# Winter 2016 MATH 631 Online University of Waterloo

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1 Course Schedule IMPORTANT: ALL TIMES EASTERN - Please see the University Policies section of your Syllabus for details. Week Lecture Content Readings Activities and Assignments End / Due Date Weight (%) Week 1 Module 1 Introduction to Statistical Sciences, Probability and Statistics, and Some Definitions Collecting Data and Data Summaries Numerical Summaries Graphical Summaries Graphical Summaries Review R and other computation materials These resources can be found on the Table of Contents. ungraded Week 2 Module 1 Module 2 Graphical Summaries 3 Probability Distributions and Statistical Models, and Data Analysis and Statistical Inference 15-21, Oldford & MacKay Notes: Chapter 2, pages 1-11; Chapter 3, pages 1-6 Assignment 1 January 19, PPDAC Problem Stage PPDAC Plan Stage Processing math: 100% Week 3 Module 2 PPDAC Plan Stage: Cause and Effect and Confounding PPDAC Plan Stage: Cause and Effect and Confounding 2 PPDAC Plan Stage: Factorial Designs PPDAC Plan Stage: Factorial Designs 2 PPDAC Plan Stage: Measurement System; PPDAC Data and 72-75, Oldford & MacKay Notes: Chapter 3, pages 7-9; Chapter 4, pages 1-8 Assignment 2 January 26,

2 Analysis Stages Week 4 Module 2 Module 3 Probability Model for Sampling Probability Model for Measurement 31-43, Oldford & MacKay Notes: Chapter 5, pages 1-9 Written Assignment 1 February 2, 1 Probability Models, Poisson Distribution, Exponential Distribution, Normal (Gaussian) Distribution, Multinomial Distribution, and Models That Include Explanatory Variables Probability Models and Estimation of Parameters (Model Fitting) Estimation of Parameters (Model Fitting) 2 Estimation of Parameters (Model Fitting) 3 Week 5 Module 3 Invariance of Likelihoods Examples Newton's Method Coliform Example Likelihoods for Multinomial Data Checking Fit Histograms and ECDF's Assignment 3 February 9, Week 6 Module 3 Graphical Checks of Models Histograms and ECDF's Graphical Checks of Models QQPlots Graphical Checks of Models QQPlots , 85-90, Assignment 4 February 23, Module 4 Estimators and Interval Estimation Interval Estimation Using the Likelihood

3 Function READING WEEK (Sunday, February 14, 2016 to Saturday, February 20, 2016) Week 7 Module 4 Interval Estimation Using the Likelihood Function 2 Interval Estimation Using the Likelihood Function 3 Confidence Intervals Confidence Intervals and the χ 2 Distribution Likelihood Ratio Statistic Assignment 5 March 1, Week 8 Module 4 Inference for the G(μ, σ) Distribution, and the Student t Distribution Confidence Intervals for μ and σ Sample Size , Written Assignment 2 March 8, 1 Module 5 Introduction to Tests of Hypotheses Example of a Simple Hypothesis Brand Preference Week 9 Module 5 Hypothesis Tests in a Gaussian Distribution Likelihood Ratio Tests for a Single Parameter Composite Hypotheses: Tests of Equality of Two Parameters Tests of Equality of Two Parameters 2 Goodness of Fit Tests Poisson Example , , Assignment 6 March 15, Week 10 Module 5 Goodness of Fit Tests Gaussian Example Tests of Independence Tests of Independence , Assignment 7 March 22, Module 6 Introduction and Simple

4 Linear Regression Simple Linear Regression Week 11 Module 6 Simple Linear Regression and Analysis of Variance Checking Model Fit Tests and Confidence Intervals Confidence Intervals and Prediction Intervals Comparing the Means of Two Populations Assignment 8 March 29, Week 12 Module 6 Comparing the Variances of Two Populations; Paired Comparisons General Gaussian Response Models General Gaussian Response Models 2 Extensions of the Gaussian Response Model , Written Assignment 3 April 5, 1 Wrap-up Written Assignment 4 Friday, April 15, 1 You must achieve a final grade of at least 70% to pass this course. Final Examination Arrangements and Schedule There is no final examination for this course. Official Grades and Course Access Official Grades and Academic Standings are available through Quest. Your access to this course will continue for the duration of the current term. You will not have access to this course once the next term begins.

6 Technical Support, Centre for Extended Learning Technical problems with Waterloo LEARN Learner Support Services, Centre for Extended Learning General inquiries WatCards (Student ID Cards) Examination information Include your full name, WatIAM user ID, student number, and course name and number. Useful Information for Students in Online Courses Include your full name, WatIAM user ID, student number, and course name and number. *Discussion topics can be accessed by clicking Connect and then Discussions on the course navigation bar above.

7 Course Description and Objectives Description This course discusses some of the mathematical and scientific aspects of empirical, or data-based, problem solving. Topics will include methods for the design of experiments and surveys, and the analysis of data using statistical models. Examples will illustrate the application of these methods to data-based problems in science, health, business, and industry. Objectives Statistical Science is a large discipline, and any single course cannot cover all aspects of the discipline. Students who complete this course will be able to understand aspects of the following: formulating problems planning empirical studies formal and informal analyses of discrete and continuous data using graphical techniques and statistical models assessing conclusions based on empirical studies This online course was developed by Steve Brown, with instructional design and multimedia development support provided by the Centre for Extended Learning. Further media production was provided by Instructional Technologies and Multimedia Services.

8 About the Course Author and Instructor Course Author and Instructor K. Steve Brown Professor Brown is a biostatistician whose research interests include the development of statistical methods for the design of community-based interventions, the analysis of longitudinal data collected from studies of interventions designed to affect health behaviours, and the design and analysis of observational studies of health behaviour. His interests include design and analysis of cluster-randomized prevention trials, correlated discrete response data, generalized linear models, statistical consulting, and statistics education.

9 Materials and Resources Textbook There is no required textbook for this course. All course readings are included in Course Notes below. Course Notes Math 631 Course Notes Oldford & MacKay Stat 231 Lecture Notes Resources Library services for co-op students on work term and distance education students The text below is the companion volume to a recommended text for Math 630. It is not required for this course, but does cover much of the same material. It also expands on ideas covered in this course. Kalbfleisch, J. G. (1985). Probability and Statistical Inference, Volume 2: Statistical Inference (2nd ed.). New York: Springer-Verlag.

10 Grade Breakdown The following table represents the grade breakdown of this course. Activities and Assignments Weight Assignments ( each) 40% Written Assignments (1 each) 60% You must achieve a final grade of at least 70% to pass this course.

11 Program Policy Program Policy Students must maintain an overall average of 7 in the program, with individual course marks of at least 70%.

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