MATH 445: Mathematical Statistics – Winter Term, 2010

 

“The best thing about being a statistician is that you get to play in everyone’s backyard.”

 

“Far better an approximate answer to the right question, which is often vague, than the exact answer to the wrong question, which can always be made precise.”

 

        John Tukey (1915 – 2000)

 

Course Goals

Traditional mathematical statistics courses are outdated—they contain only mathematical derivations and theory (much of which is not used in statistical practice), and they lack real-world methods and applications. My goal for this course is to effectively mix theory with practice. It’s important for you as math students to learn interesting and fundamental theoretical results; yet it’s equally important for you as practicing statisticians to see a wide range of methods and applications. To this end, the textbook material will be supplemented by actual journal articles and case studies, and the lectures will be supplemented by vigorous class discussion and computer-lab applications.

 

Professor Contact Information

Joy Jordan, Associate Professor of Statistics, 410 Briggs Hall  

PHONE: 832-6894, EMAIL: joy.jordan@lawrence.edu, WEB: www.lawrence.edu/fast/jordanj/

 

Please note the URL for my homepage. On this page is a link to the Math 445 web page, where I will post, for example, homework assignments and handouts. I check email regularly (2-3 times a day), but not obsessively. If you need to contact me urgently (e.g., you have a family emergency, you want to make an appointment as soon as possible), then please call me.

 

Required Textbook and Additional Reading

Modern Mathematical Statistics with Applications, Devore and Berk, 2007, Duxbury (a copy of the textbook is on 2-hour reserve at the library)

 

Additional reading (e.g., copied sections of other texts, journal articles) will be provided throughout the term; this reading is as important as the textbook reading.

 

Office Hours

Monday: 3:00 – 4:30, Tuesday: 2:30 –3:30, Wednesday: 11:30 – 12:30, Thursday: 1:30 – 3:00

 

If these times do not work with your particular class schedule, I am happy to make individual appointments for other times. (You need not make an appointment during regular office hours—just come in.) Please ask if you need help, and I will do all I can to assist you. That said, I expect you to come to office hours prepared (e.g., having done the reading, knowing the definitions) and not simply looking for easy answers. Besides office hours, anytime my door is open, feel free to come in and ask questions. If my door is closed, I am either out of the office, or I’m working and prefer not to be disturbed.

 

Coverage

A tentative course schedule is included with this syllabus. We are scheduled to cover the material in Chapters 1, 6–12 of the textbook, as well as additional reading. We may cover more or less material, though, depending on how the course unfolds. I want to be flexible with the schedule in case changes are needed to best encourage learning. (I’ll keep you posted on major changes to the schedule.)

 

Class Participation/Discussion

Class discussion is part of this course, and it will be factored into your final grade. Throughout the term, additional reading will be assigned, and you are responsible for coming to class prepared to effectively and critically discuss this material. Occasionally an individual student may be asked to explain a problem-solution to the whole class. Note that participation also includes asking thoughtful questions in class and office hours, and answering my queries in class (regardless of whether you have the “right” answer).

 


Homework (and the Honor Code)

You will turn in regular homework assignments; these problems (or a subset of the problems) will be graded. There will be two types of homework problems: 1) problems on which you are free to work together and 2) work-alone problems. On the work-together problems, your write-up should be your own (you can talk with other students about the problems, but you must write up the solutions individually—that is, you can write scratch work from your study sessions, but you must use your own words and explanations when writing up your final solution). On the work-alone problems, you should not talk with other students at all (except perhaps to clarify what a question is asking)—please see me in office hours with questions about the work-alone problems. On the assignments, I will clearly differentiate between the two types of problems.

 

Your grade will depend on both the content and exposition of your answers; write up the problems as carefully as you did—or should have done—in Math 310. That is, be sure your logic is clear, your solution reads smoothly (even if using symbols), and that one of your peers could read and understand your solution without asking any additional questions.

 

I take the Lawrence Honor Code very seriously, and recently I’ve been deeply disappointed to hear of more frequent violations of this code. I think the Honor Code is a special quality of the Lawrence experience; a quality that translates beautifully into a life-long behavior. If you are feeling particularly stressed in this class, come talk with me, but don’t violate the Honor Code—I will pursue any case I feel is an honor code violation.

 

Exams

There will one in-class exam during the term and a final exam. The first exam is on Wednesday, February 10 and the final exam is Tuesday, March 16 at 8:30 a.m.

 

Computer Lab (Thursdays 9:50 – 11:00, Briggs 421)

The weekly computer lab should be thought of as an extension of the lectures, and new material will sometimes be presented in lab. The lab will also be used to investigate and interpret real data (using statistical software). Furthermore, statistical analysis via computer (and interpretation via your brain) will be part of homework assignments.

 

Grading

Your final grade is based on a weighting of class participation (10%), work-together homework (25%), work-alone homework (25%), and exams (first exam – 20%, second exam – 20%). The letter grades will be assigned as follows, corresponding to Lawrence’s GPA system (note: the cutoff is the lowest percentage that receives that letter grade):

 

Cutoff

Grade

93.75

A

90.00

A-

86.25

B+

83.75

B

80.00

B-

76.25

C+

73.75

C

70.00

C-

66.25

D+

63.75

D

60.00

D-

 

Life Balance

Because I love statistics so much, I will encourage you to work hard to learn the material. (You thought I loved probability, but I really, really love statistics!) Please realize, though, that your self-worth is not associated with your letter grade on a particular homework or exam (or even with your final course grade). You are all good people, regardless of your official class performance on tasks.

 

Furthermore, I think as a society in general, and at Lawrence in particular, we are over-scheduled and allow precious little downtime and quiet reflection. I encourage you to think carefully about the intensity and number of courses, activities, and obligations in your life, and to seek balance as much as possible. (I’m happy to talk with you more about this—that is, we can discuss life as well as statistics.)


Tentative Course Schedule

 

Date

General Material

Textbook Reading

M 1/4

General sampling distributions and the distribution of the sample mean (Central Limit Theorem)

Sections 6.1 – 6.2

W 1/6

Central Limit Theorem and distribution of a linear combination

Sections 6.2 – 6.3

R 1/7

Lab: Simple data analysis—One-variable numerical summaries and graphics

Chapter 1

F 1/8

Finish Central Limit Theorem; class discussion of data collection

Sections 6.2 – 6.3

M 1/11

Chi-square distribution and t distributions

Section 6.4

W 1/13

T and F distributions; Estimation and properties of estimators

Section 7.1

R 1/14

Lab: Properties of estimators; introduction to the bootstrap

Section 7.1

F 1/15

Methods of estimation: method of moments and maximum-likelihood estimation

Section 7.2

M 1/18

No class – Martin Luther King Jr. Day

 

W 1/20

Maximum-likelihood estimation

Section 7.2

R 1/21

Lab: Estimation activity

 

F 1/22

Finish point estimation and begin confidence-interval estimation

Sections 8.1 – 8.2

M 1/25

General confidence intervals and t confidence intervals

Sections 8.1 – 8.3

W 1/27

Prediction intervals; class discussion of articles (bootstrap and confidence interval for a population proportion)

Sections 8.1 – 8.3

R 1/28

Lab: Introduction to R and bootstrap confidence intervals

Section 8.5

F 1/29

Finish confidence intervals; begin hypothesis testing for a population mean

Sections 9.1 – 9.2, 9.4

M 2/1

Hypothesis testing for a population mean (including power calculations)

Sections 9.1 – 9.2, 9.4

W 2/3

Finish power; relationship between confidence intervals and hypothesis testing; t-test

Sections 9.1 – 9.2, 9.4

R 2/4

Lab: To be announced

 

F 2/5

T-test; hypothesis testing for a population proportion; practical significance

Sections 9.1 – 9.4

M 2/8

Class discussion of journal article (assumptions for inference); exam review

Reread Chapters 1, 6 – 9

W 2/10

Exam 1(Chapters 1, 6 – 9)

 

R 2/11

No Lab – Reading Period

 

F 2/12

No class – Reading Period

 

M 2/15

Two-sample problems (confidence intervals and hypothesis tests)

Sections 10.1 – 10.2

W 2/17

Two-sample and paired-data problems

Sections 10.1 – 10.4

R 2/18

Lab: Two-sample and paired-data bootstrap confidence intervals

Section 10.6

F 2/19

Finish two-sample problems

 

M 2/22

One-factor ANOVA

Sections 11.1 

W 2/24

One-factor ANOVA

Sections 11.1 – 11.3

T 2/25

Lab: Two-sample problems using Minitab; one-factor ANOVA

 

F 2/26

One-factor ANOVA

Sections 11.1 – 11.3

M 3/1

Two-factor ANOVA

Section 11.4 – 11.5 

W 3/3

Two-factor ANOVA

Section 11.4 – 11.5 

T 3/4

Lab: Two-factor ANOVA; class discussion of article (ANOVA)

 

F 3/5

Simple linear regression model

Sections12.1 – 12.2

M 3/8

Properties of and inference about regression coefficients

Section 12.3 

W 3/10

Confidence and prediction intervals; regression diagnostics

Sections 12.4, 12.6

T 3/11

Lab: Regression (simple linear regression and quick look at multiple regression)

 

F 3/12

Quick summary of non-parametric tests and tests on categorical data; class discussion of article (data mining); review

Reread Chapters 10 – 12

T 3/16

Exam 2 (Chapters 10 – 12, and relevant previous material) – 8:30am