Statistics

Topics from survey statistics: simple random sampling; systematic sampling, question composition, scaling techniques. Topics from basic statistics: descriptive statistics; estimating/testing means, standard deviations, proportions, paired data versus two independent samples, chi-square tests.

Emphasis on applications to forestry and biology, using a statistical package. Graphical and numerical summaries of data; Populations, samples, sampling techniques; Normal distribution; Estimation and tests for means, medians, proportions; Individual versus mean behaviour; Matched pairs, independent samples, analysis of variance; Regression; Chi-squared tests for categorical data. NOTE: Credit can be obtained for only one of STAT 2043, STAT 2253, STAT 2263, STAT 2264 or STAT 2593. 

An introductory course in statistics. Experiments, sampling, basic descriptive statistics. Probability, random variables, Normal distribution. Confidence intervals for means and proportions. Tests of hypotheses. Paired samples vs. two independent samples. Contingency tables. Regression, correlation. Introduction to analysis of variance. Examples drawn from the health sciences. Use of a statistical computer package. 

An introductory course in statistics. Probability, Bayes' Theorem, applications of probability to genetics, random variable, expectation, binomial and normal random variables, confidence intervals for means and proportions, prediction intervals, tests of hypotheses, paired data versus two independent samples, brief introduction to analysis of variance, regression, correlation, contingency tables, examples drawn from medicine and biology, use of a statistical computer package. 

Probability spaces: combinatorial probability; conditional probability and independence. Random variables: discrete distributions; continuous distributions; expectation, variance, and covariance; linear combinations. Statistics: descriptive and graphical statistics; sampling distributions. Inference: point estimation; confidence intervals; hypothesis tests; paired data designs; two sample inference. 

Topics from survey statistics: stratified sampling; cluster sampling. Questionnaires: construction, administration, interpretation and reporting. Topics from basic statistics: regression; one way and two way analysis of variance. 

The first half of a two-part sequence covering various topics in probability and statistics. This course provides an introduction to probability theory and the theory of random variables and their distributions. Probability laws. Discrete and continuous random variables. Means, variances, and moment generating functions. Sums of random variables. Joint discrete distributions. Central Limit Theorem. Examples drawn from engineering, science, computing science and business. 

Randomization, one and two way classifications. Latin squares, factorial experiments, nesting, incomplete blocks, linear regression. Emphasis on applications. Extensive use of a statistical computer package.

Exact contents may vary from year to year, e.g.: counting processes and Poisson processes; renewal processes (discrete); finite state Markov chains; stationary covariance processes.

Simple random sampling; stratified sampling; systematic sampling; multi-stage sampling; double sampling; ratio and regression estimates; sources of error in surveys. 

Simple and multiple linear regression. Regression diagnostics. Prediction and model testing. Qualitative variables as predictors. Transformation of variables. Analysis of collinear data. Variable Selection and model reduction procedures. Data analysis using software. NOTE: Credit may be obtained for only one of STAT 4053 or ECON 4625.

Logistic regression models for binary response variables, log-linear models for contingency tables, Poisson regression models for count response variables, multinomial regression models for categorical response variables, cumulative logic and continuation-ratio regression models for ordinal response variables, model selection, some special topics in generalized linear models. Emphasis will be on computer implementation and applications in social sciences, psychology, education, medicine, sciences and engineering.

Multivariate normal distribution; variance and correlation matrices. Visualization of multivariate data. Dimension reduction for numerical and categorical data. Simple modelling of covariances by means of exploratory and confirmatory factor analysis. Methodology and techniques of supervised and unsupervised statistical learning.

Statistics Honours students must complete a project under the supervision of a faculty member. The project is to include a written report and an oral presentation. Prior to being admitted into STAT 4100, the student must have been admitted to the Honours Program and have submitted an acceptable project proposal to the department. Normally students would begin preparation and research for the project during their third year of study, submit the proposal by October of their fourth (final) year of study, and complete the written and oral presentation by the end of the winter term, to graduate in May of that year. Honours students in an interdepartmental program with statistics may choose to complete their honours project in statistics.

Discrete time series and stochastic processes; autocorrelation and partial correlation functions; white noise; moving averages; autoregressive, mixed and integrated processes; stochastic models, fitting, estimation and diagnostic checkup; forecasting; forecasting in seasonal time series; applications would include problems from Economics, Engineering, Physics.

Advanced topic in Statistics to be chosen jointly by student, advisor, and Department Chair. May be taken for credit more than once. Title of topic chosen will appear on transcript.