# XII. Course Descriptions

## Statistics

Department of Mathematics and Statistics

Suggested initial course sequences:

1. For students interested in applied statistics a minimal course sequence is: (STAT*2040 or STAT*2100), STAT*2050, STAT*3210, STAT*3240, STAT*3320.

2. Credit may be obtained in only 1 of STAT*2050 or STAT*2090 and only 1 of STAT*2040, STAT*2060, STAT*2080, STAT*2100, STAT*2120.

3. Graduate students may be admitted to later parts of a sequence by permission of the department.

4. Students who major or minor in Statistics may not receive credit for the following courses unless taken to satisfy the requirements of another program: ECON*2740, PSYC*2010, PSYC*3320, .

STAT*2040 Statistics I S,F,W (3-2) [0.50]
A course stressing the practical methods of Statistics. Topics include: descriptive statistics; univariate models such as binomial, Poisson, uniform and normal; central limit theorem; expected value; the t, F and chi-square models; point and interval estimation; hypothesis testing methods up to two-sample data; simple regression and correlation; ANOVA for CRD and RCBD. Assignments will deal with real data from the natural sciences. Laboratory sessions involve statistical computing and visualization using appropriate statistical software.
Prerequisite(s): 1 of 4U Advanced Functions and Calculus, OAC calculus, equivalent
Restriction(s): STAT*1000, STAT*2060, STAT*2080, STAT*2100, STAT*2120
STAT*2050 Statistics II S,F,W (3-2) [0.50]
The methods of STAT*2040 are extended to the multi-sample cases. Methods include: simple and multiple regression analysis including ANOVA and lack-of-fit; experimental design including analysis for CRD, RCBD, LSD, SPD and factorial experiments with interaction; ANCOVA; Bioassay. Assignments employing data from the natural sciences will be processed in the microcomputer laboratory.
Prerequisite(s): STAT*2040 or STAT*2100 (or equivalent)
Restriction(s): STAT*2090, STAT*2250
STAT*2060 Statistics for Business Decisions W (3-2) [0.50]
A course designed for students interested in the application of statistics in a business setting. Topics covered will include the role of statistics in business decisions, organization of data, frequency distributions, probability, normal and sampling distributions, hypothesis tests, linear regression and an introduction to time series, quality control and operations research. (Also offered through distance education format.)
Prerequisite(s): (1 of 4U mathematics, OAC mathematics, equivalent) or 0.50 credit in mathematics
Restriction(s): STAT*1000, STAT*2040, STAT*2080, STAT*2100, STAT*2120
STAT*2080 Introductory Applied Statistics I F (3-2) [0.50]
Frequency distributions, graphing and tabulation of data. Measures of central tendency, variability and association. Elementary probability. Hypothesis testing and confidence intervals. Basic concepts of experimental design; treatment designs. Simple linear regression and correlation. Illustrated with examples from a variety of disciplines, including family studies, education, marketing, medicine, psychology and sociology.
Prerequisite(s): (1 of 4U mathematics, OAC mathematics, equivalent) or 0.50 credit in mathematics
Restriction(s): STAT*1000, STAT*2040, STAT*2060, STAT*2100, STAT*2120
STAT*2090 Introductory Applied Statistics II W (3-2) [0.50]
Design of sample surveys. Analysis of qualitative data. Analysis of variance for designed experiments. Multiple regression and analysis of covariance. Some non-parametric methods. Survey of special topics such as factor analysis and cluster analysis.
Prerequisite(s): STAT*2080
Restriction(s): STAT*2050
STAT*2120 Probability and Statistics for Engineers W (3-1) [0.50]
Sample spaces. Probability, conditional probability, independence. Bayes' theorem. Probability distributions. Probability densities. Algebra of expected values. Descriptive statistics. Inferences concerning means, variances, and proportions. Curve fitting, the method of least squares, correlation. Introduction to quality control and reliability. Recommended especially for students in the B.Sc.(Eng.) program.
Prerequisite(s): 1 of MATH*1010, MATH*1210, MATH*2080, IPS*1210
Restriction(s): STAT*1000, STAT*2040, STAT*2060, STAT*2080, STAT*2100
STAT*2250 Biostatistics and the Life Sciences W (3-2) [0.50]
This course in biostatistical methods will emphasize the design of research projects, data gathering, analysis and the interpretation of results. Statistical concepts underlying practical aspects of biological research will be acquired while working through the process of scientific enquiry. Weekly computer laboratory sessions will focus on practical data visualization and statistical analysis using computer statistical packages. Simple parametric and nonparametric methods are reviewed, followed by more advanced topics that will include some or all of the following: two factor ANOVA and multiple regression, and introductions to discriminant analysis, cluster analysis, principal components analysis, logistic regression, and resampling methods. (Also listed as BIOL*2250.) Departments of Mathematics and Statistics and Zoology.
Prerequisite(s): STAT*2040 or STAT*2100
Equate(s): BIOL*2250
Restriction(s): STAT*2050
STAT*3100 Introductory Mathematical Statistics I F (3-0) [0.50]
Probability spaces; discrete and continuous random variables; multivariate distributions; expectations; moments, Chebyshev's inequality, product moments; sums of random variables, generating functions; Gamma, Beta, t and F distributions; central limit theorem; sampling distributions.
Prerequisite(s): (IPS*1210 or MATH*1210 ), (STAT*2040 or STAT*2100)
STAT*3110 Introductory Mathematical Statistics II W (3-0) [0.50]
Estimation, unbiasedness, Cramer-Rao inequality, consistency, sufficiency, method of moments, maximum likelihood estimation; hypothesis testing, Neyman-Pearson lemma, likelihood ratio test, uniformly most powerful test; linear regression and correlation; non-parametric methods.
Prerequisite(s): STAT*3100
STAT*3210 Experimental Design W (3-0) [0.50]
Basic principles of design: randomization, replication, and local control (blocking); RCBD, Latin square and crossover designs, incomplete block designs, factorial and split-plot experiments, confounding and fractional factorial designs, response surface methodology; linear mixed model computer analysis of the designs; nonparametric methods; Taguchi philosophy.
Prerequisite(s): STAT*2050, STAT*3240
Restriction(s): STAT*4220
STAT*3240 Applied Regression Analysis F (3-2) [0.50]
Theory and applications of regression techniques; linear, non-linear and multiple regression and correlation; analysis of residuals; other statistical techniques including: response surfaces and covariance analysis, prediction and time-series analysis. The computer lab involves interactive data analysis and investigation of the methodology using SAS and/or S-PLUS statistical software.
Prerequisite(s): (IPS*1210 or MATH*1210 ), (MATH*2150 or MATH*2160, may be taken concurrently or with instructor consent), (STAT*2050 or STAT*2100)
STAT*3320 Sampling Theory with Applications F (3-0) [0.50]
Non-probability and probability sampling. Simple random sampling, stratified sampling, cluster sampling, systematic sampling, double sampling, two-phase sampling, multi-stage cluster sampling. Expectation and variance estimation procedures and applications of above techniques.
Prerequisite(s): (IPS*1210 or MATH*1210 ), (1 of STAT*2050, STAT*3240, STAT*3100)
STAT*3510 Environmental Risk Assessment W (3-0) [0.50]
Contemporary statistical methods for assessing risk, including dose-response models, survival analysis, relative risk analysis, bioassay, estimating methods for zero risk, trend analysis, survey of models for assessing risk. Case studies illustrate the methods.
Prerequisite(s): (1 of IPS*1110, MATH*1000, MATH*1080, MATH*1200), (STAT*2050 or STAT*2250)
STAT*4050 Topics in Applied Statistics I W (3-0) [0.50]
Topics such as statistical computing procedures, quality control, bioassay, survival analysis and introductory stochastic processes. Intended for statistics students and interested students in other disciplines with appropriate previous courses in statistics. Information on particular offerings will be available at the beginning of each academic year. (Offered in odd-numbered years.)
Prerequisite(s): STAT*3110, STAT*3240
STAT*4060 Topics in Applied Statistics II W (3-0) [0.50]
Same as for STAT*4050. (Offered in even-numbered years.)
Prerequisite(s): STAT*3110, STAT*3240
STAT*4080 Data Analysis F (3-2) [0.50]
Principles of statistical modelling; the likelihood function; model fitting; model choice; analysis of non-normal data; generalized linear models; binomial regression models; regression models for counts; Poisson and multinomial data; overdispersion. Statistical modelling and analysis using appropriate software (eg. Splus and/or SAS) in the computing lab.
Prerequisite(s): (MATH*2150 or MATH*2160), STAT*3110, STAT*3240
STAT*4100 Survival Analysis W (3-1) [0.50]
Theory and methodology of survival analysis. A set of techniques for modelling the time of a well-defined event (typically failure or death), and for dealing with censored data. The emphasis will be on regression, including parametric, proportional hazards and accelerated life regression models. Areas of application include environmental sciences, medicine, industrial reliability, and economics, where the events of interest may be respectively early death, organ failure, component failure, or strikes. Students will learn specialized techniques for modelling censored data and understand why they are necessary. The interpretation of real data will be emphasized throughout the course. Statistical computing packages (S-Plus or SAS) will be used extensively.
Prerequisite(s): STAT*3110 and STAT*3240
STAT*4340 Statistical Inference W (3-0) [0.50]
This course on methods of statistical inference reviews and extends the theory of estimation introduced in STAT*3110: interval estimation tests for simple and composite hypotheses, likelihood ratio tests. Recent likelihood concepts as well as classical large sample theory, asymptotics and approximations and their applications are covered. This material is directly relevant to current research and applications in areas as diverse as survival analysis, nonparametric regression and environmetrics.
Prerequisite(s): STAT*3110, STAT*3240
STAT*4350 Applied Multivariate Statistical Methods F (3-0) [0.50]
Samplings from the multivariate normal distribution, Wishart and Hotelling's T@ distribution statistical inference on the mean vector, canonical correlations, multivariate analysis of variance and covariance, multivariate regression, principal components analysis, factor analysis. Topics will be illustrated using examples from various disciplines.
Prerequisite(s): (MATH*2150 or MATH*2160), STAT*3110, STAT*3240
STAT*4360 Applied Time Series Analysis W (3-2) [0.50]
This course will investigate the nature of stationary stochastic processes from the spectral and time domain points of view. Aspects of parameter estimation and prediction in a computationally intensive environment will be the presentation style. The methods developed in this course will have applicability in many sciences such as engineering, environmental sciences, geography, soil sciences, and life sciences.
Prerequisite(s): STAT*3240 or instructor consent