerequisite: MAT223H/240H, STA352Y/437H

Methods of Applied Statistics 39L

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.
Prerequisite: ECO327Y/357Y/STA302H

Methods of Applied Statistics 39L

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)

Time Series Analysis 39L

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.
Prerequisite: ECO327Y/357Y/STA302H
Recommended preparation: MAT235Y/239Y/257Y

Readings in Statistics TBA

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.

Readings in Statistics TBA

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.

Top of page [Calendar: Contents |  Calendar Search | Programs & Courses |

We welcome your comments and enquiries.
Revised: April 6, 1998

All contents copyright , 1998. University of Toronto. All rights reserved.