# Course Descriptions - Statistics

## Mathematics and Statistics

This not a complete listing of courses. For a complete listing see the ACADEMIC CALENDAR and TIMETABLE for current course offerings.

Be sure to read the University Course Calendar entry in your course planning to ensure you have all the pre-requisites and complete details such as restrictions.

### Not all courses are listed here.

## First Year Courses

#### STAT-1301(3) Statistical Analysis I

This course introduces students in the natural, physical, social and human sciences to elementary statistical analysis and its applications. Topics include descriptive statistics, probability theory including counting techniques, discrete random variables and their expected values and variances, normal distribution and applications, sampling distributions and estimation of parameters.

#### STAT-1302(3) Statistical Analysis II

This course is an extension of STAT-1301(3). Topics includes review of sampling distributions and estimation of parameters; statistical testing and confidence intervals using z, t, F, and chi-square distributions; analysis of variance; goodness-of-fit tests and contingency tables; linear regression and correlation; and non-parametric procedures.

#### STAT-1501(3) Elementary Biological Statistics I

This is an elementary course providing students in biological and health sciences with an introduction to statistical analysis of data and the making of inferences about them. Topics include: descriptive statistics, probability and probability distributions, and tests of hypotheses and estimation. Applications are drawn from biology, chemistry and other sciences.

#### STAT-2001(3) Elementary Biological Statistics II

This course is an extension of STAT-1501(3) for further aspects of statistical analysis. Topics include a review of one sample statistical testing and confidence intervals; two sample inferences; analysis of variance including contrasts and multiple comparisons; analysis of qualitative data based on chi-square distribution; regression and correlation analyses; and nonparametric procedures. Applications are drawn from biology, chemistry and other sciences.

## Second Year Courses

STAT-2102(3) Business and Management Statistics

Much of business and management activity requires an understanding, both theoretical and practical, of quantitative aspects of economics and financial activities of a complex society such as ours. This course exposes students to some of the statistical methods which are routinely used to construct economic index numbers (such as the Consumer Price Index), simple investment decisions, numerical forecasting techniques, and basic concepts of human demography such as population growth and life expectance.

The terms "business'' and "management'' are here interpreted in a general sense, to mean any social and/or economic activity where quantitative information is required to form rational decisions concerning the present and future. Since many choices are often open to us, and the future is always uncertain, the term ``rational'' is taken to mean a decision process which attempts to minimize uncertainty as much as possible, by utilizing objective quantitative information. By doing so it is hoped that planning activities, within a social institution be it private or government, national or international, will provide us with sound decisions (although this is not always guaranteed!). This is particularly important in an age when an ever increasing volume of data and information is available, and it becomes of ever greater importance to ``boil down'' large bodies of data in order to gain understanding and control of the social and natural processes which confront and affect us every day.

The course surveys quantitative management science techniques used in both the private sector and government. The contents include: classical decision-making, utility for money, statistical and Bayesian decision-making, decision trees, index numbers and their properties, elementary quality control, and decomposition of time series and seasonal and cyclical analysis. Emphasis may be on having students communicate effectively through essays and term projects.

#### STAT-2103(3) Intermediate Biological Statistics

In modern scientific research, statistical methodology plays an essential role in helping researchers: to efficiently and effectively design experiments; to identify, explore and clarify relationships between key variables; to analyze and objectively interpret experimental results; and to report experimental findings so that they meet rigorous publication standards for scientific journals.

This course is designed to provide students with the underlying concepts and techniques for applying biometrical procedures to problems arising in biological and health care research. Topics include basic experimental designs, analysis of variance with one and two factors, multiple comparison procedures, data transformations, multiple linear regression, analysis of count data, analysis of proportions, analysis of covariance, and an overview of the methods of biological assay.

#### STAT-2104(3) Nonparametric Statistics

An introductory course such as STAT-1301(3) and STAT-1302(3) (formerly STAT-1201(6)) in statistics deals with statistical procedures based on t-statistic, analysis of variance, etc. known as parametric statistical procedures. These procedures require certain assumptions on the characteristics of populations from which samples are drawn for inferential purposes. The analysis of variance, for example, assumes that samples have been drawn from normal populations with equal variances. Since some populations do not meet the above or other assumptions, alternative sets of statistical procedures known as nonparametric procedures have been developed whose validity does not depend on rigid assumptions. The nonparametric procedures are simple and easy to execute as they are based on signs of differences, ranks of measurements, counts of objects falling into categories and order statistics of observations rather than the mean and variance of observations in case of parametric procedures.

This course considers statistical methods for analysing data when the distribution of the population is unknown and/or the measurement is on a nominal, ordinal, or interval scale. The contents include: inference based on the binomial distribution, the Mann-Whitney-Wilcoxon test, the Wilcoxon signed rank test, measures of association for ranked data, the Kruskal-Wallis and Friedman tests, and elements of contingency table analysis.

#### STAT-2301(3) Survey Sampling I

This course emphasizes practical aspects of conducting sample surveys. The four most common sample survey designs, simple random sampling, stratified random sampling, systematic sampling, and cluster sampling are examined. The course also deals with ratio and regression type estimators.

#### STAT-2501(3) Statistical Quality Control

Have you ever wondered why Japanese automobiles, cameras, TVs, stereos, to name a few are so popular world wide? The answer lies in the fact that Japan decided to use statistical quality control in the late 1940s and the 1950s while the rest of the world was watching them do so. Ironically, the person responsible for implementing statistical quality control into Japanese industry was Dr. W. Edwards Deming, a prominent American statistician. Japan is a leader even today as a quality practitioner in the world. Quality control techniques are currently used by almost every manufacturing enterprise to minimize internal waste and maintain a uniformly high quality product. This course will deal with modern statistical techniques used in various branches of industry to control and improve quality of production. Special attention will be given to the techniques most widely used in business and manufacturing industries. The contents include: common control charts, sampling inspection by attributes and by variables, sampling plans for continuous production, OC and ASN functions, and curtailed inspections.

#### STAT-2903(3) Introduction to Statistical Computing

When playing table tennis, is it better to smash often or to play conservatively? Such a question can be answered by simulating table tennis players of differing abilities. Simulation is an important aspect of modern statistical computing.

Another aspect of modern statistical computing is the visualization of data using graphical techniques. Often, an appropriate plot will reveal interesting or unexpected features. For example, a very simple graph can tell you how you can best play the lottery.

These topics and more will be introduced in the course. Students with limited computer experience will be introduced to the use of modern statistical computer packages for data management and data analysis. Specifically, students will learn how to use the computer for testing of pseudorandom numbers, simulation of discrete and continuous random variables, bootstrapping, analysis of single and multiple samples, linear and nonlinear regression, and analysis of contingency tables. Particular attention will be paid to the effects of departures from standard assumptions.

**Third and Fourth Year Courses**

#### STAT-3102(3) Applied Multivariate Methods

This course is designed to provide an introduction to an important area in statistics which deals with the analysis of three or more intercorrelated random variables. It will cover the following topics: Euclidian vector spaces, vector projections and orthogonalization methods, quadratic forms and symmetric positive (semi) definite matrices and their eigen structures (eigenroots/vectors), the bivariate and multivariate normal probability functions, principal components analysis, cannonical correlation analysis, and multi-group classification.

#### STAT-3103(3) Statistics in Research I

This course is intended to provide an introduction to the practice of statistical research via concepts selected from applied regression analysis. Topics include linear and multiple linear regression, and related simultaneous inference procedures. Diagnostic methods and remedial measures for assessing the adequacy of regression models are presented in detail. Various criteria for model selection and validation are discussed. Topics may also include an introduction to nonlinear and logistic regression.

#### STAT-3104(3) Analysis of Variance and Covariance

This course provides students with insight into the practice of statistical research. Emphasis is placed upon the development of various analysis of variance (ANOVA) models for single-factor and multi-factor studies. Topics are chosen from design and analysis of completely randomized, randomized block, Latin square designs and the analysis of covariance (ANCOVA). Random, fixed and mixed effects models as well as sample size determination, power analysis, diagnostics and remedial measures are discussed. Split-plot, nested, partially nested and repeated measure designs may be presented. Restriction: A student may not receive credit for this course and the former STAT-3101(6).

#### STAT-3105(3) Time Series and Forecasting

A time series is a sequence of measurements, usually taken at regular time intervals. Such series are often studied in fields such as economics (e.g. stock prices) and meteorology (e.g. daily rainfall).

The main objective of time series analysis is to describe such sequences. This can sometimes help to explain something about the underlying mechanism that generated the sequence, and in some cases, one is able to sensibly predict future values of the sequence. The benefits of this in the economic and meteorology examples suggested above should be obvious. Finally, there may be input variables which can be manipulated in ways to influence the future behaviour of the time series. The course deals with the general problem of analysing data which is ordered over time, for the purpose of forecasting and statistical prediction. Such data do not represent an independent sample and thus can not be analyzed using other statistical methods. Topics include: trend analysis, smoothing by moving averages, seasonal indices; forecasting using exponential smoothing and Box-Jenkins models.

#### STAT-3401(3) Stochastic Processes

This course is designed to introduce students to important aspects of stochastic modelling including Markov chains, Poisson processes, and renewal processes. Markov chains in both discrete and continuous time will be considered. This course emphasizes the application of theory to problems in manufacturing, telecommunications, and biological systems.

#### STAT-3412(3) Introductions to Operations Research (cross-lilsted with MATH-3412)

This course provides a practical introduction to the formulation and solution of some economics and industrial problems using Operations Research models. It emphasizes model-building and problem-solving using computer packages. Topics covered are chosen from linear programming, transportation, assignment and transshipment problems, network models, integer programming, nonlinear programming, decision making, inventory models, and queuing theory.

#### STAT-3501(3) Simulation

This course is designed to show students how a computer can be utilized to model phenomena with stochastic elements and how analysis can be carried out in the context of a simulation study. Topics will be drawn from the following: generating an arbitrary random variable; the discrete event simulation approach; variance reduction techniques; statistical validation techniques; bootstrapping and other resampling methods; statistical analysis of simulated data; and simulation languages.

#### STAT-3602(3) Demography

This course introduces students to the statistical study of the structure of human populations and changes in population over time. Emphasis is placed on the statistical aspects of the methods and materials of demography. Topics include population size, distribution and composition, population change, mortality and health, life tables, population models, fertility, migration, and methods used in the study of population, including rates and standardization (direct and indirect), and population estimation and projection. There is some use of statistical and spreadsheet software.

#### STAT-3611(3) Mathematical Statistics I (formerly STAT-2701 Applied Probability) | Cross-listed with MATH-3611

Probability is an area that has many and varied applications to the solution of real-world problems. For example, you may ponder the question: What is the probability of an ace when a card is drawn from a deck of 52 playing cards? Similarly, an insurance company may like to estimate on the number of accidents, say traffic accidents in the future in order to set the premium for a policy that the policyholder pays for in advance. The foundation of statistical inference rests on the subject of probability. The course is intended to give students a firm foundation in probability theory which is necessary for a complete understanding of any advanced statistics. Topics include: counting, joint and conditional distributions, random variables, special distributions, stochastic processes, and Markov chains.

#### STAT-3612(3) Mathematical Statistics II | Cross-listed with MATH-3612

The course will study the continuous probability distributions and their general properties, distributions of functions of random variables, sampling distributions, including t and F and introduction to estimation and theory of hypotheses testing.

#### STAT-3701(3) Epidemiology

This course provides a comprehensive introduction to the basic concepts, principles, and methods of studying disease occurrence in human populations. It covers the applications of epidemiology in public health practice and preventive medicine. Topics include: definitions, measures of disease frequency and effect, measures of risk, diagnostic and screening tests, epidemiological study designs, causality, interaction, bias, confounding, and internal and external validity. The class may be interspersed with special selected topics.

#### STAT-4102(3) Survival and Reliability Analysis

Survival analysis deals with statistical methods for analyzing failure time data in biological organisms. Students are introduced to the estimation of survival functions using nonparametric and parametric methods. When the failure occurs in mechanical systems, the study is called Reliability Analysis in Engineering.

Classical and Bayesian methods is introduced in order to estimate the reliability functions of some well known reliability models.

#### STAT-4202(3) Statistical Inference

This course expands on Mathematical Statistics II (STAT-3612(3)). Topics include the following: Theory of point and interval estimations; completeness and minimal sufficiency, Rao-Blackwell theorem; theory of tests and hypotheses; likelihood ratio tests; unbiased and invariant tests; sequential probability ratio tests; and Bayesian Inference.

#### STAT-4401(3) Probability Theory

This course is a continuation of Mathematical Statistics I (STAT-3611(3)) (the former STAT-2701(3)) and Mathematical Statistics II (STAT-3612(3)) and is intended to give students a firm foundation in probability theory. Topics include random walks, characteristic functions and central limit theorem concepts of convergence, laws of large numbers, and martingales and stochastic differential equations.

#### STAT-4501(3) Spatial Statistics

This course considers the theory and application of statistical techniques for analysis of spatial (geographic) data. Topics include: characteristics of spatial data, types of maps and issues in mapping, spatial analysis of areal units (Moran’s I statistic and extensions), point pattern analysis (centrography, measures of density, distance, and dispersion), spatial statistics for fields (spatial interpolation, semivariogram, and kriging), location quotient, Gini index and Lorenz curve. Use of R statistical software and some spreadsheet software is required. Examples are drawn from demography, developmental practice, geography, epidemiology, environmental science, and biology

PREREQUISITE: STAT-1302(3) or STAT-2001(3) or GEOG-2309(3) or the former STAT-1201(6) or STAT-1601(3)

#### STAT-4601(3) Statistical Design of Experiments

This course explores basic principles of statistical experimental design including randomization, replication, blocking, confounding, nested versus crossed factors, split-plot designs, fixed, random and mixed models, and the contrast between designed experiments and observational studies. It investigates factorial and fractional factorial designs with an emphasis on 2k factorial designs and 2k-p fractional factorial designs. Other potential topics include robust parameter design, 3k-p fractional factorial designs, balanced incomplete block designs, mixture experiments and response surface methodology. There may be a requirement for statistical communication (written reports and presentations) and group work.