# 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 Calculus and Vectors, Advanced Functions and Calculus, OAC Calculus, MATH*1080
Restriction(s): STAT*1000, STAT*2060, STAT*2080, STAT*2100, STAT*2120
STAT*2050 Statistics II S,F,W (3-2) [0.50]
In this course, students will learn how to implement good study design and analyze data from complex studies. This course follows naturally from STAT*2040 and features both previously unseen statistical techniques, as well as studying in greater depth some topics covered in STAT*2040. These topics will include: experiments and observational studies; a review of t-tests and confidence intervals; confounding variables; association and causality; Analysis of Variance (ANOVA); simple and multiple linear regression; binary responses (logistic regression); odds ratios and relative risk; and an introduction to experimental design (including blocked designs and factorial treatment designs). Assignments carried out using modern statistical software will form the basis for mastering the material.
Prerequisite(s): STAT*2040
Restriction(s): BIOL*2250, STAT*2090, STAT*2250
STAT*2060 Statistics for Business Decisions F (3-2) [0.50]
This course is 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): (4U mathematics or equivalent) or 0.50 credit in mathematics
Restriction(s): STAT*2040, STAT*2080, STAT*2120 Not available to B.Sc. students.
STAT*2080 Introductory Applied Statistics I F (3-2) [0.50]
The topics covered in this course include: 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. Examples come from a variety of disciplines, including family studies, education, marketing, medicine, psychology and sociology.
Prerequisite(s): (4U mathematics or equivalent) or 0.50 credit in mathematics
Restriction(s): STAT*2040, STAT*2060, STAT*2100, STAT*2120 B.Sc. students cannot take this course for credit.
STAT*2090 Introductory Applied Statistics II W (3-2) [0.50]
The topics covered in this course include: analysis of qualitative data; analysis of variance for designed experiments; multiple regression; exposure to non-parametric methods; power and sample size calculations; special topics such as logistic regression. Examples come from a variety of disciplines, including nutrition, family studies, education, marketing, medicine, psychology and sociology.
Prerequisite(s): STAT*2080
Restriction(s): BIOL*2250, STAT*2050, STAT*2250
STAT*2120 Probability and Statistics for Engineers F,W (3-1) [0.50]
The topics covered in this course include: Sample spaces; probability, conditional probability and 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 and correlation. An introduction to quality control and reliability is provided. This course is recommended for students in the B.Sc.(Eng.) program.
Prerequisite(s): MATH*1210 or MATH*2080
Restriction(s): 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. Computer laboratory sessions will focus on practical data visualization and statistical analysis using statistical software. Basic statistical methods are reviewed, followed by more advanced topics that will include some or all of the following: two-factor and multi-factor Analysis of Variance (ANOVA), simple and multiple linear regression, analysis of covariance, the general linear model, contingency table analysis and logistic regression. Concepts related to study design that will be discussed include sampling, confounding, paired designs, blocked designs, and factorial treatment designs. (Also listed as BIOL*2250.) Department of Mathematics and Statistics and Department of Integrative Biology.
Prerequisite(s): STAT*2040
Equate(s): BIOL*2250
Restriction(s): STAT*2050, STAT*2090
STAT*3100 Introductory Mathematical Statistics I F (3-0) [0.50]
The topics covered in this course include: 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): (MATH*1210 or MATH*2080 ), (STAT*2040 or STAT*2120)
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]
This course reviews simple linear regression and introduces multiple regression with emphasis on theory of least squares estimation, residual analysis, and model interpretation. Within the multiple regression context, transformations of variables, interactions, model selection techniques, ANOVA, influence diagnostics and multicollinearity will be discussed. Topics may also include Box-Cox transformations, weighted regression, and logistic and Poisson regression. This course is supplemented with computer labs involving interactive data analysis using statistical software.
Prerequisite(s): (MATH*1210 or MATH*2080 ), (MATH*2150 or MATH*2160, may be taken concurrently), STAT*2050
STAT*3320 Sampling Theory with Applications F (3-0) [0.50]
This course focuses on the design and analysis of survey samples for finite populations. Topics covered include: non-probability and probability sampling, simple random sampling, stratified sampling, cluster sampling, systematic sampling, double sampling, two-phase sampling and multi-stage cluster sampling. Expectation, variance estimation procedures and sample size calculations for the above techniques are included.
Prerequisite(s): (MATH*1210 or MATH*2080 ), (1 of STAT*2050, STAT*3240, STAT*3100)
STAT*3510 Environmental Risk Assessment W (3-0) [0.50]
Contemporary statistical methods for assessing risk are discussed. Topics covered include: dose-response models, survival analysis, relative risk analysis, bioassay, estimating methods for zero risk, trend analysis, survey of models for assessing risk. Case studies are used to illustrate the methods.
Prerequisite(s): (1 of MATH*1000, MATH*1080, MATH*1200), (1 of BIOL*2250, STAT*2050, STAT*2250)
STAT*4050 Topics in Applied Statistics I F (3-0) [0.50]
Topics such as statistical computing procedures, quality control, bioassay, survival analysis and introductory stochastic processes will be covered. This course is intended for statistics students and interested students from other disciplines who have 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 F (3-0) [0.50]
Same as for STAT*4050. (Offered in even-numbered years.)
Prerequisite(s): STAT*3110, STAT*3240
STAT*4340 Statistical Inference W (3-0) [0.50]
This course reviews and extends the theory of estimation introduced in STAT*3110. Topics including point estimation, interval estimation, hypothesis testing and decision theory will be presented from both the frequentist and likelihood-based perspectives. Foundational issues concerning the frequentist and Bayesian paradigms will also be discussed.
Prerequisite(s): STAT*3110, STAT*3240
STAT*4350 Applied Multivariate Statistical Methods F (3-0) [0.50]
This course incroduces the multivariate normal, and Wishart and Hotelling's T-square distributions. Topics covered include: statistical inference on the mean vector, canonical correlation, multivariate analysis of variance and covariance, multivariate regression, principal components analysis, and 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
STAT*4600 Advanced Research Project in Statistics F,W (0-6) [1.00]
Each student in this course will undertake an individual research project in some area of statistics, under the supervision of a faculty member. A written report and a public presentation of the project will be required.
Restriction(s): Approval of a supervisor and the course coordinator.
University of Guelph